**RD Sharma PDF Download** SOLUTIONS FOR CLASS 6 CHAPTER 1 UNDERSTANDING OUR NUMBERS FREE ONLINE

Workout 1.1 web page: 1.7

**Write every of the next in numeral form:**

**(i) 8 thousand twelve.**

**(ii) Seventy thousand fifty 3.**

**(iii) 5 lakh seven thousand 4 hundred six.**

**(iv) Six lakh thousand 9.**

**(v) Thirty lakh 11 thousand one.**

**(vi) 8 crore 4 lakh twenty 5.**

**(vii) 3 crore 3 lakh 3 thousand 3 hundred 3.**

**(viii) Seventeen crore sixty lakh thirty thousand 57.**

**Answer:**

(i) The numeral form of 8 thousand twelve is 8,012.

(ii) The numeral type of seventy thousand 53 is 70,053.

(iii) The numeral form of 5 lakh seven thousand 4 hundred six is 5, 07, 406.

(iv) The numeral form of six lakh thousand 9 is 6, 02, 009.

(v) The numeral type of thirty lakh 11 thousand one is 30, 11, 001.

(vi) The numeral type of 8 crore 4 lakh twenty 5 is 8, 04, 00, 1/2.

(vii) The numeral form of three crore 3 lakh 3 thousand 300 3 is 3, 03, 03, 303.

(viii) The numeral form of seventeen crore sixty lakh thirty thousand 57 is 17, 60, 30, 057.

**Write the next numbers in words throughout the Indian machine of numeration:**

(i) 42,007

(ii) 4,05,0.5

(iii) 35, 42, 012

(iv) 7, 06, 04, 014

(v) 25, 05, 05,500

(vi) 5, 50, 50, 050

(vii) 5, 03, 04, 012

**Answer:**

(i) 42,007 is written as 40 thousand seven throughout the Indian device of numeration.

(ii) 4,05,1/2 is written as 4 lakh 5 thousand 45 throughout the Indian software of numeration.

(iii) 35, 42, 012 is written as thirty 5 lakh 40 thousand twelve throughout the Indian machine of numeration.

(iv) 7, 06, 04, 014 is written as seven crore six lakh 4 thousand fourteen within the Indian software of numeration.

(v) 25, 05, 05,500 is written as twenty 5 crore 5 lakh 5 thousand 5 hundred within the Indian machine of numeration.

(vi) 5, 50, 50, 050 is written as 5 crore fifty lakh fifty thousand fifty throughout the Indian gadget of numeration.

(vii) 5, 03, 04, 012 is written as 5 crore 3 lakh 4 thousand twelve throughout the Indian software of numeration.

**Insert commas in the proper positions to split periods and write the following numbers in words:**

(i) 4375

(ii) 24798

(iii) 857367

(iv) 9050784

(v) 10105607

(vi) 10000007

(vii) 910107104

**Resolution:**

(i) 4375 by means of hanging commas is written as 4, 375.

(ii) 24798 by means of putting commas is written as 24, 798.

(iii) 857367 with the help of putting commas is written as 8,57,367.

(iv) 9050784 thru hanging commas is written as 90,50,784.

(v) 10105607 with the help of hanging commas is written as 1,01,05,607.

(vi) 10000007 by means of hanging commas is written as 1,00,00,007.

(vii) 91010714 with the help of hanging commas is written as 91,01,07,104.

**Write each and every of the next in larger notation:**

(i) 3057

(ii) 12345

(iii) 10205

(iv) 235060

**Answer:**

(i) 3057 = 3 × one thousand + 0 × 100 + 5 × 10 + 7 × 1

(ii) 12345 = 1 × 10000 + 2 × one thousand + 3 × 100 + 4 × 10 + 5 × 1

(iii) 10205 = 1 × 10000 + 0 × 1000 + 2 × 100 + 0 × 10 + 5 × 1

(iv) 235060 = 2 × 100 thousand + 3 × 10000 + 5 × 1000 + 0 × 100 + 6 × 10 + 0 × 1

**Write the corresponding numeral for each and every of the next:**

(i) 7 × 1000 + 2 × 1000 + 5 × 100 + 9 × 10 + 6 × 1

(ii) 4 × 100 thousand + 5 × 1000 + 1 × 100 + 7 × 1

(iii) 8 × 1000000 + 3 × 1000 + 6 × 1

(iv) 5 × 10000000 + 7 × 1000000 + 8 × one thousand + 9 × 10 + 4

**Resolution:**

(i) 7 × 1000 + 2 × 1000 + 5 × 100 + 9 × 10 + 6 × 1 = 72, 596.

(ii) 4 × 100 thousand + 5 × 1000 + 1 × 100 + 7 × 1 = 4, 05, 107.

(iii) 8 × a million + 3 × one thousand + 6 × 1 = 80, 03, 006.

(iv) 5 × 10000000 + 7 × 1,000,000 + 8 × 1000 + 9 × 10 + 4 = 5, 70, 08, 094.

**Find where price of the digit 4 in every of the following:**

(i) 74983160

(ii) 8745836

**Resolution:**

(i) The positioning price of digit 4 in 74983160 is 4 × 10, 00, 000 = 40, 00, 000.

(ii) The neighborhood value of digit 4 in 8745836 is 4 × 10, 000 = 40, 000.

#### Come to a decision the made of the neighborhood values of 2 fives in 450758.

**Answer:**

Where price of first 5 is 5 × 10 = 50

The neighborhood value of 2nd 5 is 5 × 10, 000 = 50, 000

So the required product = 50 × 50, 000 = 25, 00, 000.

Subsequently, the manufactured from where values of 2 fives in 450758 is 25, 00, 000.

**Come to a decision the adaptation of the area values of seven’s in 257839705.**

**Answer:**

The area price of first seven is 7 × 100 = 700

The area value of 2d seven is 7 × 10, 00, 000 = 70, 00, 000

So the required distinction = 700 – 70, 00, 000 = 69, 90 9, 300

Subsequently, the adaptation of the neighborhood values of seven’s in 257839705 is 69, 99, 300.

**Decide the adaptation between the area price and the face price of 5 in 78654321.**

**Resolution:**

The given amount is 78654321

The area price of five = 5 × 10, 000 = 50, 000

The face price of five = 5

So the desired difference = 50, 000 – 5 = 40 9, 995

As a result, the adaptation some of the location price and the face price of five in 78654321 is 40 9, 995.

**Which digits have the similar face price and area value in 92078634?**

**Answer:**

We all know that the face price depends upon the price of the digit and the site price is predicated upon on its area of prevalence.

So the digits that have similar position and face price in a variety of are the ones digit and zeros of the amount.

The given quantity is 92078634 and 9, 20, 78, 634 we notice that 4 which could be the ones digit and 0 that is the lakhs digit have equivalent face and position price.

**What selection of unique three-digit numbers is also formed by means of the use of the digits 0, 2, 5 with out repeating any digit throughout the selection?**

**Resolution:**

The other 3-digit numbers which may also be shaped by way of the digits 0, 2, 5 with out repeating any digit within the amount are 205, 250, 502 and 520.

As a result, 4 3 digit numbers is also shaped by means of using the digits 0, 2, 5.

**Write all possible 3-digit numbers the use of the digits 6, 0, 4 while**

(i) repetition of digits isn’t allowed

(ii) repetition of digits is authorized.

**Answer:**

(i) The viable 3 digit numbers using the digits 6, 0, 4 whilst repetition of digits is not all the time allowed are 604, 640, 406 and 460.

(ii) The imaginable 3 digit numbers using the digits 6, 0, 4 when repetition of digits is authorized are 400, 406, 460, 466, 444, 404, 440, 446, 464, 600, 604, 640, 644, 646, 664, 606, 660 and 666.

**Fill within the blank:**

(i) 1 lakh = ………. 10000

(ii) 1 lakh = ……… Thousand

(iii) 1 lakh = ……… Hundred

(iv) 1 lakh = ………. Ten

(v) 1 crore = ………. Ten lakh

(vi) 1 crore = ……… lakh

(vii) 1 crore = ……… 10000

(viii) 1 crore = ……… thousand

(ix) 1 crore = ……….. Hundred

(x) 1 crore = …………. Ten

**Answer:**

(i) 1 lakh = 10 10000

(ii) 1 lakh = 100 Thousand

(iii) 1 lakh = 1000 Hundred

(iv) 1 lakh = 10000 Ten

(v) 1 crore = 10 ten lakh

(vi) 1 crore = 100 lakh

(vii) 1 crore = 1000 10000

(viii) 1 crore = 10000 thousand

(ix) 1 crore = 100000 Hundred

(x) 1 crore = a million Ten

Exercise 1.2 web page: 1.13

**Write each and every of the next numbers in digits by means of using international neighborhood price chart. Moreover, write them in speeded up form**

(i) Seven million 3 hundred 3 thousand hundred six.

(ii) Fifty 5 million twenty 9 thousand seven.

(iii) Six billion 110 million 3 thousand seven.

**Answer:**

(i) Seven million 3 hundred 3 thousand 2 hundred six is written as 7, 303, 206 the use of international position price chart.

It is in a position to be written in prolonged shape as

7, 303, 206 = 7 × a million + 3 × 100 thousand + 2 × 100 + 0 × 10 + 6 × 1

(ii) Fifty 5 million twenty 9 thousand seven is written as fifty 5, 029, 007 the use of global area price chart.

**It can be written in prolonged form as**

Fifty 5, 029, 007 = 5 × 10000000 + 5 × a million + 0 × 100 thousand + 2 × 10000 + 9 × one thousand + 0 × 100 + 0 × 10 + 7 × 1

(iii) Six billion 110 million 3 thousand seven is written as 6, 100 ten, 003, 007 the use of international position price chart.

It may be written in multiplied form as

6, 100 and ten, 003, 007 = 6 × one thousand million + 1 × 100000000 + 1 × 10000000 + 0 × 1000000 + 0 × 100000 + 0 × 10000 + 3 × one thousand + 0 × 100 + 0 × 10 + 7 × 1

#### Rewrite each and every of the next numerals with proper commas throughout the global gadget of numeration. Additionally, write the amount name of each and every throughout the global gadget of numeration

(i) 513625

(ii) 4035672

(iii) 65954923

(iv) 70902005

Answer:

(i) 513625 is written as 513, 625 that is 5 hundred 13 thousand 600 twenty 5 throughout the international device of numeration.

(ii) 4035672 is written as 4, 1/2, 672 which is 4 million thirty 5 thousand 600 72 throughout the international device of numeration.

(iii) 65954923 is written as 65, 954, 923 this is sixty 5 million 9 hundred fifty 4 thousand 9 hundred twenty 3 throughout the international device of numeration.

(iv) 70902005 is written as 70, 902, 1/2 that is seventy million 9 hundred thousand 5 within the global device of numeration.

#### Write each and every of the following numbers throughout the international device of numeration:

(i) 43 lakh 4 thousand 80 4.

(ii) Six crore thirty 4 lakh 4 thousand 40 4.

(iii) Seven lakh thirty 5 thousand 8 hundred 90 9 handiest.

Answer:

(i) 40 3 lakh 4 thousand 80 4 is also written as 4, 304, 084 which is 4 million 3 hundred 4 thousand 84 using global device of numeration.

(ii) Six crore thirty 4 lakh 4 thousand 40 4 is also written as 63, 404, 044 that is 63 million 400 4 thousand 40 4 the use of global software of numeration.

(iii) Seven lakh thirty 5 thousand 8 hundred 90 9 most efficient is also written as 735, 899 this is 700 thirty 5 thousand 8 hundred 99 most efficient using global device of numeration.

#### Write the following numbers within the Indian device of numeration:

(i) Six million 5 hundred 40 3 thousand hundred ten.

(ii) 76 million 80 5 thousand 9 hundred 80 seven.

(iii) 300 twenty 5 million 4 hundred 79 thousand 8 hundred thirty 8.

Answer:

(i) Six million 5 hundred 40 3 thousand hundred ten is also written as 65, 43, 210 that is sixty 5 lakh 43 thousand hundred ten the use of the Indian device of numeration.

(ii) 76 million 80 5 thousand 9 hundred 80 seven may also be written as 7, 60, 85, 987 this is seven crore sixty lakh 8 5 thousand 9 hundred 80 seven the use of the Indian software of numeration.

(iii) 300 twenty 5 million 400 seventy 9 thousand 8 hundred thirty 8 may also be written as 32, 54, seventy 9, 838 that is thirty crore fifty 4 lakh seventy 9 thousand 8 hundred thirty 8 using the Indian device of numeration.

#### A definite 9 digit vary has most straightforward ones in ones period, most efficient twos throughout the so much period and most efficient threes in loads of 1000’s period. Write this vary in phrases within the Indian device.

Resolution:

It is a ways for the reason that a 9 digit amount has most straightforward ones in ones period, best twos within the 1000’s length and perfect threes in tens of hundreds of thousands length.

So we get the range as 333, 222, 111

We’re in a position to put in writing it as 33, 32, 22, 111 which is thirty 3 crore thirty two lakh twenty thousand 100 and 11 the use of the Indian software.

#### What number of so much make a million?

Resolution:

We all know that

1000 = 1000 and a million = 1, 000, 000

Broad number of loads which make a million = a million/ 1000

Via the use of substituting the values

Amount of tons which make 1,000,000 = 1, 000, 000/ 1000

So we get

Vary of loads which make a million = 1000

As a result, 1000 1000’s make a million.

#### What number of hundreds of thousands make a thousand million?

Resolution:

We notice that

a million = 1, 000, 000 and a thousand million = 1, 000, 000, 000

Amount of loads of 1000’s which make a thousand million = 1000 million/ a million

Via the use of substituting the values

Broad number of loads of 1000’s which make 1000 million = 1, 000, 000, 000/ 1, 000, 000

So we get

Vary of tens of hundreds of thousands which make 1000000000 = 1000

Subsequently, one thousand million make 1000000000.

#### (i) what selection of lakhs make a million?

#### (ii) what selection of lakhs make a thousand million?

Resolution:

(i) We recognise that

One lakh = 1, 00, 000 and 1,000,000 = 1, 000, 000

Amount of lakhs which make 1,000,000 = 1,000,000/ One lakh

Via substituting the values

Broad number of lakhs which make 1,000,000 = 1, 000, 000/ 1, 00, 000

So we get

Choice of lakhs which make a million = 10

As a result, 10 lakhs make a million.

(ii) We all know that

One lakh = 1, 00, 000 and 1000000000 = 1, 000, 000, 000

Amount of lakhs which make 1000 million = a thousand million/ One lakh

Via substituting the values

Choice of lakhs which make 1000000000 = 1, 000, 000, 000/ 1, 00, 000

So we get

Number of lakhs which make 1000 million = 10, 000

As a result, 10, 000 lakhs make a thousand million.

#### Write each and every of the following in numeral form:

(i) 8 million 700 8 thousand 4.

(ii) 600 seven million twelve thousand 80 4.

(iii) 4 billion twenty 5 million 45 thousand.

Resolution:

(i) 8 million 700 8 thousand 4 may also be written as

8 × 1, 000, 000 + 7 × 100, 000 + 0 × 10, 000 + 8 × 1000 + 0 × 100 + 0 × 10 + 4 × 1 = 8, 708, 004

(ii) 600 seven million twelve thousand 80 4 may also be written as

6 × 100, 000, 000 + 0 × 10, 000, 000 + 7 × 1, 000, 000 + 0 × 100, 000 + 1 × 10, 000 + 2 × one thousand + 0 × 100 + 8 × 10 + 4 × 1 = 607, 012, 084

(iii) 4 billion twenty 5 million 45 thousand may also be written as

4 × 1, 000, 000, 000 + 0 × 100, 000, 000 + 2 × 10, 000, 000 + 5 × 1, 000, 000 + 0 × 100, 000 + 4 × 10, 000 + 5 × 1000 + 0 × 100 + 0 × 10 + 0 × 1 = 4, part, part, 000

#### Write the big variety names of each and every of the following in global machine of numeration:

(i) 435, 002

(ii) 1, 047, 509

(iii) fifty 9, 064, 523

(iv) 25, 201, 905

Resolution:

(i) 435, 002 may also be written as 4 hundred thirty 5 thousand two in international device of numeration.

(ii) 1, 047, 509 may also be written as a million 47 thousand 5 hundred 9 in global device of numeration.

(iii) fifty 9, 064, 523 is also written as fifty 9 million 64 thousand 5 hundred twenty 3 in international software of numeration.

(iv) 25, 201, 905 may also be written as twenty 5 million hundred one thousand 9 hundred 5 in international machine of numeration.

Exercise 1.3 internet web page: 1.16

#### What selection of 4 digit numbers are there in all?

Resolution:

We all know that the 10 digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

0 can’t be utilized in loads position so most straightforward 9 digits can be utilized.

10 digits can be utilized in loads, tens and gadgets location

The volume of 4 digit numbers = 9 × 10 × 10 × 10 = 9000

Subsequently, 9000 4 digit numbers are there in all.

#### Write the smallest and a very powerful six digit numbers. What number of numbers are between those .

Answer:

We recognise that the smallest digit is 0 which cannot be used within the most position price.

So 1 this is the second smallest digit is also used throughout the easiest position price

The required smallest six digit selection is 100 thousand

We needless to say the most important digit is 9 that may be used in any location

The required biggest six digit selection is 999999

So we get the honour = 999999 – 100 thousand = 899999

Subsequently, the smallest six digit quantity is 100000, the most important six digit amount is 999999 and 899998 numbers are between those two numbers.

#### What number of 8-digit numbers are there in all?

Answer:

We needless to say the 10 digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

0 cannot be used throughout the most house price and 9 is also used within the most neighborhood price

So the 10 digits can be utilized inside of the rest puts of 8 digit numbers

The total selection of 8 digit numbers = 9 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 90000000

Subsequently, 90000000 8 digit numbers are there in all.

#### Write 10075302 in words and rearrange the digits to get the smallest and the most important numbers.

Answer:

The given vary 10075302 may also be written as one crore 75 thousand 300 and two.

To get smallest 8 digit wide range using 0, 1, 2, 3, 5 and 7

We use 1 that’s the smallest digit throughout the most neighborhood and biggest digit 7 at the units neighborhood

As well as we located 5 within the tens house, 3 throughout the loads location and 2 in 1000’s neighborhood

So the specified smallest amount is 10002357

To get largest 8 digit vary the use of 0, 1, 2, 3, 5 and 7

We use 7 this is a very powerful digit throughout the easiest neighborhood price, 5 in a spot after most location, 3 as the next one, 2 because the smallest digit and 1.

So the desired biggest quantity is 75321000.

#### What is the smallest three-digit wide range with exact digits?

Answer:

102 is the smallest three-digit selection with explicit digits.

What’s a very powerful 5-digit vary with specific digits?

Answer:

98765 is the most important 5-digit selection with distinctive digits.

#### Write the smallest three-digit vary which doesn’t alternate if the digits are in reverse order.

Answer:

100 and one is the smallest 3-digit quantity which does not industry if the digits are in opposite order.

#### Find the adaptation some of the amount 279 and that won on reversing its digits.

Resolution:

The opposite of 279 is 972

Difference between each the numbers = 972 – 279 = 693

Subsequently, the adaptation between the variety 279 and that got on reversing its digits is 693.

Shape a very powerful and smallest 4-digit numbers using every of digits 7, 1, 0, 5 perfect once.

Resolution:

The biggest 4 digit quantity = 7510

Smallest 4 digit wide range = 1057

As a result, a very powerful and smallest 4-digit numbers using every of digits 7, 1, 0, 5 handiest once is 7510 and 1057.

Workout 1.4 internet web page: 1.18

#### Positioned the proper image (<, >) in every of the next packing containers:

(i) 102394 ☐ 99887

(ii) 2507324 ☐ 2517324

(iii) 3572014 ☐ 10253104

(iv) 47983505 ☐ 47894012

Answer:

(i) 102394 > 99887

(ii) 2507324 < 2517324

(iii) 3572014 < 10253104

(iv) 47983505 > 47894012

#### Arrange the following numbers in ascending order:

(i) 102345694, 8354208, 6539542, 63547201, 12345678

(ii) 1808090, 188088, 181888, 190909, 16060666.

Answer:

(i) it is in a position to be written as

6539542 < 8354208 < 12345678 < 63547201 < 102345694

(ii) it may be written as

181888 < 190909 < 188088 < 1808090 < 16060666.

Prepare the next numbers in descending order:

(i) 56943300, 56943201, 5695440, 56944000, 5694437

(ii) 1020216, 1020308, 1021430, 893245, 893425.

Answer:

(i) It may be written as

56944000 > 56943300 > 56943201 > 5695440 > 5694437

(ii) it can be written as

1021430 > 1020308 > 1020216 > 893425 > 893245.

Workout 1.5 internet web page: 1.21

What number of milligrams make one kilogram?

Answer:

a million or ten lakh milligrams make one kilogram.

A field of drugs medicine carries 2, 00, 000 medicine each and every weighing 20mg. What is the complete weight of all of the medicine throughout the box in grams? In kilograms?

Resolution:

It is miles for the reason that

Weight of every pill = 20mg

So we get

Weight of 2, 00, 000 medicine = 2, 00, 000 × 20

We get the weight of 2, 00, 000 drugs = 40, 00, 000mg

We needless to say

Common weight of drugs throughout the container = 40, 00, 000mg

It may well be written as

1g = 1000mg

So the weight of field having drugs = 40, 00, 000/ 1000 = 4000g

We recognise that 1kg = 1000g

So the burden of container having tablets = 4000/ one thousand = 4kg

As a result, the entire weight of all of the drugs within the container is 4000g or 4kg.

Inhabitants of Sundarnagar turned into 2, 35, 471 within the 12 months 1991. Within the one year 2001 it was found out to have expanded with the help of 72, 958. What grow to be the populace of the city in 2001?

Resolution:

It is miles for the reason that

Populace of sundarnagar in 1991 = 2, 35, 471

Growth in populace in 2001 = 72, 958

We recognise that

Inhabitants of the city in 2001 = populace of sundarnagar in 1991 + build up in inhabitants in 2001

By way of substituting the values

Populace of the city in 2001 = 2, 35, 471 + 72, 958

By means of addition

Populace of the town in 2001 = 3, 08, 429

As a result, the populace of the city in 2001 is 3, 08, 429.

A ebook exhibition became held for 4 days in a college. The variability of tickets purchased at the counter at the number one, 2nd, 3rd and ultimate days had been respectively 1094, 1812, 2050 and 2751. Uncover the entire selection of tickets introduced on the entire 4 days.

Answer:

It is miles for the reason that

Amount of tickets offered at the counter at the number one = 1094

Choice of tickets introduced at the counter on the second one = 1812

Number of tickets offered at the counter at the 0.33 = 2050

Choice of tickets introduced at the counter at the very ultimate days = 2751

We acknowledge that

Common vary of tickets introduced = 1094 + 1812 + 2050 + 2751 = 7707

Subsequently, the entire vary of tickets offered on the entire 4 days is 7, 707.

The town newspaper is posted on a regular basis. One replica has 12 pages. Standard 11,980 copies are printed. What selection of pages are in all revealed extraordinary? Every month?

Resolution:

It is a ways for the reason that

1 copy of newspaper comprises = 12 pages

So the selection of pages in 11, 980 copies = 12 × 11, 980 = 1, 43, 760

Subsequently, 1, 43, 760 pages are printed on a regular basis

We notice that

Vary of pages printed in a month = 1, 43, 760 × 30 = 43, 12, 800

Subsequently, 1, 43, 760 pages are revealed on a daily basis and 43, 12, 800 pages are revealed each and every month.

A gadget, on a mean, manufactures 2825 screws a day. What selection of screws did it produce throughout the month of January 2006?

Resolution:

It is a ways given that

Number of screws produced in keeping with day = 2, 825

So the number of screws produced within the month of January = 2, 825 × 31 = 87, 575

Subsequently, the gadget produced 87, 575 screws throughout the month of January 2006.

A well known cricket participant has up to now scored 6978 runs in check out fits. He wishes to complete 10, 000 runs. What number of extra runs does he want?

Answer:

It is a ways given that

Runs ranking by way of a well-known cricket player = 6978

So the runs required to complete 10, 000 runs = 10, 000 – 6978 = 3022

Subsequently, 3, 022 runs are needed by means of the cricket player to complete 10, 000 runs.

Ravish has ₹ 78, 592 with him. He situated an order for purchasing 39 radio gadgets at ₹ 1234 each and every. How a complete lot money will proceed to be with him after the acquisition?

Resolution:

It is miles for the reason that

Quantity with Ravish = ₹ 78, 592

Value of one hello fi = ₹ 1234

Number of radio gadgets purchased = 39

We notice that

Amount spent to shop for 39 radio units = ₹ (1234 × 39) = ₹ 48126

Quantity ultimate with Ravish = quantity with Ravish – quantity spent to shop for 39 radio gadgets

Via substituting the values

Amount ultimate with Ravish = ₹ 78, 592 – ₹ 48126 = ₹ 30466

As a result, ₹ 30466 cash will proceed to be with Ravish after the purchase.

In an election, the a hit candidate registered 5, 77, 570 votes and his nearest rival secured 3, 48, 685 votes. By way of what margin did the a hit candidate win the election?

Answer:

It’s given that

Amount of votes registered by way of successful candidate = 5, 77, 570

Choice of votes secured by means of nearest rival = 3, 48, 685

We needless to say

Margin of victory the successful candidate achieve to win the election = vary of votes registered through a hit candidate – number of votes secured with the help of nearest rival

By way of substituting the values

Margin of victory the a luck candidate download to win the election = 5, 77, 570 – 3, 48, 685 = 2, 28, 885

Subsequently, the margin of victory for the successful candidate is 2, 28, 885.

To sew a shirt 2m 15cm material is sought after. Out of 40m subject material, what number of shirts is also stitched and how much material will keep?

Resolution:

It is a ways for the reason that

Period of fabric = 40m

Duration of fabric required to sew a shirt = 2m 15cm = 200 + 15 = 215cm

Broad number of shirts that can be stitched the use of 40m material = 4000/ 215 = 18.60

We all know that the big variety of shirts should be a complete vary, 18 shirts may also be stitched.

Duration of subject material required to stitch 18 shirts = 215 × 18 = 3870cm

So without equal material = 4000 – 3870 = 130cm = 1.3m = 1m 30cm

Subsequently, 18 shirts is also stitched and 1m 30cm material will stay.

A vessel has 4 litre and 650ml of curd. In what number of glasses, each and every of 25ml capacity, can or not it’s disbursed?

Answer:

It is a ways given that

Total amount of curd = 4 litre 650ml

We notice that 1 litre = 1000ml

Common quantity of curd = 4650ml

Capacity of each and every glass = 25ml

So we get

Broad number of glasses of curd which may also be dispensed = normal quantity of curd/ attainable of each and every glass

With the help of substituting the values

Choice of glasses of curd that may be allotted = 4650/ 25 = 186

Subsequently, 186 glasses each and every of 25ml capacity of curd may also be allotted.

Medicine is packed in packing containers, every such container weighing 4kg 500g. What number of such boxes may also be loaded in a van which cannot put across previous 800kg?

Resolution:

It’s given that

Skill of van dressed in medicinal drug bins = 800kg

We recognise that 1kg = 1000g

Skill of van wearing drugs boxes = 8, 00, 000g

Weight of each and every box = 4kg 500g = 4500g

We recognise that

Common number of packing containers that can be loaded in a van = attainable of van wearing medicinal drug boxes/ Weight of each and every box

By the use of substituting the values

Common amount of packing containers that may be loaded in a van = 8, 00, 000/ 4500 = 177.77

Vary of packing containers needs to be a complete wide range

We get

Weight of 177 boxes = 177 × 4500 = 7, 96, 500g this is underneath the permissible restrict

Weight of 178 boxes = 178 × 4500 = 8, 01, 000g this is past the permissible limit

As a result, 177 boxes may also be loaded in a van which cannot lift previous 800kg.

The space between the school and the place of abode of a scholar is 1km 875m. Strange she walks each tactics between her school and residential. Find the entire distance blanketed through her in a week.

Resolution:

It’s for the reason that

Distance amongst faculty and space = 1km 875m = 1875m

We needless to say

Distance incorporated by the use of a scholar in keeping with day = 2 × 1875 = 3750m

So we get

Total distance coated with the help of the scholar in a week = 7 × 3750 = 26250m = 26km 250m

Subsequently, the entire distance coated through the use of her in each and every week is 26km 250m.

Exercise 1.6 internet web page: 1.26

Round off every of the following numbers to nearest tens:

(i) 84

(ii) 98

(iii) 984

(iv) 808

(v) 998

(vi) 12, 096

(vii) 10, 908

(viii) 28, 925

Resolution:

(i) 84 is rounded off to the nearest tens as 80.

(ii) 98 is rounded off to the closest tens as 100.

(iii) 984 is rounded off to the nearest tens as 980.

(iv) 808 is rounded off to the closest tens as 810.

(v) 998 is rounded off to the nearest tens as 1000.

(vi) 12, 096 is rounded off to the nearest tens as 12, 100.

(vii) 10, 908 is rounded off to the closest tens as 10, 910.

(viii) 28, 925 is rounded off to the closest tens as 28, 930.

Spherical off every of the following numbers to nearest loads:

(i) 3, 985

(ii) 7, 289

(iii) 8, 074

(iv) 14, 627

(v) 28, 826

(vi) 4, 20, 387

(vii) 43, 68, 973

(viii) 7, 42, 898

Resolution:

(i) 3, 985 is rounded off to the closest loads as 4, 000.

(ii) 7, 289 is rounded off to the closest loads as 7, 300.

(iii) 8, 074 is rounded off to the nearest plenty as 8, 100.

(iv) 14, 627 is rounded off to the nearest loads as 14, 600.

(v) 28, 826 is rounded off to the closest so much as 28, 800.

(vi) 4, 20, 387 is rounded off to the nearest so much as 4, 20, 400.

(vii) 43, 68, 973 is rounded off to the closest so much as 43, 69, 000.

(viii) 7, 42, 898 is rounded off to the closest plenty as 7, 42, 900.

Spherical off each and every of the following numbers to nearest tons:

(i) 2, 401

(ii) 9, 600

(iii) 4, 278

(iv) 7, 832

(v) 9, 567

(vi) 26, 019

(vii) 20, 963

(viii) 4, 36, 952

Resolution:

(i) 2, 401 is rounded off to the closest 1000’s as 2, 000.

(ii) 9, 600 is rounded off to the closest so much as 10, 000.

(iii) 4, 278 is rounded off to the nearest 1000’s as 4, 000.

(iv) 7, 832 is rounded off to the nearest so much as 8, 000.

(v) 9, 567 is rounded off to the nearest tons as 10, 000.

(vi) 26, 019 is rounded off to the nearest 1000’s as 26, 000.

(vii) 20, 963 is rounded off to the closest loads as 21, 000.

(viii) 4, 36, 952 is rounded off to the closest 1000’s as 4, 37, 000.

Round off every of the following to the nearest tens, loads and loads:

(i) 964

(ii) 1, 049

(iii) 45, 634

(iv) seventy 9, 0.5

Answer:

(i) 964 is rounded off to the closest tens as 960.

964 is rounded off to the closest loads as 1, 000.

964 is rounded off to the nearest 1000’s as 1, 000.

(ii) 1, 049 is rounded off to the nearest tens as 1, 050.

1, 049 is rounded off to the nearest plenty as 1, 000.

1, 049 is rounded off to the nearest so much as 1, 000.

(iii) 45, 634 is rounded off to the closest tens as 45, 630.

45, 634 is rounded off to the closest plenty as 45, 600.

45, 634 is rounded off to the closest so much as 46, 000.

(iv) 79, part is rounded off to the closest tens as 79, 090.

79, 1/2 is rounded off to the closest so much as 79, 100.

79, 1/2 is rounded off to the closest so much as 79, 000.

Spherical off the following measures to the nearest loads:

(i) Rs 666

(ii) Rs 850

(iii) Rs 3, 428

(iv) Rs 9, 080

(v) 1, 265 km

(vi) 417m

(vii) 550cm

(viii) 2, 486m

(ix) 360gm

(x) 940kg

(xi) 273l

(xii) 820mg

Resolution:

(i) Rs 666 is rounded off to the nearest loads as Rs 700.

(ii) Rs 850 is rounded off to the nearest plenty as Rs 900.

(iii) Rs 3, 428 is rounded off to the nearest loads as Rs 3, 400.

(iv) Rs 9, 080 is rounded off to the nearest plenty as Rs 9, 100.

(v) 1, 265 km is rounded off to the nearest loads as 1, 300km.

(vi) 417m is rounded off to the nearest loads as 400m.

(vii) 550cm is rounded off to the closest loads as 600cm.

(viii) 2, 486m is rounded off to the nearest plenty as 2, 500m.

(ix) 360gm is rounded off to the nearest so much as 400gm.

(x) 940kg is rounded off to the closest so much as 900kg.

(xi) 273l is rounded off to the nearest plenty as 300l.

(xii) 820mg is rounded off to the nearest plenty as 800mg.

Checklist all numbers which can be rounded off to nearest ten as 370.

Resolution:

The list of numbers which can be rounded off to nearest ten as 370 are

365, 366, 367, 368, 369, 370, 371, 372, 373, 374.

Uncover the smallest and largest numbers which can be rounded off to the closest loads as 900.

Answer:

The smallest selection this is rounded off to the nearest plenty as 900 is 850.

The most efficient selection this is rounded off to the closest so much as 900 is 949.

Find the smallest and best numbers which may also be rounded off to the closest loads as 9000.

Answer:

The smallest vary which is rounded off to the closest so much as 9000 is 8, 500.

The best quantity this is rounded off to the closest 1000’s as 9000 is 9, 499.

Exercise 1.7 internet web page: 1.29

Estimate the next with the help of rounding off each and every facet to nearest so much:

(i) 730 + 998

(ii) 796 – 314

(iii) 875 – 384

Answer:

(i) it is in a position to be rounded off to the closest so much as 700 + 1000 = 1, 700.

(ii) it can be rounded off to the closest so much as 800 – 300 = 500.

(iii) it is in a position to be rounded off to the nearest so much as 900 – 400 = 500.

Estimate the next with the help of rounding off every factor to nearest loads:

(i) 12, 094 + 2, 888

(ii) 28, 292 – 21, 496

Resolution:

(i) it may be rounded off to the closest so much as 13, 000 + 3, 000 = 16, 000.

(ii) it is in a position to be rounded off to the closest tons as 28, 000 – 21, 000 = 7, 000.

Estimate the next through rounding off every vary to its best neighborhood:

(i) 439 + 334 + 4, 317

(ii) 8, 325 – 491

(iii) 1, 08, 734 – 47, 599

(iv) 898 × 785

(v) 9 × 795

(vi) 87 × 317

Answer:

(i) it may well be rounded off to its best location as 400 + 300 + 4, 000 = 4, 700.

(ii) it may be rounded off to its perfect position as 8, 000 – 500 = 7, 500.

(iii) it may be rounded off to its perfect neighborhood as 1, 00, 000 – 50, 000 = 50, 000.

(iv) it may well be rounded off to its largest neighborhood as 900 × 800 = 7, 20, 000.

(v) it may well be rounded off to its best neighborhood as 10 × 800 = 8, 000.

(vi) it may well be rounded off to its perfect location as 90 × 300 = 27, 000.

Uncover the estimated quotient for each and every of the following with the help of rounding off every selection to its largest house:

(i) 878 ÷ 28

(ii) 745 ÷ 24

(iii) 4489 ÷ 394

Answer:

(i) it is in a position to be rounded off to its best house as 900 ÷ 30 = 30.

(ii) it may be rounded off to its best location as 700 ÷ 20 = 35.

(iii) it can be rounded off to its best area as 4000 ÷ 400 = 10.

Exercising 1.8 web page: 1.30

Write the expression for every of the following statements the use of brackets:

(i) 4 advanced by means of the sum of 13 and 7.

(ii) 8 prolonged through the use of the adaptation of 4 from 9.

(iii) Divide the honour of twenty 8 and seven thru 3.

(iv) The sum of three and seven is speeded up during the distinction of twelve and 8.

Answer:

(i) The expression for 4 increased during the sum of 13 and seven is 4 × (13 + 7).

(ii) 8 speeded up during the difference of 4 from 9 is 8 × (9 – 4).

(iii) Divide the adaptation of twenty 8 and 7 through 3 is (28 – 7) ÷ 3.

(iv) The sum of three and seven is larger through the use of the adaptation of twelve and eight

Simplify each and every of the following:

(i) 124 – (12 – 2) × 9

(ii) (13 + 7) × (9 – 4) – 18

(iii) 210 – (14 – 4) × (18 + 2) – 10

Answer:

(i) 124 – (12 – 2) × 9 on additional simplification we download

124 – (12 – 2) × 9

= 124 – 10 × 9

= 124 – 90

= 34

(ii) (13 + 7) × (9 – 4) – 18 on in a similar way simplification we reach

(13 + 7) × (9 – 4) – 18

= 20 × 5 – 18

= 100 – 18

= 92

(iii) 210 – (14 – 4) × (18 + 2) – 10 on additional simplification we acquire

210 – (14 – 4) × (18 + 2) – 10

= 210 – 10 × 20 – 10

= 210 – 2 hundred – 10

= 0

Workout 1.9 internet web page: 1.31

Simplify every of the next:

7 × 109

6 × 112

9 × one 0 5

17 × 109

16 × 108

12 × 100 and 5

102 × 103

One hundred and one × 105

109 × 107

Answer:

On simplification of 7 × 109 we get

7 × 109 = 763.

On simplification of 6 × 112 get

6 × 112 = 672.

On simplification of 9 × 105 we get

9 × one 0 5 = 945.

On simplification of 17 × 109 we get

17 × 109 = 1853.

On simplification of 16 × 108 we get

16 × 108 = 1728.

On simplification of 12 × one 0 5 we get

12 × 105 = 1260.

On simplification of 102 × 103 we get

102 × 103 = 10506.

On simplification of 101 × 100 and 5 we get

100 and one × one 0 5 = 10605.

On simplification of 109 × 107 we get

109 × 107 = 11663.

Workout 1.10 internet web page: 1.35

Write the roman-numerals for each and every of the following:

(i) 33

(ii) 48

(iii) 76

(iv) 95

Answer:

(i) The roman-numeral of 33 is XXXIII.

(ii) The roman-numeral of 48 is XLVIII.

(iii) The roman-numeral of 76 is LXXVI.

(iv) The roman-numeral of 90 5 is XCV.

Write the following in Roman numerals:

(i) 154

(ii) 173

(iii) 248

(iv) 319

Resolution:

(i) The roman-numeral of 154 is CLIV.

(ii) The roman-numeral of 173 is CLXXIII.

(iii) The roman-numeral of 248 is CCXLVIII.

(iv) The roman-numeral of 319 is CCCXIX.

Write the following in Roman numerals:

(i) 1008

(ii) 2718

(iii) 3906

(iv) 3794

Answer:

(i) The roman-numeral of 1008 is KVIII.

(ii) The roman-numeral of 2718 is KKDCCXVIII.

(iii) The roman-numeral of 3906 is KKKCKVI.

(iv) The roman-numeral of 3794 is KKKDCCXCIV.

Write the next in Roman numerals:

(i) 4201

(ii) 10009

(iii) 44000

(iv) 25819

Resolution:

(i) The roman-numeral of 4201 is

CCI.

(ii) The roman-numeral of 10009 is XIX.

(iii) The roman-numeral of 44000 is

.

(iv) The roman-numeral of 25819 is

DCCCXIX.

Write the next in Hindu-Arabic numerals:

(i) XXVI

(ii) XXIX

(iii) LXXII

(iv) XCI

Answer:

(i) The Hindu-Arabic numerals of XXVI is 26.

(ii) The Hindu-Arabic numerals of XXIX is 29.

(iii) The Hindu-Arabic numerals of LXXII is 72.

(iv) The Hindu-Arabic numerals of XCI is 91.

Write the corresponding Hindu-Arabic numerals for every of the next:

(i) CIX

(ii) CLXXII

(iii) CCLIV

(iv) CCCXXIX

Resolution:

(i) The Hindu-Arabic numerals of CIX is 109.

(ii) The Hindu-Arabic numerals of CLXXII is 172.

(iii) The Hindu-Arabic numerals of CCLIV is 254.

(iv) The Hindu-Arabic numerals of CCCXXIX is 329.

Write the corresponding Hindu-Arabic numerals for every of the next:

(i) KXIX

(ii) KDLXV

(iii) KKCXXIII

(iv) KKKDCXL

Resolution:

(i) The Hindu-Arabic numerals of KXIX is 1019.

(ii) The Hindu-Arabic numerals of KDLXV is 1565.

(iii) The Hindu-Arabic numerals of KKCXXIII is 2123.

(iv) The Hindu-Arabic numerals of KKKDCXL is 3640.

Write the following in Hindu-Arabic numerals:

Resolution:

(i) The Hindu-Arabic numerals of

Is 4444.

(ii) The Hindu-Arabic numerals of

Is 6949.

(iii) The Hindu-Arabic numerals of

Is 9391.

(iv) The Hindu-Arabic numerals of

Is 70009.

#### Which of the following are meaningless?

(i) CC

(ii) KKKCCXI

(iii) XD

(iv) VC

Answer:

Throughout the given query we notice that (i) and (iii) are meaningless.

Goal type Questions web page: 1.36

Mark the right kind alternative in each and every of the following:

The adaptation some of the location value and face price of 8 in 658742 is

(a) 0 (b) 42 (c) 735 (d) 693

Answer:

The given choices are improper.

Position value of 8 in 6,58,742 = 8,000

Face price of 8 = 8

Distinction between them = 8,000 − 8 = 7,992

The consideration some of the location values of 6 and 3 in 256839 is

(a) 3 (b) 9 (c) 6800 (d) 5930

Resolution:

The given choices are improper.

Neighborhood price of 6 in 2,56,839 = 6,000

The positioning price of 3 in 2,56,839 = 30

Difference amongst them = 6,000 − 30 = 5,970

The consideration of the smallest 3 digit vary and the most important two digit amount is

(a) 100 (b) 1 (c) 10 (d) 90 9

Resolution:

The choice (b) is the proper resolution.

We notice that

The smallest 3-digit selection is 100 and a very powerful two-digit quantity is 99.

So the adaptation amongst them= 100 − 99 = 1

The largest 3 digit selection shaped by means of the digits 8, 5, 9 is

(a) 859 (b) 985 (c) 958 (d) 589

Answer:

The selection (b) is the best resolution.

We needless to say a very powerful vary is shaped thru writing the digits in descending order.

The smallest 3 digit amount having 3 superior digits is

(a) 123 (b) 100 and one (c) 102 (d) 201

Answer:

The selection (c) is an acceptable resolution.

We notice that the smallest 3 digit numbers are 0, 1 and a couple of

By way of arranging them in ascending order we get 012 which is a digit amount.

Subsequently, 102 is the smallest 3 digit wide range.

The biggest 3 digit wide range having superior digits is

(a) 987 (b) 789 (c) 999 (d) 900

Resolution:

The choice (a) is the very best resolution.

The biggest 3 digit numbers are 7, 8 and 9. A very powerful quantity is received thru arranging them in descending order.

The consideration between a very powerful 3 digit selection and the largest 3 digit quantity with glorious digits is

(a) 10 (b) 0 (c) 12 (d) 13

Resolution:

The selection (c) is the fitting resolution.

We all know that largest 3 digit wide range = 999

Largest three-digit amount with distinct digits = 987

Difference between them = 999 − 987 = 12

The fabricated from the site values of 2 threes in 53432 is

(a) 9000 (b) 90000 (c) 10000 (d) 99000

Resolution:

The choice (b) is the fitting resolution.

We recognise that 3 throughout the 2nd neighborhood from correct is at tens neighborhood.

So the site value of 3 at tens house = 30

We notice that 3 within the fourth area from proper is at 1000’s house.

So the area value of three at 1000’s location = 3,000

Made of the neighborhood values = 3,000 × 30 = 90,000

The smallest counting vary is

(a) 0 (b) 1 (c) 10 (d) None of the ones

Resolution:

The selection (b) is the very best resolution.

We notice that the smallest digit is 0 and the smallest counting quantity is 1.

The total vary of 4 digit numbers is

(a) 8999 (b) 9000 (c) 8000 (d) 9999

Answer:

The choice (b) is the best resolution.

We acknowledge that the smallest 4 digit vary = 1,000

Greatest 4 digit selection = 9,999.

So the whole amount of 4-digit numbers = [9,999 − 1,000 ] + 1 = 9,000

The selection of 3 digit numbers shaped by way of using digits 3, 5, 9, taking every digit precisely as soon as, is

(a) 3 (b) 4 (c) 5 (d) 6

Answer:

The choice (d) is the best resolution.

359, 395, 539, 593, 935 and 953 are the numbers.

Overall amount of numbers which when rounded off to nearest ten give us 2 hundred is

(a) 9 (b) 10 (c) 8 (d) 7

Resolution:

The choice (b) is the proper resolution.

195, 196, 197, 198, 199, two hundred, 201, 202, 203, 204 are the numbers that after rounded off to nearest ten provide us.

The smallest amount which while rounded off to the nearest hundred as 600, is

(a) 550 (b) 595 (c) 604 (d) 599

Resolution:

The selection (a) is the proper resolution.

The wide range from 550 to 649 are rounded off nearest hundred as 600. Subsequently, the smallest selection is 550.

The best selection which while rounded off to the closest thousand 7000, is

(a) 6500 (b) 6549 (c) 7499 (d) 6499

Resolution:

The selection (c) is the most productive resolution.

Numbers from 6500 to 7499 are rounded off to nearest thousand as 7000. Subsequently, the best quantity is 7499.

The adaptation between the most productive and smallest numbers which while rounded off more than a few to the closest tens as 540, is

(a) 10 (b) 9 (c) 8 (d) 10

Resolution:

The choice (b) is the fitting resolution.

We all know that the best selection that after rounded off to the nearest tens becomes 540 = 544

Least quantity that after rounded off to the closest tens will grow to be 540 = 535

So, the adaptation between them = 544 − 535 = 9

The adaptation between the best and smallest numbers which while rounded off a host to the closest hundred as 6700, is

(a) 100 (b) 99 (c) 98 (d) 100 and one

Answer:

The selection (b) is the right kind resolution.

We all know that the best amount that when rounded off to the closest hundred turns into 6,7000 = 6749

Least amount that when rounded off to the closest hundred will grow to be 6,700 = 6650

So, the honour between them = 6,749 − 6,650 = 90 9

The consideration one of the best and the smallest numbers which whilst rounded off to the nearest thousand as 9000, is

(a) 1000 (b) 990 (c) 999 (d) 900

Answer:

The choice (c) is an acceptable resolution.

We notice that the most productive quantity that when rounded off to the closest thousand turns into 9,000 = 9499

Smallest vary that when rounded off to the nearest thousand becomes 9,000 = 8500

So, the adaptation between them = 9,499 − 8,500 = 999

#### Which of the next numbers is similar to a minimum of a thousand million?

(a) 10 lakh (b) 1 crore (c) 10 crore (d) 100 crore

Resolution:

The choice (d) is the proper resolution.

1 billion = 100 crore

Inside the global area price gadget, we write a million for

(a) 1 lakh (b) 10 lakh (c) 100 lakh (d) 1 crore

Answer:

The choice (b) is the fitting resolution.

1,000,000 = 10 lakh

#### Which of the next is not all the time vital?

(a) XIV (b) XXXV (c) XXV (d) VX

Resolution:

The choice (d) is the very best resolution.

In Roman numerals V is 5 and X is 10

5 cannot be written prior to 10

#### Which of the following isn’t significant?

(a) XXII (b) XII (c) XVV (d) XIV

Resolution:

The choice (c) is the proper resolution.

In Roman numerals V is 5 and X is 10

5 can’t be written two circumstances.

RD Sharma answers for class 6 bankruptcy 1 figuring out Our Numbers

RD SHARMA solutions for sophistication 6 chapter 1 figuring out OUR NUMBERS loose on-line

Workout 1.1 web page: 1.7

Write every of the following in numeral shape:

(i) 8 thousand twelve.

(ii) Seventy thousand 53.

(iii) 5 lakh seven thousand 4 hundred six.

(iv) Six lakh two thousand 9.

(v) Thirty lakh 11 thousand one.

(vi) 8 crore 4 lakh twenty 5.

(vii) 3 crore 3 lakh 3 thousand 3 hundred 3.

(viii) Seventeen crore sixty lakh thirty thousand 57.

Answer:

(i) The numeral form of 8 thousand twelve is 8,012.

(ii) The numeral type of seventy thousand 53 is 70,053.

(iii) The numeral form of 5 lakh seven thousand 4 hundred six is 5, 07, 406.

(iv) The numeral form of six lakh two thousand 9 is 6, 02, 009.

(v) The numeral form of thirty lakh 11 thousand one is 30, 11, 001.

(vi) The numeral form of 8 crore 4 lakh twenty 5 is 8, 04, 00, 0.5.

(vii) The numeral type of 3 crore 3 lakh 3 thousand 3 hundred 3 is 3, 03, 03, 303.

(viii) The numeral form of seventeen crore sixty lakh thirty thousand 57 is 17, 60, 30, 057.

Write the following numbers in phrases throughout the Indian device of numeration:

(i) 42,007

(ii) 4,05,0.5

(iii) 35, 42, 012

(iv) 7, 06, 04, 014

(v) 25, 05, 05,500

(vi) 5, 50, 50, 050

(vii) 5, 03, 04, 012

Resolution:

(i) 42,007 is written as 42 thousand seven throughout the Indian device of numeration.

(ii) 4,05,1/2 is written as 4 lakh 5 thousand 45 within the Indian software of numeration.

(iii) 35, 42, 012 is written as thirty 5 lakh 42 thousand twelve within the Indian device of numeration.

(iv) 7, 06, 04, 014 is written as seven crore six lakh 4 thousand fourteen throughout the Indian device of numeration.

(v) 25, 05, 05,500 is written as twenty 5 crore 5 lakh 5 thousand 5 hundred within the Indian device of numeration.

(vi) 5, 50, 50, 050 is written as 5 crore fifty lakh fifty thousand fifty throughout the Indian machine of numeration.

(vii) 5, 03, 04, 012 is written as 5 crore 3 lakh 4 thousand twelve throughout the Indian software of numeration.

#### Insert commas in a suitable positions to split classes and write the next numbers in phrases:

(i) 4375

(ii) 24798

(iii) 857367

(iv) 9050784

(v) 10105607

(vi) 10000007

(vii) 910107104

Answer:

(i) 4375 with the help of putting commas is written as 4, 375.

(ii) 24798 thru hanging commas is written as 24, 798.

(iii) 857367 by way of hanging commas is written as 8,57,367.

(iv) 9050784 by means of putting commas is written as 90,50,784.

(v) 10105607 through hanging commas is written as 1,01,05,607.

(vi) 10000007 by the use of hanging commas is written as 1,00,00,007.

(vii) 91010714 through hanging commas is written as 91,01,07,104.

#### Write every of the following in multiplied notation:

(i) 3057

(ii) 12345

(iii) 10205

(iv) 235060

Resolution:

(i) 3057 = 3 × 1000 + 0 × 100 + 5 × 10 + 7 × 1

(ii) 12345 = 1 × 10000 + 2 × 1000 + 3 × 100 + 4 × 10 + 5 × 1

(iii) 10205 = 1 × 10000 + 0 × 1000 + 2 × 100 + 0 × 10 + 5 × 1

(iv) 235060 = 2 × 100 thousand + 3 × 10000 + 5 × 1000 + 0 × 100 + 6 × 10 + 0 × 1

Write the corresponding numeral for each and every of the following:

(i) 7 × 1000 + 2 × 1000 + 5 × 100 + 9 × 10 + 6 × 1

(ii) 4 × 100 thousand + 5 × 1000 + 1 × 100 + 7 × 1

(iii) 8 × 1000000 + 3 × 1000 + 6 × 1

(iv) 5 × 10000000 + 7 × a million + 8 × one thousand + 9 × 10 + 4

Answer:

(i) 7 × 1000 + 2 × one thousand + 5 × 100 + 9 × 10 + 6 × 1 = 72, 596.

(ii) 4 × 100000 + 5 × 1000 + 1 × 100 + 7 × 1 = 4, 05, 107.

(iii) 8 × 1,000,000 + 3 × 1000 + 6 × 1 = 80, 03, 006.

(iv) 5 × 10000000 + 7 × 1,000,000 + 8 × one thousand + 9 × 10 + 4 = 5, 70, 08, 094.

In finding the world price of the digit 4 in each and every of the next:

(i) 74983160

(ii) 8745836

Resolution:

(i) Where price of digit 4 in 74983160 is 4 × 10, 00, 000 = 40, 00, 000.

(ii) The positioning price of digit 4 in 8745836 is 4 × 10, 000 = 40, 000.

#### Come to a decision the made of where values of fives in 450758.

Resolution:

The area price of first 5 is 5 × 10 = 50

The realm price of 2nd 5 is 5 × 10, 000 = 50, 000

So the specified product = 50 × 50, 000 = 25, 00, 000.

Subsequently, the made of the world values of 2 fives in 450758 is 25, 00, 000.

Come to a decision the honour of the site values of 2 7’s in 257839705.

Resolution:

Where price of first seven is 7 × 100 = 700

The realm price of 2d seven is 7 × 10, 00, 000 = 70, 00, 000

So the specified difference = 700 – 70, 00, 000 = 69, 90 9, 300

Subsequently, the honour of the area values of 2 7’s in 257839705 is sixty 9, 90 9, 300.

#### Decide the adaptation some of the location value and the face value of five in 78654321.

Resolution:

The given quantity is 78654321

The positioning price of five = 5 × 10, 000 = 50, 000

The face price of 5 = 5

So the required difference = 50, 000 – 5 = 40 9, 995

Subsequently, the adaptation some of the position price and the face price of 5 in 78654321 is 49, 995.

#### Which digits have the similar face price and house price in 92078634?

Resolution:

We needless to say the face price is dependent on the price of the digit and the world value is predicated upon on its position of prevalence.

So the digits that have equivalent position and face price in a variety of are the ones digit and zeros of the amount.

The given selection is 92078634 and 9, 20, 78, 634 we recognise that 4 which may also be the ones digit and 0 which is the lakhs digit have equivalent face and neighborhood price.

**What number of unique 3-digit numbers may also be formed with the help of the use of the digits 0, 2, 5 without repeating any digit within the big variety?**

Answer:

The unique three-digit numbers which may also be shaped through the use of the use of the digits 0, 2, 5 with out repeating any digit within the amount are 205, 250, 502 and 520.

As a result, 4 3 digit numbers is also formed by the use of the use of the digits 0, 2, 5.

Write all possible three-digit numbers the use of the digits 6, 0, 4 whilst

(i) repetition of digits isn’t allowed

(ii) repetition of digits is permitted.

Resolution:

(i) The possible 3 digit numbers the use of the digits 6, 0, 4 whilst repetition of digits is not allowed are 604, 640, 406 and 460.

(ii) The possible 3 digit numbers the use of the digits 6, 0, 4 whilst repetition of digits is permitted are 400, 406, 460, 466, 444, 404, 440, 446, 464, 600, 604, 640, 644, 646, 664, 606, 660 and 666.

Fill throughout the blank:

(i) 1 lakh = ………. 10000

(ii) 1 lakh = ……… Thousand

(iii) 1 lakh = ……… Hundred

(iv) 1 lakh = ………. Ten

(v) 1 crore = ………. Ten lakh

(vi) 1 crore = ……… lakh

(vii) 1 crore = ……… 10000

(viii) 1 crore = ……… thousand

(ix) 1 crore = ……….. Hundred

(x) 1 crore = …………. Ten

Resolution:

(i) 1 lakh = 10 10000

(ii) 1 lakh = 100 Thousand

(iii) 1 lakh = 1000 Hundred

(iv) 1 lakh = 10000 Ten

(v) 1 crore = 10 ten lakh

(vi) 1 crore = 100 lakh

(vii) 1 crore = 1000 10000

(viii) 1 crore = 10000 thousand

(ix) 1 crore = 100000 Hundred

(x) 1 crore = 1,000,000 Ten

Workout 1.2 web page: 1.13

Write each and every of the following numbers in digits by the use of the use of international house price chart. Moreover, write them in prolonged shape

(i) Seven million 300 3 thousand hundred six.

(ii) Fifty 5 million twenty 9 thousand seven.

(iii) Six billion 110 million 3 thousand seven.

Resolution:

(i) Seven million 3 hundred 3 thousand hundred six is written as 7, 303, 206 the use of international location value chart.

It is in a position to be written in increased form as

7, 303, 206 = 7 × 1,000,000 + 3 × 100000 + 2 × 100 + 0 × 10 + 6 × 1

(ii) Fifty 5 million twenty 9 thousand seven is written as 55, 029, 007 the use of international neighborhood price chart.

It may well be written in increased shape as

Fifty 5, 029, 007 = 5 × 10000000 + 5 × 1,000,000 + 0 × 100 thousand + 2 × 10000 + 9 × one thousand + 0 × 100 + 0 × 10 + 7 × 1

(iii) Six billion 100 ten million 3 thousand seven is written as 6, 100 and ten, 003, 007 the use of international neighborhood price chart.

It is in a position to be written in prolonged form as

6, 100 and ten, 003, 007 = 6 × 1000000000 + 1 × 100000000 + 1 × 10000000 + 0 × a million + 0 × 100000 + 0 × 10000 + 3 × one thousand + 0 × 100 + 0 × 10 + 7 × 1

Rewrite each and every of the following numerals with correct commas throughout the international device of numeration. Moreover, write the amount name of every throughout the international device of numeration

(i) 513625

(ii) 4035672

(iii) 65954923

(iv) 70902005

Resolution:

(i) 513625 is written as 513, 625 that is 5 hundred 13 thousand 600 twenty 5 within the international software of numeration.

(ii) 4035672 is written as 4, 0.5, 672 this is 4 million thirty 5 thousand 600 72 within the international gadget of numeration.

(iii) 65954923 is written as sixty 5, 954, 923 this is sixty 5 million 9 hundred fifty 4 thousand 9 hundred twenty 3 throughout the global gadget of numeration.

(iv) 70902005 is written as 70, 902, 0.5 which is seventy million 9 hundred two thousand 5 throughout the international device of numeration.

Write every of the following numbers throughout the international machine of numeration:

(i) 40 3 lakh 4 thousand 84.

(ii) Six crore thirty 4 lakh 4 thousand 40 4.

(iii) Seven lakh thirty 5 thousand 8 hundred 90 9 perfect.

Resolution:

(i) 40 3 lakh 4 thousand 80 4 may also be written as 4, 304, 084 that is 4 million 300 4 thousand 80 4 using international device of numeration.

(ii) Six crore thirty 4 lakh 4 thousand 40 4 is also written as 63, 404, 044 this is sixty 3 million 400 4 thousand 44 the use of international gadget of numeration.

(iii) Seven lakh thirty 5 thousand 8 hundred 99 best is also written as 735, 899 this is 700 thirty 5 thousand 8 hundred 99 best the use of global software of numeration.

Write the following numbers within the Indian software of numeration:

(i) Six million 5 hundred 43 thousand hundred ten.

(ii) 76 million 80 5 thousand 9 hundred 80 seven.

(iii) 3 hundred twenty 5 million 4 hundred seventy 9 thousand 8 hundred thirty 8.

Answer:

(i) Six million 5 hundred 40 3 thousand hundred ten is also written as 65, 43, 210 that is sixty 5 lakh 40 3 thousand 2 hundred ten using the Indian machine of numeration.

(ii) 76 million 80 5 thousand 9 hundred 80 seven may also be written as 7, 60, 85, 987 this is seven crore sixty lakh 8 5 thousand 9 hundred 80 seven using the Indian gadget of numeration.

(iii) 300 twenty 5 million 4 hundred seventy 9 thousand 8 hundred thirty 8 may also be written as 32, 54, seventy 9, 838 that is thirty crore fifty 4 lakh 79 thousand 8 hundred thirty 8 the use of the Indian machine of numeration.

A good 9 digit wide range has most straightforward ones in ones length, most straightforward twos throughout the tons length and perfect threes in loads of 1000’s length. Write this wide range in phrases throughout the Indian gadget.

Resolution:

It is a ways for the reason that a 9 digit amount has handiest ones in ones length, most efficient twos within the tons length and most straightforward threes in hundreds of thousands period.

So we get the variety as 333, 222, 111

We will write it as 33, 32, 22, 111 that is thirty 3 crore thirty lakh twenty two thousand 100 and 11 the use of the Indian machine.

**What selection of tons make a million?**

Resolution:

We all know that

1000 = 1000 and 1,000,000 = 1, 000, 000

Vary of so much which make a million = a million/ 1000

Via the use of substituting the values

Choice of 1000’s which make a million = 1, 000, 000/ 1000

So we get

Amount of tons which make a million = one thousand

Subsequently, one thousand tons make a million.

#### What selection of hundreds of thousands make a thousand million?

Answer:

We recognise that

One million = 1, 000, 000 and 1000000000 = 1, 000, 000, 000

Vary of loads of 1000’s which make 1000 million = 1000000000/ a million

Via substituting the values

Amount of hundreds of thousands which make one thousand million = 1, 000, 000, 000/ 1, 000, 000

So we get

Amount of hundreds of thousands which make 1000 million = 1000

As a result, one thousand million make 1000 million.

#### (i) what selection of lakhs make 1,000,000?

#### (ii) what number of lakhs make a thousand million?

Answer:

(i) We all know that

One lakh = 1, 00, 000 and 1,000,000 = 1, 000, 000

Number of lakhs which make a million = a million/ One lakh

By the use of substituting the values

Broad number of lakhs which make a million = 1, 000, 000/ 1, 00, 000

So we get

Broad number of lakhs which make a million = 10

Subsequently, 10 lakhs make a million.

(ii) We needless to say

One lakh = 1, 00, 000 and 1000 million = 1, 000, 000, 000

Broad number of lakhs which make 1000 million = a thousand million/ One lakh

Via substituting the values

Choice of lakhs which make 1000000000 = 1, 000, 000, 000/ 1, 00, 000

So we get

Number of lakhs which make 1000 million = 10, 000

Subsequently, 10, 000 lakhs make one thousand million.

Write each and every of the following in numeral form:

(i) 8 million 700 8 thousand 4.

(ii) 600 seven million twelve thousand 84.

(iii) 4 billion twenty 5 million 45 thousand.

Resolution:

(i) 8 million 700 8 thousand 4 is also written as

8 × 1, 000, 000 + 7 × 100, 000 + 0 × 10, 000 + 8 × 1000 + 0 × 100 + 0 × 10 + 4 × 1 = 8, 708, 004

(ii) 600 seven million twelve thousand 84 is also written as

6 × 100, 000, 000 + 0 × 10, 000, 000 + 7 × 1, 000, 000 + 0 × 100, 000 + 1 × 10, 000 + 2 × 1000 + 0 × 100 + 8 × 10 + 4 × 1 = 607, 012, 084

(iii) 4 billion twenty 5 million 45 thousand is also written as

4 × 1, 000, 000, 000 + 0 × 100, 000, 000 + 2 × 10, 000, 000 + 5 × 1, 000, 000 + 0 × 100, 000 + 4 × 10, 000 + 5 × one thousand + 0 × 100 + 0 × 10 + 0 × 1 = 4, 1/2, 0.5, 000

Write the variety names of each and every of the following in international gadget of numeration:

(i) 435, 002

(ii) 1, 047, 509

(iii) 59, 064, 523

(iv) 25, 201, 905

Resolution:

(i) 435, 002 may also be written as 4 hundred thirty 5 thousand in international device of numeration.

(ii) 1, 047, 509 is also written as 1,000,000 47 thousand 5 hundred 9 in international gadget of numeration.

(iii) fifty 9, 064, 523 is also written as fifty 9 million sixty 4 thousand 5 hundred twenty 3 in international gadget of numeration.

(iv) 25, 201, 905 may also be written as twenty 5 million 2 hundred 1000 9 hundred 5 in international machine of numeration.

Exercising 1.3 web page: 1.16

#### What selection of 4 digit numbers are there in all?

Resolution:

We recognise that the ten digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

0 cannot be used in 1000’s location so most straightforward 9 digits can be utilized.

10 digits can be used in loads, tens and units house

The number of 4 digit numbers = 9 × 10 × 10 × 10 = 9000

As a result, 9000 4 digit numbers are there in all.

Write the smallest and the largest six digit numbers. What selection of numbers are amongst the ones .

Answer:

We needless to say the smallest digit is 0 which cannot be used throughout the most area price.

So 1 that is the second one smallest digit is also used throughout the easiest area value

The specified smallest six digit vary is 100000

We acknowledge that the most important digit is 9 that may be used in any house

The specified biggest six digit selection is 999999

So we get the adaptation = 999999 – 100 thousand = 899999

As a result, the smallest six digit vary is 100000, the largest six digit vary is 999999 and 899998 numbers are amongst those numbers.

#### What number of 8-digit numbers are there in all?

Answer:

We needless to say the 10 digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

0 cannot be used within the most position price and 9 is also used throughout the most position value

So the 10 digits can be utilized throughout the final puts of 8 digit numbers

The full huge number of 8 digit numbers = 9 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 90000000

Subsequently, 90000000 8 digit numbers are there in all.

Write 10075302 in words and rearrange the digits to get the smallest and the most important numbers.

Answer:

The given quantity 10075302 is also written as one crore 75 thousand 3 hundred and two.

To get smallest 8 digit selection using 0, 1, 2, 3, 5 and seven

We use 1 that is the smallest digit throughout the most position and largest digit 7 on the gadgets neighborhood

Additional we positioned 5 throughout the tens neighborhood, 3 within the loads house and 2 in tons neighborhood

So the specified smallest selection is 10002357

To get biggest 8 digit quantity using 0, 1, 2, 3, 5 and 7

We use 7 that is the biggest digit within the most location price, 5 in a spot after most location, 3 as the following one, 2 for the reason that smallest digit and 1.

So the specified biggest quantity is 75321000.

#### What is the smallest three-digit wide range with exact digits?

Resolution:

102 is the smallest three-digit quantity with exact digits.

#### What is a very powerful five-digit selection with exact digits?

Resolution:

98765 is a very powerful 5-digit amount with distinctive digits.

Write the smallest three-digit amount which doesn’t exchange if the digits are in reverse order.

Answer:

One hundred and one is the smallest 3-digit selection which does now not exchange if the digits are in opposite order.

Find the adaptation some of the wide range 279 and that got on reversing its digits.

Resolution:

The opposite of 279 is 972

Distinction amongst every the numbers = 972 – 279 = 693

As a result, the adaptation some of the selection 279 and that won on reversing its digits is 693.

Form the largest and smallest 4-digit numbers using each and every of digits 7, 1, 0, 5 most straightforward as soon as.

Resolution:

A very powerful 4 digit quantity = 7510

Smallest 4 digit vary = 1057

Subsequently, the most important and smallest 4-digit numbers the use of each and every of digits 7, 1, 0, 5 perfect as soon as is 7510 and 1057.

Exercising 1.4 web page: 1.18

Located the fitting image (<, >) in every of the next boxes:

(i) 102394 ☐ 99887

(ii) 2507324 ☐ 2517324

(iii) 3572014 ☐ 10253104

(iv) 47983505 ☐ 47894012

Resolution:

(i) 102394 > 99887

(ii) 2507324 < 2517324

(iii) 3572014 < 10253104

(iv) 47983505 > 47894012

Arrange the following numbers in ascending order:

(i) 102345694, 8354208, 6539542, 63547201, 12345678

(ii) 1808090, 188088, 181888, 190909, 16060666.

Answer:

(i) it can be written as

6539542 < 8354208 < 12345678 < 63547201 < 102345694

(ii) it may well be written as

181888 < 190909 < 188088 < 1808090 < 16060666.

Prepare the next numbers in descending order:

(i) 56943300, 56943201, 5695440, 56944000, 5694437

(ii) 1020216, 1020308, 1021430, 893245, 893425.

Answer:

(i) It may be written as

56944000 > 56943300 > 56943201 > 5695440 > 5694437

(ii) it can be written as

1021430 > 1020308 > 1020216 > 893425 > 893245.

Exercise 1.5 web page: 1.21

#### What selection of milligrams make one kilogram?

Answer:

One million or ten lakh milligrams make one kilogram.

#### A container of gear medicine contains 2, 00, 000 drugs each and every weighing 20mg. What is all of the weight of the entire drugs within the container in grams? In kilograms?

Resolution:

It is miles given that

Weight of each and every pill = 20mg

So we get

Weight of two, 00, 000 drugs = 2, 00, 000 × 20

We get the weight of 2, 00, 000 drugs = 40, 00, 000mg

We notice that

Overall weight of drugs within the box = 40, 00, 000mg

It can be written as

1g = 1000mg

So the burden of box having tablets = 40, 00, 000/ 1000 = 4000g

We notice that 1kg = 1000g

So the weight of field having drugs = 4000/ one thousand = 4kg

Subsequently, the entire weight of the entire medicine within the field is 4000g or 4kg.

#### Inhabitants of Sundarnagar was 2, 35, 471 throughout the year 1991. Within the year 2001 it was once found out to have multiplied through the use of 72, 958. What grow to be the populace of the city in 2001?

Resolution:

It is miles given that

Populace of sundarnagar in 1991 = 2, 35, 471

Building up in populace in 2001 = 72, 958

We acknowledge that

Populace of the city in 2001 = inhabitants of sundarnagar in 1991 + increase in populace in 2001

Via substituting the values

Populace of the city in 2001 = 2, 35, 471 + 72, 958

By way of addition

Inhabitants of the town in 2001 = 3, 08, 429

As a result, the populace of the town in 2001 is 3, 08, 429.

#### A e-book exhibition became held for 4 days in a college. The number of tickets purchased at the counter at the number one, 2nd, 0.33 and ultimate days have been respectively 1094, 1812, 2050 and 2751. Uncover the whole amount of tickets purchased on the entire 4 days.

Resolution:

It is a ways given that

Vary of tickets purchased at the counter at the number one = 1094

Choice of tickets introduced on the counter on the second = 1812

Vary of tickets introduced on the counter on the 1/3 = 2050

Number of tickets purchased at the counter on the very ultimate days = 2751

We recognise that

Common number of tickets offered = 1094 + 1812 + 2050 + 2751 = 7707

Subsequently, the entire selection of tickets offered on all of the 4 days is 7, 707.

#### The city newspaper is posted commonplace. One reproduction has 12 pages. On a regular basis 11,980 copies are revealed. What number of pages are in all revealed commonplace? Every month?

Answer:

It’s for the reason that

1 replica of newspaper accommodates = 12 pages

So the amount of pages in 11, 980 copies = 12 × 11, 980 = 1, 43, 760

Consequently, 1, 43, 760 pages are printed on a regular basis

We needless to say

Number of pages printed in a month = 1, 43, 760 × 30 = 43, 12, 800

As a result, 1, 43, 760 pages are printed on a daily basis and 43, 12, 800 pages are printed every month.

#### A machine, on a median, manufactures 2825 screws a day. What selection of screws did it produce throughout the month of January 2006?

Answer:

It is a ways given that

Choice of screws produced in keeping with day = 2, 825

So the number of screws produced within the month of January = 2, 825 × 31 = 87, 575

Subsequently, the machine produced 87, 575 screws throughout the month of January 2006.

A well known cricket participant has up to now scored 6978 runs in check out fits. He needs to finish 10, 000 runs. What number of higher runs does he want?

Answer:

It is a ways given that

Runs ranking with the help of a well-known cricket participant = 6978

So the runs required to complete 10, 000 runs = 10, 000 – 6978 = 3022

Subsequently, 3, 022 runs are needed through the cricket player to finish 10, 000 runs.

#### Ravish has ₹ 78, 592 with him. He located an order for purchasing 39 radio gadgets at ₹ 1234 each and every. How so much cash will stick with him after the acquisition?

Answer:

It is miles for the reason that

Amount with Ravish = ₹ 78, 592

Price of 1 hi fi = ₹ 1234

Number of radio units purchased = 39

We needless to say

Amount spent to buy 39 radio units = ₹ (1234 × 39) = ₹ 48126

Quantity final with Ravish = amount with Ravish – quantity spent to shop for 39 radio gadgets

By way of substituting the values

Quantity ultimate with Ravish = ₹ 78, 592 – ₹ 48126 = ₹ 30466

As a result, ₹ 30466 money will stay with Ravish after the acquisition.

#### In an election, the successful candidate registered 5, 77, 570 votes and his nearest rival secured 3, 48, 685 votes. Via the use of what margin did the a luck candidate win the election?

Resolution:

It’s for the reason that

Amount of votes registered through the use of a luck candidate = 5, 77, 570

Number of votes secured thru nearest rival = 3, 48, 685

We recognise that

Margin of victory the a hit candidate download to win the election = selection of votes registered with the help of successful candidate – selection of votes secured by means of nearest rival

Via substituting the values

Margin of victory the a luck candidate reach to win the election = 5, 77, 570 – 3, 48, 685 = 2, 28, 885

As a result, the margin of victory for the a luck candidate is 2, 28, 885.

#### To sew a shirt 2m 15cm subject material is wanted. Out of 40m subject material, what number of shirts is also stitched and what kind of material will keep?

Resolution:

It is a ways given that

Duration of material = 40m

Period of subject material required to stitch a blouse = 2m 15cm = 2 hundred + 15 = 215cm

Number of shirts that can be stitched the use of 40m material = 4000/ 215 = 18.60

We notice that the selection of shirts must be a complete selection, 18 shirts may also be stitched.

Duration of subject material required to stitch 18 shirts = 215 × 18 = 3870cm

So the rest material = 4000 – 3870 = 130cm = 1.3m = 1m 30cm

As a result, 18 shirts is also stitched and 1m 30cm material will keep.

#### A vessel has 4 litre and 650ml of curd. In what selection of glasses, every of 25ml talent, can or now not it is allocated?

Answer:

It’s for the reason that

Overall quantity of curd = 4 litre 650ml

We needless to say 1 litre = 1000ml

Overall quantity of curd = 4650ml

Skill of every glass = 25ml

So we get

Choice of glasses of curd which may also be disbursed = normal quantity of curd/ attainable of every glass

By the use of substituting the values

Choice of glasses of curd which may also be disbursed = 4650/ 25 = 186

As a result, 186 glasses every of 25ml talent of curd is also dispensed.

#### Medicinal drug is packed in packing containers, every such container weighing 4kg 500g. What number of such boxes is also loaded in a van which cannot deliver past 800kg?

Answer:

It’s for the reason that

Capacity of van wearing treatment boxes = 800kg

We needless to say 1kg = 1000g

Skill of van wearing drugs boxes = 8, 00, 000g

Weight of each and every box = 4kg 500g = 4500g

We all know that

Total selection of packing containers that can be loaded in a van = talent of van wearing drugs boxes/ Weight of each and every field

Via the use of substituting the values

Common vary of packing containers that may be loaded in a van = 8, 00, 000/ 4500 = 177.77

Vary of bins should be a complete amount

We get

Weight of 177 bins = 177 × 4500 = 7, 96, 500g which is below the permissible restriction

Weight of 178 boxes = 178 × 4500 = 8, 01, 000g that is past the permissible limit

Subsequently, 177 boxes is also loaded in a van which cannot put across previous 800kg.

The space between the college and the home of a pupil is 1km 875m. On a regular basis she walks every strategies between her faculty and home. Find all of the distance secure by means of her in a week.

Answer:

It is miles given that

Distance between faculty and place of abode = 1km 875m = 1875m

We notice that

Distance blanketed by means of a pupil in keeping with day = 2 × 1875 = 3750m

So we get

Overall distance secure by means of the scholar in per week = 7 × 3750 = 26250m = 26km 250m

Subsequently, the entire distance secure by the use of her in per week is 26km 250m.

Exercising 1.6 internet web page: 1.26

#### Round off each and every of the following numbers to nearest tens:

(i) 84

(ii) 98

(iii) 984

(iv) 808

(v) 998

(vi) 12, 096

(vii) 10, 908

(viii) 28, 925

Answer:

(i) 84 is rounded off to the nearest tens as 80.

(ii) 98 is rounded off to the nearest tens as 100.

(iii) 984 is rounded off to the nearest tens as 980.

(iv) 808 is rounded off to the nearest tens as 810.

(v) 998 is rounded off to the nearest tens as 1000.

(vi) 12, 096 is rounded off to the closest tens as 12, 100.

(vii) 10, 908 is rounded off to the closest tens as 10, 910.

(viii) 28, 925 is rounded off to the closest tens as 28, 930.

#### Round off each and every of the following numbers to nearest plenty:

(i) 3, 985

(ii) 7, 289

(iii) 8, 074

(iv) 14, 627

(v) 28, 826

(vi) 4, 20, 387

(vii) 43, 68, 973

(viii) 7, 42, 898

Resolution:

(i) 3, 985 is rounded off to the nearest so much as 4, 000.

(ii) 7, 289 is rounded off to the nearest loads as 7, 300.

(iii) 8, 074 is rounded off to the closest plenty as 8, 100.

(iv) 14, 627 is rounded off to the closest plenty as 14, 600.

(v) 28, 826 is rounded off to the nearest loads as 28, 800.

(vi) 4, 20, 387 is rounded off to the closest loads as 4, 20, 400.

(vii) 43, 68, 973 is rounded off to the closest loads as 43, sixty 9, 000.

(viii) 7, 42, 898 is rounded off to the closest so much as 7, 42, 900.

#### Round off every of the following numbers to nearest loads:

(i) 2, 401

(ii) 9, 600

(iii) 4, 278

(iv) 7, 832

(v) 9, 567

(vi) 26, 019

(vii) 20, 963

(viii) 4, 36, 952

Resolution:

(i) 2, 401 is rounded off to the nearest so much as 2, 000.

(ii) 9, 600 is rounded off to the nearest tons as 10, 000.

(iii) 4, 278 is rounded off to the closest so much as 4, 000.

(iv) 7, 832 is rounded off to the closest 1000’s as 8, 000.

(v) 9, 567 is rounded off to the closest 1000’s as 10, 000.

(vi) 26, 019 is rounded off to the nearest 1000’s as 26, 000.

(vii) 20, 963 is rounded off to the closest so much as 21, 000.

(viii) 4, 36, 952 is rounded off to the closest tons as 4, 37, 000.

#### Spherical off every of the following to the closest tens, loads and tons:

(i) 964

(ii) 1, 049

(iii) 45, 634

(iv) seventy 9, part

Answer:

(i) 964 is rounded off to the nearest tens as 960.

964 is rounded off to the closest so much as 1, 000.

964 is rounded off to the nearest tons as 1, 000.

(ii) 1, 049 is rounded off to the closest tens as 1, 050.

1, 049 is rounded off to the closest plenty as 1, 000.

1, 049 is rounded off to the closest so much as 1, 000.

(iii) 45, 634 is rounded off to the closest tens as 45, 630.

45, 634 is rounded off to the closest loads as 45, 600.

45, 634 is rounded off to the closest 1000’s as 46, 000.

(iv) seventy 9, 1/2 is rounded off to the nearest tens as 79, 090.

Seventy 9, 1/2 is rounded off to the nearest loads as seventy 9, 100.

79, 1/2 is rounded off to the nearest tons as seventy 9, 000.

#### Round off the next measures to the closest so much:

(i) Rs 666

(ii) Rs 850

(iii) Rs 3, 428

(iv) Rs 9, 080

(v) 1, 265 km

(vi) 417m

(vii) 550cm

(viii) 2, 486m

(ix) 360gm

(x) 940kg

(xi) 273l

(xii) 820mg

Resolution:

(i) Rs 666 is rounded off to the closest so much as Rs 700.

(ii) Rs 850 is rounded off to the closest so much as Rs 900.

(iii) Rs 3, 428 is rounded off to the nearest plenty as Rs 3, 400.

(iv) Rs 9, 080 is rounded off to the closest plenty as Rs 9, 100.

(v) 1, 265 km is rounded off to the nearest plenty as 1, 300km.

(vi) 417m is rounded off to the nearest plenty as 400m.

(vii) 550cm is rounded off to the closest loads as 600cm.

(viii) 2, 486m is rounded off to the closest so much as 2, 500m.

(ix) 360gm is rounded off to the nearest loads as 400gm.

(x) 940kg is rounded off to the nearest loads as 900kg.

(xi) 273l is rounded off to the closest so much as 300l.

(xii) 820mg is rounded off to the closest plenty as 800mg.

Record all numbers which may also be rounded off to nearest ten as 370.

Resolution:

The list of numbers which can be rounded off to nearest ten as 370 are

365, 366, 367, 368, 369, 370, 371, 372, 373, 374.

Uncover the smallest and perfect numbers which may also be rounded off to the closest so much as 900.

Answer:

The smallest vary that is rounded off to the nearest plenty as 900 is 850.

The best selection which is rounded off to the closest plenty as 900 is 949.

In finding the smallest and best numbers which can be rounded off to the closest tons as 9000.

Answer:

The smallest quantity which is rounded off to the closest 1000’s as 9000 is 8, 500.

The most efficient wide range that is rounded off to the nearest so much as 9000 is 9, 499.

Exercising 1.7 web page: 1.29

#### Estimate the following thru rounding off every facet to nearest so much:

(i) 730 + 998

(ii) 796 – 314

(iii) 875 – 384

Answer:

(i) it may be rounded off to the nearest loads as 700 + one thousand = 1, 700.

(ii) it may well be rounded off to the nearest loads as 800 – 300 = 500.

(iii) it may well be rounded off to the nearest loads as 900 – 400 = 500.

#### Estimate the next by way of rounding off every factor to nearest 1000’s:

(i) 12, 094 + 2, 888

(ii) 28, 292 – 21, 496

Answer:

(i) it may well be rounded off to the nearest so much as 13, 000 + 3, 000 = 16, 000.

(ii) it may well be rounded off to the closest so much as 28, 000 – 21, 000 = 7, 000.

#### Estimate the following thru rounding off each and every selection to its perfect location:

(i) 439 + 334 + 4, 317

(ii) 8, 325 – 491

(iii) 1, 08, 734 – 47, 599

(iv) 898 × 785

(v) 9 × 795

(vi) 87 × 317

Resolution:

(i) it may well be rounded off to its largest house as 400 + 300 + 4, 000 = 4, 700.

(ii) it may be rounded off to its perfect location as 8, 000 – 500 = 7, 500.

(iii) it may well be rounded off to its largest house as 1, 00, 000 – 50, 000 = 50, 000.

(iv) it may well be rounded off to its perfect neighborhood as 900 × 800 = 7, 20, 000.

(v) it may be rounded off to its largest location as 10 × 800 = 8, 000.

(vi) it may be rounded off to its largest neighborhood as 90 × 300 = 27, 000.

**Uncover the anticipated quotient for each and every of the following by the use of rounding off each and every amount to its largest house:**

(i) 878 ÷ 28

(ii) 745 ÷ 24

(iii) 4489 ÷ 394

Resolution:

(i) it may be rounded off to its perfect area as 900 ÷ 30 = 30.

(ii) it can be rounded off to its best neighborhood as 700 ÷ 20 = 35.

(iii) it may be rounded off to its best location as 4000 ÷ 400 = 10.

Exercise 1.8 web page: 1.30

**Write the expression for every of the following statements the use of brackets:**

(i) 4 advanced by way of the sum of 13 and 7.

(ii) 8 larger through the use of the honour of four from 9.

(iii) Divide the honour of twenty 8 and 7 thru 3.

(iv) The sum of three and 7 is speeded up by the use of the honour of twelve and eight.

Resolution:

(i) The expression for 4 increased by the use of the sum of 13 and seven is 4 × (13 + 7).

(ii) 8 larger during the distinction of 4 from 9 is 8 × (9 – 4).

(iii) Divide the honour of twenty 8 and 7 through the use of 3 is (28 – 7) ÷ 3.

(iv) The sum of three and seven is advanced during the distinction of twelve and 8

Simplify every of the next:

(i) 124 – (12 – 2) × 9

(ii) (13 + 7) × (9 – 4) – 18

(iii) 210 – (14 – 4) × (18 + 2) – 10

Answer:

(i) 124 – (12 – 2) × 9 on additional simplification we reach

124 – (12 – 2) × 9

= 124 – 10 × 9

= 124 – 90

= 34

(ii) (13 + 7) × (9 – 4) – 18 on as well as simplification we succeed in

(13 + 7) × (9 – 4) – 18

= 20 × 5 – 18

= 100 – 18

= 92

(iii) 210 – (14 – 4) × (18 + 2) – 10 on in a similar way simplification we download

210 – (14 – 4) × (18 + 2) – 10

= 210 – 10 × 20 – 10

= 210 – two hundred – 10

= 0

Exercising 1.9 internet web page: 1.31

Simplify every of the following:

7 × 109

6 × 112

9 × one 0 5

17 × 109

16 × 108

12 × 100 and 5

102 × 103

One hundred and one × 100 and 5

109 × 107

Answer:

On simplification of 7 × 109 we get

7 × 109 = 763.

On simplification of 6 × 112 get

6 × 112 = 672.

On simplification of 9 × 100 and 5 we get

9 × one 0 5 = 945.

On simplification of 17 × 109 we get

17 × 109 = 1853.

On simplification of 16 × 108 we get

16 × 108 = 1728.

On simplification of 12 × one 0 5 we get

12 × one 0 5 = 1260.

On simplification of 102 × 103 we get

102 × 103 = 10506.

On simplification of 100 and one × 105 we get

100 and one × 100 and 5 = 10605.

On simplification of 109 × 107 we get

109 × 107 = 11663.

Exercising 1.10 web page: 1.35

**Write the roman-numerals for each and every of the next:**

(i) 33

(ii) 48

(iii) 76

(iv) 90 5

Resolution:

(i) The roman-numeral of 33 is XXXIII.

(ii) The roman-numeral of 48 is XLVIII.

(iii) The roman-numeral of 76 is LXXVI.

(iv) The roman-numeral of 95 is XCV.

**Write the next in Roman numerals:**

(i) 154

(ii) 173

(iii) 248

(iv) 319

Answer:

(i) The roman-numeral of 154 is CLIV.

(ii) The roman-numeral of 173 is CLXXIII.

(iii) The roman-numeral of 248 is CCXLVIII.

(iv) The roman-numeral of 319 is CCCXIX.

**Write the next in Roman numerals:**

(i) 1008

(ii) 2718

(iii) 3906

(iv) 3794

Resolution:

(i) The roman-numeral of 1008 is KVIII.

(ii) The roman-numeral of 2718 is KKDCCXVIII.

(iii) The roman-numeral of 3906 is KKKCKVI.

(iv) The roman-numeral of 3794 is KKKDCCXCIV.

**Write the following in Roman numerals:**

(i) 4201

(ii) 10009

(iii) 44000

(iv) 25819

Resolution:

**(i) The roman-numeral of 4201 is**

CCI.

(ii) The roman-numeral of 10009 is XIX.

(iii) The roman-numeral of 44000 is

.

(iv) The roman-numeral of 25819 is

DCCCXIX.

**Write the next in Hindu-Arabic numerals:**

(i) XXVI

(ii) XXIX

(iii) LXXII

(iv) XCI

Resolution:

(i) The Hindu-Arabic numerals of XXVI is 26.

(ii) The Hindu-Arabic numerals of XXIX is 29.

(iii) The Hindu-Arabic numerals of LXXII is 72.

(iv) The Hindu-Arabic numerals of XCI is 91.

**Write the corresponding Hindu-Arabic numerals for each and every of the following:**

(i) CIX

(ii) CLXXII

(iii) CCLIV

(iv) CCCXXIX

Answer:

(i) The Hindu-Arabic numerals of CIX is 109.

(ii) The Hindu-Arabic numerals of CLXXII is 172.

(iii) The Hindu-Arabic numerals of CCLIV is 254.

(iv) The Hindu-Arabic numerals of CCCXXIX is 329.

**Write the corresponding Hindu-Arabic numerals for each and every of the next:**

(i) KXIX

(ii) KDLXV

(iii) KKCXXIII

(iv) KKKDCXL

Answer:

(i) The Hindu-Arabic numerals of KXIX is 1019.

(ii) The Hindu-Arabic numerals of KDLXV is 1565.

(iii) The Hindu-Arabic numerals of KKCXXIII is 2123.

(iv) The Hindu-Arabic numerals of KKKDCXL is 3640.

**Write the next in Hindu-Arabic numerals:**

Resolution:

(i) The Hindu-Arabic numerals of

Is 4444.

(ii) The Hindu-Arabic numerals of

Is 6949.

(iii) The Hindu-Arabic numerals of

Is 9391.

(iv) The Hindu-Arabic numerals of

Is 70009.

**Which of the following are meaningless?**

(i) CC

(ii) KKKCCXI

(iii) XD

(iv) VC

Answer:

Within the given query we all know that (i) and (iii) are meaningless.

Goal sort Questions internet web page: 1.36

Mark a suitable alternative in each and every of the following:

**The consideration between where price and face price of 8 in 658742 is**

(a) 0 (b) 42 (c) 735 (d) 693

Resolution:

The given choices are improper.

Neighborhood price of 8 in 6,58,742 = 8,000

Face price of 8 = 8

Distinction amongst them = 8,000 − 8 = 7,992

**The consideration between where values of 6 and three in 256839 is**

(a) 3 (b) 9 (c) 6800 (d) 5930

Resolution:

The given choices are improper.

Area price of 6 in 2,56,839 = 6,000

The area value of 3 in 2,56,839 = 30

Difference between them = 6,000 − 30 = 5,970

**The adaptation of the smallest 3 digit selection and a very powerful digit wide range is**

(a) 100 (b) 1 (c) 10 (d) 99

Resolution:

The selection (b) is the best resolution.

We acknowledge that

The smallest three-digit wide range is 100 and the most important two-digit vary is 99.

So the honour between them= 100 − 90 9 = 1

**A very powerful 3 digit wide range formed by means of the digits 8, 5, 9** is

(a) 859 (b) 985 (c) 958 (d) 589

Resolution:

The choice (b) is the very best resolution.

We recognise that a very powerful selection is formed by way of writing the digits in descending order.

**The smallest 3 digit amount having 3 glorious digits is**

(a) 123 (b) 101 (c) 102 (d) 201

Answer:

The selection (c) is an acceptable resolution.

We all know that the smallest 3 digit numbers are 0, 1 and 2

Via the use of arranging them in ascending order we get 012 which is a two digit wide range.

Due to this fact, 102 is the smallest 3 digit quantity.

**The biggest 3 digit vary having glorious digits is**

(a) 987 (b) 789 (c) 999 (d) 900

Resolution:

The selection (a) is the most productive resolution.

The biggest 3 digit numbers are 7, 8 and 9. A very powerful selection is received by means of arranging them in descending order.

**The consideration between a very powerful 3 digit wide range and a very powerful 3 digit selection with glorious digits is**

(a) 10 (b) 0 (c) 12 (d) 13

Answer:

The selection (c) is the proper resolution.

We acknowledge that biggest 3 digit vary = 999

Largest three-digit quantity with glorious digits = 987

Difference between them = 999 − 987 = 12

**The made out of the site values of threes in 53432 is**

(a) 9000 (b) 90000 (c) 10000 (d) 99000

Answer:

The choice (b) is the most productive resolution.

We needless to say 3 throughout the 2d position from correct is at tens area.

So the neighborhood price of three at tens position = 30

We all know that 3 throughout the fourth area from proper is at loads neighborhood.

So the neighborhood value of 3 at loads location = 3,000

Made of the area values = 3,000 × 30 = 90,000

#### The smallest counting selection is

(a) 0 (b) 1 (c) 10 (d) None of the ones

Resolution:

The selection (b) is the most productive resolution.

We all know that the smallest digit is 0 and the smallest counting vary is 1.

#### The total selection of 4 digit numbers is

(a) 8999 (b) 9000 (c) 8000 (d) 9999

Answer:

The choice (b) is the very best resolution.

We needless to say the smallest 4 digit vary = 1,000

Greatest 4 digit selection = 9,999.

So the whole selection of four-digit numbers = [9,999 − 1,000 ] + 1 = 9,000

**The wide range of three digit numbers shaped thru using digits 3, 5, 9, taking each and every digit exactly as soon as, is**

(a) 3 (b) 4 (c) 5 (d) 6

Resolution:

The selection (d) is the very best resolution.

359, 395, 539, 593, 935 and 953 are the numbers.

**Overall huge number of numbers which while rounded off to nearest ten supply us 200 is**

(a) 9 (b) 10 (c) 8 (d) 7

Resolution:

The choice (b) is the proper resolution.

195, 196, 197, 198, 199, two hundred, 201, 202, 203, 204 are the numbers that after rounded off to nearest ten ship us.

**The smallest quantity which whilst rounded off to the closest hundred as 600, is**

(a) 550 (b) 595 (c) 604 (d) 599

Answer:

The choice (a) is the proper resolution.

The wide range from 550 to 649 are rounded off nearest hundred as 600. Due to this fact, the smallest vary is 550.

#### The best wide range which whilst rounded off to the nearest thousand 7000, is

(a) 6500 (b) 6549 (c) 7499 (d) 6499

Resolution:

The choice (c) is the proper resolution.

Numbers from 6500 to 7499 are rounded off to nearest thousand as 7000. Consequently, the best selection is 7499.

**The consideration one of the best and smallest numbers which while rounded off moderately a host to the closest tens as 540, is**

(a) 10 (b) 9 (c) 8 (d) 10

Resolution:

The choice (b) is the best resolution.

We all know that the best wide range that when rounded off to the nearest tens turns into 540 = 544

Least amount that when rounded off to the nearest tens turns into 540 = 535

So, the honour between them = 544 − 535 = 9

**The adaptation between the best and smallest numbers which while rounded off a variety of to the nearest hundred as 6700, is**

(a) 100 (b) 99 (c) 98 (d) 101

Answer:

The selection (b) is the most productive resolution.

We recognise that the best wide range that after rounded off to the closest hundred turns into 6,7000 = 6749

Least vary that after rounded off to the closest hundred becomes 6,700 = 6650

So, the adaptation between them = 6,749 − 6,650 = 99

**The adaptation top-of-the-line and the smallest numbers which whilst rounded off to the nearest thousand as 9000, is**

(a) 1000 (b) 990 (c) 999 (d) 900

Answer:

The choice (c) is the proper resolution.

We all know that the most productive selection that when rounded off to the nearest thousand will grow to be 9,000 = 9499

Smallest wide range that when rounded off to the nearest thousand turns into 9,000 = 8500

So, the adaptation between them = 9,499 − 8,500 = 999

**Which of the next numbers is similar to at least one billion?**

(a) 10 lakh (b) 1 crore (c) 10 crore (d) 100 crore

Resolution:

#### The selection (d) is an acceptable resolution.

1 billion = 100 crore

Inside the international house price software, we write a million for

#### (a) 1 lakh (b) 10 lakh (c) 100 lakh (d) 1 crore

Resolution:

The choice (b) is the proper resolution.

a million = 10 lakh

Which of the next is not all the time significant?

**(a) XIV (b) XXXV (c) XXV (d) VX**

**Resolution:**

The selection (d) is the most productive resolution.

In Roman numerals V is 5 and X is 10

5 can’t be written previous than 10

Which of the next is not significant?

**(a) XXII (b) XII (c) XVV (d) XIV**

**Answer:**

The choice (c) is the proper resolution.

In Roman numerals V is 5 and X is 10

5 can’t be written two circumstances.

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