Rs Aggarwal Solutions for Class 6 Math Chapter 1 Number System are provided here with simple step-by-step explanations. These solutions for Number System are extremely popular among Class 6 students for Math Number System Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal Book of Class 6 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal Solutions. All Rs Aggarwal Solutions for class Class 6 Math are prepared by experts and are 100% accurate.

#### Page No 5:

#### Question 1:

Write the numeral for each of the following numbers:

(i) Nine thousand eighteen

(ii) Fifty-four thousand seventy-three

(iii) Three lakh two thousand five hundred six

(iv) Twenty lakh ten thousand eight

(v) Six crore five lakh fifty-seven

(vi) Two crore two lakh two thousand two hundred two

(vii) Twelve crore twelve lakh twelve thousand twelve

(viii) Fifteen crore fifty lakh twenty thousand sixty-eight

#### Answer:

(i) Nine thousand eighteen = 9018

(ii) Fifty-four thousand seventy-three = 54073

(iii) Three lakh two thousand five hundred six = 302506

(iv) Twenty lakh ten thousand eight = 2010008

(v) Six crore five lakh fifty-seven = 60500057

(vi) Two crore two lakh two thousand two hundred two = 20202202

(vii) Twelve crore twelve lakh twelve thousand twelve = 121212012

(viii) Fifteen crore fifty lakh twenty thousand sixty-eight = 155020068

#### Page No 5:

#### Question 2:

Write each of the following numbers in words:

(i) 63,005

(ii) 7,07,075

(iii) 34,20,019

(iv) 3,05,09,012

(v) 5,10,03,604

(vi) 6,18,05,008

(vii) 19,09,09,900

(viii) 6,15,30,807

(ix) 6,60,60,060

#### Answer:

(i) 63,005 = Sixty-three thousand five

(ii) 7,07,075 = Seven lakh seven thousand seventy-five

(iii) 34,20,019 = Thirty-four lakh twenty thousand nineteen

(iv) 3,05,09,012 = Three crore five lakh nine thousand twelve

(v) 5,10,03,604 = Five crore ten lakh three thousand six hundred four

(vi) 6,18,05,008 = Six crore eighteen lakh five thousand eight

(vii) 19,09,09,900 = Nineteen crore nine lakh nine thousand nine hundred

(viii) 6,15,30,807 = Six crore fifteen lakh thirty thousand eight hundred seven

(ix) 6,60,60,060 = Six crore sixty lakh sixty thousand sixty

#### Page No 5:

#### Question 3:

Write each of the following numbers in expanded form:

(i) 15,768

(ii) 3,08,927

(iii) 24,05,609

(iv) 5,36,18,493

(v) 6,06,06,006

(iv) 9,10,10,510

#### Answer:

(i) 15,768 = (1 x 10000) + (5 x 1000) + (7 x 100) + (6 x 10) + (8 x 1)

(ii) 3,08,927 = (3 x 100000) + (8 x 1000) + (9 x 100) + (2 x 10) + (7 x 1)

(iii) 24,05,609 = (2 x 1000000) + (4 x 100000) + (5 x 1000) + (6 x 100) + (9 x 1)

(iv) 5,36,18,493 = (5 x 10000000) + (3 x 1000000) + (6 x 100000) + (1 x 10000) + (8 x 1000) + (4 x 100) + (9 x 10) + (3 x 1)

(v) 6,06,06,006 = (6 x 10000000) + (6 x 100000) + (6 x 1000) + (6 x 1)

(iv) 9,10,10,510 = (9 x 10000000) + (1 x 1000000) + (1 x 10000) + (5 x 100) + (1 x 10)

#### Page No 6:

#### Question 4:

Write the corresponding numeral for each of the following:

(i) 6 × 10000 + 2 × 1000 + 5 × 100 + 8 × 10 + 1

(ii) 5 × 100000 + 8 × 10000 + 1 × 1000 + 6 × 100 + 2 × 10 + 3 × 1

(iii) 2 × 10000000 + 5 × 100000 + 7 × 1000 + 9 × 100 + 5 × 1

(iv) 3 × 1000000 + 4 × 100000 + 6 × 1000 + 5 × 100 + 7 × 1

#### Answer:

(i) 6 × 10000 + 2 × 1000 + 5 × 100 + 8 × 10 + 4 x 1 = 62,584

(ii) 5 × 100000 + 8 × 10000 + 1 × 1000 + 6 × 100 + 2 × 10 + 3 × 1 = 5,81,623

(iii) 2 × 10000000 + 5 × 100000 + 7 × 1000 + 9 × 100 + 5 × 1 = 2,05,07,905

(iv) 3 × 1000000 + 4 × 100000 + 6 × 1000 + 5 × 100 + 7 × 1 = 34,06,507

#### Page No 6:

#### Question 5:

Find the difference between the place values of the two nines in 79520986.

#### Answer:

The place value of 9 at ten lakhs place = 90 lakhs = 9000000

The place value of 9 at hundreds place = 9 hundreds = 900

$\therefore $ Required difference = (9000000 ‒ 900) = 8999100

#### Page No 6:

#### Question 6:

Find the difference between the place value and the face value of 7 in 27650934.

#### Answer:

The place value of 7 in 27650934 = 70 lakhs = 70,00,000

The face value of 7 in 27650934 = 7

$\therefore $ Required difference = (7000000 ‒ 7) = 69,99,993

#### Page No 6:

#### Question 7:

How many 6-digit numbers are there in all?

#### Answer:

The largest 6-digit number = 999999

The smallest 6-digit number = 100000

$\therefore $ Total number of 6-digit numbers = (999999 ‒ 100000) + 1

= 899999 + 1

= 900000

= 9 lakhs

#### Page No 6:

#### Question 8:

How many 7-digit numbers are there in all?

#### Answer:

The largest 7-digit number = 9999999

The smallest 7-digit number = 1000000

∴ Total number of 7-digit numbers = (9999999 - 1000000) + 1

= 8999999 + 1

= 9000000

= Ninety lakhs

#### Page No 6:

#### Question 9:

How many thousands make a lakh?

#### Answer:

One lakh (1,00,000) is equal to one hundred thousand (100 $\times $ 1000).

Thus, one hundred thousands make a lakh.

#### Page No 6:

#### Question 10:

How many thousands make a crore?

#### Answer:

One crore (1,00,00,000) is equal to one hundred lakh (10,000 $\times $ 1,000).

Thus, 10,000 thousands make a crore.

#### Page No 6:

#### Question 11:

Find the difference between the number 738 and that obtained on reversing its digits.

#### Answer:

The given number is 738.

On reversing the digits of this number, we get 837.

∴ Required difference = 837 ‒ 738 = 99

#### Page No 6:

#### Question 12:

What comes just after 9547999?

#### Answer:

The number just after 9547999 is 9547999 + 1 = 9548000.

#### Page No 6:

#### Question 13:

What comes just before 9900000?

#### Answer:

The number just before 9900000 is 9900000 ‒ 1 = 9899999.

#### Page No 6:

#### Question 14:

What comes just before 10000000?

#### Answer:

The number just before 10000000 is 10000000 ‒ 1 = 9999999.

#### Page No 6:

#### Question 15:

Write all 3-digit numbers using 2, 3, 4, taking each digit only once.

#### Answer:

The 3-digit numbers formed by 2, 3 and 4 by taking each digit only once are 234, 324, 243, 342, 423 and 432.

#### Page No 6:

#### Question 16:

Write the smallest number of different digits formed by using the digits 3, 1, 0, 5 and 7.

#### Answer:

The smallest number formed by using each of the given digits (i.e, 3,1,0,5 and 7) only once is 10357.

#### Page No 6:

#### Question 17:

Write the largest number of different digits formed by using the digits 2, 4, 0, 3, 6 and 9.

#### Answer:

The largest number formed by using each of the given digits only once is 964320.

#### Page No 6:

#### Question 18:

Rewrite each of the following numerals with proper commas, using the international place-value chart. Also, write the number name of each in the international system.

(i) 735821

(ii) 6057894

(iii) 56943821

(iv) 37502093

(v) 89350064

(vi) 90703006

#### Answer:

**Representation of the numbers on the international place-value chart:**

Periods |
Millions |
Thousands |
Ones |
||||||

Place | Hundred millions |
Ten millions | Millions | Hundred thousands | Ten thousands |
Thousands | Hundreds | Tens | Ones |

HM | TM | M | H Th | T Th | Th | H | T | O | |

(i) | 7 | 3 | 5 | 8 | 2 | 1 | |||

(ii) | 6 | 0 | 5 | 7 | 8 | 9 | 4 | ||

(iii) | 5 | 6 | 9 | 4 | 3 | 8 | 2 | 1 | |

(iv) | 3 | 7 | 5 | 0 | 2 | 0 | 9 | 3 | |

(v) | 8 | 9 | 3 | 5 | 0 | 0 | 6 | 4 | |

(vi) | 9 | 0 | 7 | 0 | 3 | 0 | 0 | 6 | |

Crore | Ten lakhs | Lakhs | Ten Thousand | Thousand | Hundred | Tens | Ones |

**The number names of the given numbers in the international system:**

(i) 735,821 = Seven hundred thirty-five thousand eight hundred twenty-one

(ii) 6,057,894 = Six million fifty-seven thousand eight hundred ninety-four

(iii) 56,943,821 = Fifty-six million nine hundred forty-three thousand eight hundred twenty-one

(iv) 37,502,093 = Thirty-seven million five hundred two thousand ninety-three

(v) 89,350,064 = Eighty-nine millions three hundred fifty thousand sixty-four

(vi) 90,703,006 = Ninety million seven hundred three thousand and six

#### Page No 6:

#### Question 19:

Write each of the following in figures in the international place-value chart:

(i) Thirty million one hundred five thousand sixty-three

(ii) Fifty-two million two hundred five thousand six

(iii) Five million five thousand five

#### Answer:

Periods |
Millions |
Thousands |
Ones |
||||||

Place | Hundred millions | Ten millions | Millions | Hundred thousands | Ten thousands | Thousands | Hundreds | Tens | Ones |

HM | TM | M | H Th | T Th | Th | H | T | O | |

(i) | 3 | 0 | 1 | 0 | 5 | 0 | 6 | 3 | |

(ii) | 5 | 2 | 2 | 0 | 5 | 0 | 0 | 6 | |

(iii) | 5 | 0 | 0 | 5 | 0 | 0 | 5 |

#### Page No 8:

#### Question 1:

*Fill in each of the following boxes with the correct symbol > or <:*

$1003467\overline{)}987965$

#### Answer:

1003467 $>$ 987965

We know that a 7-digit number is always greater than a 6-digit number. Since 1003467 is a 7-digit number and 987965 is a 6-digit number, 1003467 is greater than 987965.

#### Page No 8:

#### Question 2:

*Fill in each of the following boxes with the correct symbol > or <:*

$3572014\overline{)}10235401$

#### Answer:

3572014 $<$ 10235401

We know that a 7-digit number is always less than an 8-digit number. Since 3572014 is a 7-digit number and 10235401 is an 8-digit number, 3572014 is less than 10235401.

#### Page No 8:

#### Question 3:

*Fill in each of the following boxes with the correct symbol > or <:*

$3254790\overline{)}3260152$

#### Answer:

Both the numbers have the digit 3 at the ten lakhs places.

Also, both the numbers have the digit 2 at the lakhs places.

However, the digits at the ten thousands place in 3254790 and 3260152 are 5 and 6, respectively.

Clearly, 5 < 6

∴ 3254790 < 3260152

#### Page No 8:

#### Question 4:

*Fill in each of the following boxes with the correct symbol > or <:*

$10357690\overline{)}11243567$

#### Answer:

Both have the digit 1 at the crores places.

However, the digits at the ten lakhs places in 10357690 and 11243567 are 0 and 1, respectively.

Clearly, 0 < 1

∴ 10357690 < 11243567

#### Page No 8:

#### Question 5:

*Fill in each of the following boxes with the correct symbol > or <:*

$27596381\overline{)}7965412$

#### Answer:

27596381 > 7965412

We know that an 8-digit number is always greater than a 7-digit number. Since 7965412 is a 7-digit number and 27596381 is an 8-digit number, 27596381 is greater than 7965412.

#### Page No 8:

#### Question 6:

*Fill in each of the following boxes with the correct symbol > or <:*

$47893501\overline{)}47894021$

#### Answer:

Both the numbers have the same digits, namely 4, 7, 8 and 9, at the crores, ten lakhs, lakhs and ten thousands places, respectively.

However, the digits at the thousands place in 47893501 and 47894021 are 3 and 4, respectively.

Clearly, 3 < 4

∴ 47893501 < 47894021

#### Page No 8:

#### Question 7:

*Arrange the following numbers in descending order:*

63521047, 7354206, 63514759, 7355014, 102345680

#### Answer:

102345680 is a 9-digit number.

63521047 and 63514759 are both 8-digit numbers.

Both the numbers have the same digits, namely 6, 3 and 5, at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 63521047 and 63514759 are 2 and 1, respectively.

Clearly, 2 > 1

∴ 63521047 > 63514759

7355014 and 7354206 are both 7-digit numbers.

Both the numbers have the same digits, namely 7, 3 and 5 at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 7355014 and 7354206 are 5 and 4, respectively.

Clearly, 5> 4

∴ 7355014 > 7354206

The given numbers in descending order are:

102345680 > 63521047 > 63514759 > 7355014 > 7354206

#### Page No 8:

#### Question 8:

*Arrange the following numbers in descending order:*

5032786, 23794206, 5032790, 23756819, 987876

#### Answer:

23794206 and 23756819 are both 8-digit numbers.

Both the numbers have the same digits, namely 2, 3 and 7 at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 23794206 and 23756819 are 9 and 5, respectively.

Clearly, 9 > 5

∴ 23794206 > 23756819

5032790 and 5032786 are both 7-digit numbers.

Both the numbers have the same digits, namely 5, 0, 3, 2 and 7, at the ten lakhs, lakhs, ten thousands, thousands and hundreds places, respectively.

However, the digits at the tens place in 5032790 and 5032786 are 9 and 8, respectively.

Clearly, 9 > 8

∴ 5032790 > 5032786

987876 is a 6-digit number.

The given numbers in descending order are:

23794206 > 23756819 > 5032790 > 5032786 > 987876

#### Page No 8:

#### Question 9:

*Arrange the following numbers in descending order:*

190909, 1808088, 16060666, 16007777, 181888, 1808090

#### Answer:

16060666 and 16007777 are both 8-digit numbers.

Both the numbers have the same digits, namely 1, 6 and 0, at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 16060666 and 16007777 are 6 and 0, respectively.

Clearly, 6 > 0

∴ 16060666 > 16007777

1808090 and 1808088 are both 7-digit numbers.

Both the numbers have the same digits , namely 1, 8, 0, 8 and 0, at the ten lakhs, lakhs, ten thousands, thousands and hundreds places, respectively.

However, the digits at the tens place in 1808090 and 1808088 are 9 and 8, respectively.

Clearly, 9 > 8

∴ 1808090 > 1808088

190909 and 181888 are both 6-digit numbers.

Both the numbers have the same digit, 1, at the lakhs place.

However, the digits at the ten thousands place in 190909 and 181888 are 9 and 8, respectively.

Clearly, 9 > 8

∴ 190909 > 181888

Thus, the given numbers in descending order are:

16060666 > 16007777 > 1808090 > 1808088 >190909 > 181888

#### Page No 8:

#### Question 10:

**Arrange the following numbers in descending order:**

199988, 1704382, 200175, 1702497, 201200, 1712040

#### Answer:

1712040, 1704382 and 1702497 are all 7-digit numbers.

The three numbers have the same digits, namely 1 and 7, at the ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 1712040, 1704382 and 1702497 are 1, 0 and 0.

∴ 1712040 is the largest.

Of the other two numbers, the respective digits at the thousands place are 4 and 2.

Clearly, 4 > 2

∴ 1704382 > 1702497

201200, 200175 and 199988 are all 6-digit numbers.

At the lakhs place, we have 2 > 1.

So, 199988 is the smallest of the three numbers.

The other two numbers have the same digits, namely 2 and 0, at the lakhs and ten thousands places, respectively.

However, the digits at the thousands place in 201200 and 200175 are 1 and 0, respectively.

Clearly, 1 > 0

∴ 201200 > 200175

The given numbers in descending order are:

1712040 > 1704382 > 1702497 > 201200 > 200175 > 199988

#### Page No 8:

#### Question 11:

*Arrange the following numbers in ascending order:*

9873426, 24615019, 990357, 9874012, 24620010

#### Answer:

990357 is 6 digit number.

9873426 and 9874012 are both 7-digit numbers.

Both the numbers have the same digits, namely 9, 8 and 7, at the ten lakhs, lakhs and ten thousands places, respectively.

However, the digits at the thousands place in 9873426 and 9874012 are 3 and 4, respectively.

Clearly, 4 < 7

∴ 9873426 < 9874012

24615019 and 24620010 are both 8-digit numbers.

Both the numbers have the same digits, namely 2, 4 and 6, at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 24615019 and 24620010 are 2 and 1, respectively.

Clearly, 1 < 2

∴ 24615019 < 24620010

The given numbers in ascending order are:

990357 < 9873426 < 9874012 < 24615019 < 24620010

#### Page No 8:

#### Question 12:

*Arrange the following numbers in ascending order:*

56943201, 5694437, 56944000, 5695440, 56943300

#### Answer:

5694437 and 5695440 are both 7-digit numbers.

Both have the same digit, i.e., 5 at the ten lakhs place.

Both have the same digit, i.e., 6 at the lakhs place.

Both have the same digit, i.e., 9 at the ten thousands place.

However, the digits at the thousand place in 5694437 and 5695440 are 4 and 5, respectively.

Clearly, 4 < 5

∴ 5694437 < 5695440

56943201, 56943300 and 56944000 are all 8-digit numbers.

They have the same digit, i.e., 5 at the crores place.

They have the same digit, i.e., 6 at the ten lakhs place.

They have the same digit, i.e., 9 at the lakhs place.

They have the same digit, i.e., 4 at the ten thousands place.

However, at the thousands place, one number has 4 while the others have 3 .

∴ 56944000 is the largest.

The other two numbers have 3 and 2 at their hundreds places.

Clearly, 2 <3

∴ 56943201 < 56943300

The given numbers in ascending order are:

5694437 < 5695440 < 56943201 < 56943300 < 56944000

#### Page No 8:

#### Question 13:

*Arrange the following numbers in ascending order:*

700087, 8014257, 8015032, 10012458, 8014306

#### Answer:

700087 is 6-digit number.

8014257, 8014306 and 8015032 are all 7-digit numbers.

They have the same digits, namely 8, 0 and 1, at the ten lakhs, lakhs and ten thousands places, respectively.

But, at the thousands place, one number has 5 while the other two numbers have 4.

Here, 801503 is the largest.

The other two numbers have 2 and 3 at their hundreds places.

Clearly, 2 < 3

∴ 8014306 < 8015032

10012458 is an 8-digit number.

The given numbers in ascending order are:

700087 < 8014257 < 8014306 < 8015032 < 10012458

#### Page No 8:

#### Question 14:

*Arrange the following numbers in ascending order:*

1020304, 893245, 980134, 1021403, 893425, 1020216

#### Answer:

893245, 893425 and 980134 are all 6-digit numbers.

Among the three, 980134 is the largest.

The other two numbers have the same digits, namely 8, 9 and 3, at the lakhs, ten thousands and thousands places, respectively.

However, the digits at the hundreds place in 893245 and 893425 are 2 and 4, respectively.

Clearly, 2 < 4

∴ 893245 < 893425

1020216, 1020304 and 1021403 are all 7-digit numbers.

They have the same digits, namely 1, 0 and 2, at the ten lakhs, lakhs and ten thousands places, respectively.

At the thousands place, 1021403 has 1.

The other two numbers have the digits 2 and 3 at their hundreds places.

Clearly, 2 < 3

∴ 1020216 < 1020304

The given numbers in ascending order are:

893245 < 893425 < 980134 < 1020216 < 1020304 < 1021403

#### Page No 11:

#### Question 1:

The number of persons who visited the holy shrine of Mata Vaishno Devi during last two consecutive years was 13789509 and 12976498 respectively. How many persons visited the shrine during these two years?

#### Answer:

Number of persons who visited the holy shrine in the first year = 13789509

Number of persons who visited the holy shrine in the second year = 12976498

∴ Number of persons who visited the holy shrine during these two years = 13789509 + 12976498 = 26766007

#### Page No 11:

#### Question 2:

Last year, three sugar factories in a town produced 24809565 bags, 18738576 bags and 9564568 bags of sugar respectively. How many bags were produced by all the three factories during last year?

#### Answer:

Bags of sugar produced by the first factory in last year = 24809565

Bags of sugar produced by the second factory in last year = 18738576

Bags of sugar produced by the third sugar factory in last year = 9564568

∴ Total number of bags of sugar were produced by the three factories during last year = 24809565 + 18738576 + 9564568

= 53112709

#### Page No 11:

#### Question 3:

A number exceeds 37684955 by 3615045. What is that number?

#### Answer:

New number = Sum of 37684955 and 3615045

= 37684955 + 3615045

= 41300000

#### Page No 11:

#### Question 4:

There were three candidates in an election. They received 687905 votes, 495086 votes and 93756 votes respectively. The number of invalid votes was 13849. If 25467 persons did not vote, find how many votes were registered.

#### Answer:

Total number of votes received by the three candidates = 687905 + 495086 + 93756 = 1276747

Number of invalid votes = 13849

Number of persons who did not vote = 25467

∴ Total number of registered voters = 1276747 + 13849 + 25467

= 1316063

#### Page No 11:

#### Question 5:

A survey conducted on an Indian state shows that 1623546 people have only primary education; 9768678 people have secondary education; 6837954 people have higher education and 2684536 people are illiterate. If the number of children below the age of school admission is 698781, find the total population of the state.

#### Answer:

People who had only primary education = 1623546

People who had secondary education = 9768678

People who had higher education = 6837954

Illiterate people in the state = 2684536

Children below the age of school admission = 698781

∴ Total population of the state = 1623546 + 9768678 + 6837954 + 2684536 + 698781

= 21613495

#### Page No 11:

#### Question 6:

In a particular year a company produced 8765435 bicycles. Next year, the number of bicycles produced was 1378689 more than those produced in the preceding year.

How many bicycles were produced during the second year?

How many bicycles were produced during these two years?

#### Answer:

Bicycles produced by the company in the first year = 8765435

Bicycles produced by the company in the second year = 8765435 + 1378689

= 10144124

∴ Total number of bicycles produced during these two years = 8765435 + 10144124

= 18909559

#### Page No 11:

#### Question 7:

The sale receipt of a company during a year was Rs 20956480. Next year, it increased by Rs 6709570. What was the total sale receipt of the company during these two years?

#### Answer:

Sale receipts of a company during the first year = Rs 20956480

Sale receipts of the company during the second year = Rs 20956480 + Rs 6709570

= Rs 27666050

∴ Total number of sale receipts of the company during these two years = Rs 20956480 + Rs 27666050

= Rs 48622530

#### Page No 11:

#### Question 8:

The total population of a city is 28756304. If the number of males is 16987059, find the number of females in the city.

#### Answer:

Total population of the city = 28756304

Number of males in the city = 16987059

∴ Number of females in the city = 28756304 ‒ 16987059

= 11769245

#### Page No 12:

#### Question 9:

By how much is 13246510 larger than 4658642?

#### Answer:

Required number = 13246510 ‒ 4658642 = 8587868

∴ 13246510 is larger than 4658642 by 8587868.

#### Page No 12:

#### Question 10:

By how much is 5643879 smaller than one crore?

#### Answer:

Required number = 1 crore ‒ 564387

= 10000000 ‒ 5643879

= 4356121

∴ 5643879 is smaller than one crore by 4356121.

#### Page No 12:

#### Question 11:

What number must be subtracted from 11010101 to get 2635967?

#### Answer:

11010101 ‒ required number = 2635967

Thus, required number = 11010101 ‒ 2635967

= 8374134

∴ The number 8374134 must be subtracted from 11010101 to get 2635967.

#### Page No 12:

#### Question 12:

The sum of two numbers is 10750308. If one of them is 8967519, what is the other number?

#### Answer:

Sum of the two numbers = 10750308

One of the number = 8967519

∴ The other number = 10750308 ‒ 8967519

= 1782789

#### Page No 12:

#### Question 13:

A man had Rs 20000000 with him. He spent Rs 13607085 on buying a school building. How much money is left with him?

#### Answer:

Initial amount with the man = Rs 20000000

Amount spent on buying a school building = Rs 13607085

∴ Amount left with the man = Rs 20000000 ‒ Rs 13607085

= Rs 6392915

#### Page No 12:

#### Question 14:

A society needed Rs 18536000 to buy a property. It collected Rs 7253840 as membership fee, took a loan of Rs 5675450 from a bank and collected Rs 2937680 as donation. How much is the society still short of?

#### Answer:

Money need by the society to buy the property = Rs 18536000

Amount collected as membership fee = Rs 7253840

Amount taken on loan from the bank = Rs 5675450

Amount collected as donation = Rs 2937680

∴ Amount of money short = Rs 18536000 ‒ (Rs 7253840 + Rs 5675450 + Rs 2937680)

= Rs 18536000 ‒ Rs 15866970

= Rs 2669030

#### Page No 12:

#### Question 15:

A man had Rs 10672540 with him. He gave Rs 4836980 to his wife, Rs 3964790 to his son and the rest to his daughter. How much money was received by the daughter?

#### Answer:

Initial amount with the man = Rs 10672540

Amount given to his wife = Rs 4836980

Amount given to his son = Rs 3964790

∴ Amount received by his daughter = Rs 10672540 ‒ (Rs 4836980 + Rs 3964790)

= Rs 10672540 ‒ Rs 8801770

= Rs 1870770

#### Page No 12:

#### Question 16:

The cost of a chair is Rs 1485. How much will 469 such chairs cost?

#### Answer:

Cost of one chair = Rs 1485

Cost of 469 chairs = Rs 1485 $\times $ 469

= Rs 696465

∴ Cost of 469 chairs is Rs 696465.

#### Page No 12:

#### Question 17:

How much money was collected from 1786 students of a school for a charity show if each student contributed Rs 625?

#### Answer:

Contribution from one student for the charity program = Rs 625

Contribution from 1786 students = Rs 625 x 1786 = Rs 1116250

∴ Rs 1116250 was collected from 1786 students for the charity program.

#### Page No 12:

#### Question 18:

A factory produces 6985 screws per day. How many screws will it produce in 358 days?

#### Answer:

Number of screws produced by the factory in one day = 6985

Number of screws produced in 358 days = 6985 x 358

= 2500630

∴ The factory will produce 2500630 screws in 358 days.

#### Page No 12:

#### Question 19:

Mr Bhaskar saves Rs 8756 every month. How much money will he save in 13 years?

#### Answer:

We know that

1 year = 12 months

13 years = 13 x 12 = 156 months

Now, we have:

Amount saved by Mr Bhaskar in one month = Rs 8756

Amount saved in 156 months = Rs 8756 $\times $ 156 = Rs 1365936

∴ Mr Bhaskar will save Rs 1365936 in 13 years.

#### Page No 12:

#### Question 20:

A scooter costs Rs 36725. How much will 487 such scooters cost?

#### Answer:

Cost of one scooter = Rs 36725

Cost of 487 scooter = Rs 36725 $\times $ 487

= Rs 17885075

∴ The cost of 487 scooters will be Rs 17885075.

#### Page No 12:

#### Question 21:

An aeroplane covers 1485 km in 1 hour. How much distance will it cover in 72 hours?

#### Answer:

Distance covered by the aeroplane in one hour = 1485 km

Distance covered in 72 hours = 1485 km $\times $ 72 = 106920 km

∴ The distance covered by the aeroplane in 72 hours will be 106920 km.

#### Page No 12:

#### Question 22:

The product of two numbers is 13421408. If one of the numbers is 364, find the other.

#### Answer:

Product of two numbers = 13421408

One of the number = 364

∴ The other number = 13421408 ÷ 364

= 36872

#### Page No 12:

#### Question 23:

If 36 flats cost Rs 68251500, what is the cost of each such flat?

#### Answer:

Cost of 36 flats = Rs 68251500

Cost of one flat = Rs 68251500 ÷ 36

= Rs 1895875

∴ Each flat costs Rs 1895875.

#### Page No 12:

#### Question 24:

The mass of a cylinder filled with gas is 30 kg 250 g and the mass of the empty cylinder is 14 kg 480 g. How much is the mass of the gas contained in it?

#### Answer:

We know that 1 kg = 1000 g

Now, mass of the gas-filled cylinder = 30 kg 250 g = 30.25 kg

Mass of an empty cylinder = 14 kg 480 g = 14.48 kg

∴ Mass of the gas contained in the cylinder = 30.25 kg ‒ 14.48 kg

= 15.77 kg = 15 kg 770 g

#### Page No 12:

#### Question 25:

From a cloth 5 m long, a piece of length 2 m 85 cm is cut off. What is the length of the remaining piece?

#### Answer:

We know that 1 m = 100 cm

Length of the cloth = 5 m

Length of the piece cut off from the cloth = 2 m 85 cm

∴ Length of the remaining piece of cloth = 5 m ‒ 2.85 m

= 2.15 m = 2 m 15 cm

#### Page No 12:

#### Question 26:

In order to make a shirt, a length of 2 m 75 cm of cloth is needed. How much length of the cloth will be required for 16 such shirts?

#### Answer:

We know that 1 m = 100 cm

Now, length of the cloth required to make one shirt = 2 m 75 cm

Length of the cloth required to make 16 such shirts = 2 m 75 cm $\times $ 16

= 2.75 m $\times $ 16

= 44 m

∴ The length of the cloth required to make 16 shirts will be 44 m.

#### Page No 12:

#### Question 27:

For making 8 trousers of the same size, 14 m 80 cm of cloth is needed. How much cloth will be required for each such trouser?

#### Answer:

We know that 1 m = 100 cm

Cloth needed for making 8 trousers = 14 m 80 cm

Cloth needed for making 1 trousers = 14 m 80 cm ÷ 8

= 14 .8 m ÷ 8

= 1.85 m = 1 m 85 cm

∴ 1 m 85 cm of cloth will be required to make one shirt.

#### Page No 12:

#### Question 28:

The mass of a brick is 2 kg 750 g. What is the total mass of 14 such bricks?

#### Answer:

We know that 1 kg = 1000 g

Now, mass of one brick = 2 kg 750 g

∴ Mass of 14 such bricks = 2 kg 750 g $\times $ 14

= 2.75 kg $\times $ 14

= 38.5 kg = 38 kg 500 g

#### Page No 12:

#### Question 29:

The total mass of 8 packets, each of the same size, is 10 kg 600 g. What is the mass of each such packet?

#### Answer:

We know that 1 kg = 1000 g

Now, total mass of 8 packets of the same size = 10 kg 600 g

∴ Mass of one such packet = 10 kg 600 g ÷ 8

= 10.6 kg ÷ 8

= 1.325 kg = 1 kg 325 g

#### Page No 12:

#### Question 30:

A rope of length 10 m has been divided into 8 pieces of the same length. What is the length of each piece?

#### Answer:

Length of the rope divided into 8 equal pieces = 10 m

Length of one piece = 10 m ÷ 8

= 1.25 m = 1 m 25 cm [∵ 1 m = 100 cm]

#### Page No 14:

#### Question 1:

Round each of the following numbers to the nearest ten:

(a) 36

(b) 173

(c) 3869

(d) 16378

#### Answer:

(i) In 36, the ones digit is 6 > 5.

∴ The required rounded number = 40

(ii) In 173, the ones digit is 3 < 5.

∴ The required rounded number = 170

(iii) In 3869, the ones digit is 9 > 5.

∴ The required rounded number = 3870

(iv) In 16378, the ones digit is 8 > 5.

∴ The required rounded number = 16380

#### Page No 14:

#### Question 2:

Round each of the following numbers to the nearest hundred:

(a) 814

(b) 1254

(c) 43126

(d) 98165

#### Answer:

(i) In 814, the tens digit is 1 < 5.

∴ The required rounded number = 800

(ii) In 1254, the tens digit is 5 = 5

∴ The required rounded number = 1300

(iii) In 43126, the tens digit is 2 < 5

∴ The required rounded number = 43100

(iv) In 98165, the tens digit is 6 > 5

∴ The required rounded number = 98200

#### Page No 14:

#### Question 3:

Round each of the following numbers to the nearest thousand:

(a) 793

(b) 4826

(c) 16719

(d) 28394

#### Answer:

(i) In 793, the hundreds digit is 7 > 5

∴ The required rounded number = 1000

(ii) In 4826, the hundreds digit is 8 > 5

∴ The required rounded number = 5000

(iii) In 16719, the hundreds digit is 7 > 5

∴ The required rounded number = 17000

(iv) In 28394, the hundreds digit is 3 < 5

∴ The required rounded number = 28000

#### Page No 14:

#### Question 4:

Round each of the following numbers to the nearest ten thousand:

(a) 17514

(b) 26340

(c) 34890

(d) 272685

#### Answer:

(i) In 17514, the thousands digit is 7 > 5

∴ The required rounded number = 20000

(ii) In 26340, the thousands digit is 6 > 5

∴ The required rounded number = 30000

(iii) In 34890, the thousands digit is 4 < 5

∴ The required rounded number = 30000

(iv) In 272685, the thousands digit is 2 < 5

∴ The required rounded number = 270000

#### Page No 14:

#### Question 5:

*Estimate each sum to the nearest ten:*

(57 + 34)

#### Answer:

57 estimated to the nearest ten = 60

34 estimated to the nearest ten = 30

∴ The required estimation = (60 + 30) = 90

#### Page No 14:

#### Question 6:

*Estimate each sum to the nearest ten:*

(43 + 78)

#### Answer:

43 estimated to the nearest ten = 40

78 estimated to the nearest ten = 80

∴ The required estimation = (40 + 80) = 120

#### Page No 14:

#### Question 7:

*Estimate each sum to the nearest ten:*

(14 + 69)

#### Answer:

14 estimated to the nearest ten = 10

69 estimated to the nearest ten = 70

∴ The required estimation = (10 + 70) = 80

#### Page No 14:

#### Question 8:

*Estimate each sum to the nearest ten:*

(86 + 19)

#### Answer:

86 estimated to the nearest ten = 90

19 estimated to the nearest ten = 20

∴ The required estimation = (90 + 20) = 110

#### Page No 14:

#### Question 9:

*Estimate each sum to the nearest ten:*

(95 + 58)

#### Answer:

95 estimated to the nearest ten = 100

58 estimated to the nearest ten = 60

∴ The required estimation = (100 + 60) = 160

#### Page No 14:

#### Question 10:

*Estimate each sum to the nearest ten:*

(77 + 63)

#### Answer:

77 estimated to the nearest ten = 80

63 estimated to the nearest ten = 60

∴ The required estimation = (80 + 60) = 140

#### Page No 14:

#### Question 11:

*Estimate each sum to the nearest ten:*

(356 + 275)

#### Answer:

356 estimated to the nearest ten = 360

275 estimated to the nearest ten = 280

∴ The required estimation = (360 + 280) = 640

#### Page No 14:

#### Question 12:

*Estimate each sum to the nearest ten:*

(463 + 182)

#### Answer:

463 estimated to the nearest ten = 460

182 estimated to the nearest ten = 180

∴ The required estimation = (460 + 180) = 640

#### Page No 14:

#### Question 13:

*Estimate each sum to the nearest ten:*

(538 + 276)

#### Answer:

538 estimated to the nearest ten = 540

276 estimated to the nearest ten = 280

∴ The required estimation = (540 + 280) = 820

#### Page No 14:

#### Question 14:

*Estimate each sum to the nearest hundred:*

(236 + 689)

#### Answer:

236 estimated to the nearest hundred = 200

689 estimated to the nearest hundred = 700

∴ The required estimation = (200 + 700) = 900

#### Page No 14:

#### Question 15:

*Estimate each sum to the nearest hundred:*

(458 + 324)

#### Answer:

458 estimated to the nearest hundred = 500

324 estimated to the nearest hundred = 300

∴ The required estimation = (500 + 300) = 800

#### Page No 14:

#### Question 16:

*Estimate each sum to the nearest hundred:*

(170 + 395)

#### Answer:

170 estimated to the nearest hundred = 200

395 estimated to the nearest hundred = 400

∴ The required estimation = (200 + 400) = 600

#### Page No 15:

#### Question 17:

*Estimate each sum to the nearest hundred:*

(3280 + 4395)

#### Answer:

3280 estimated to the nearest hundred = 3300

4395 estimated to the nearest hundred = 4400

∴ The required estimation = (3300 + 4400) = 7700

#### Page No 15:

#### Question 18:

*Estimate each sum to the nearest hundred:*

(5130 + 1410)

#### Answer:

5130 estimated to the nearest hundred = 5100

1410 estimated to the nearest hundred = 1400

∴ The required estimation = (5100 + 1400) = 6500

#### Page No 15:

#### Question 19:

*Estimate each sum to the nearest hundred:*

(10083 + 29380)

#### Answer:

10083 estimated to the nearest hundred = 10100

29380 estimated to the nearest hundred = 29400

∴ The required estimation = (10100 + 29400) = 39500

#### Page No 15:

#### Question 20:

*Estimate each sum to the nearest thousand:*

(32836 + 16466)

#### Answer:

32836 estimated to the nearest thousand = 33000

16466 estimated to the nearest thousand = 16000

∴ The required estimation = (33000 + 16000) = 49000

#### Page No 15:

#### Question 21:

*Estimate each sum to the nearest thousand:*

(46703 + 11375)

#### Answer:

46703 estimated to the nearest thousand = 47000

11375 estimated to the nearest thousand = 11000

∴ The required estimation = (47000 + 11000) = 58000

#### Page No 15:

#### Question 22:

*Estimate each sum to the nearest thousand:*

There are 54 balls in box A and 79 balls in box B. Estimate the total number of balls in both the boxes taken together.

#### Answer:

Number of balls in box A = 54

Number of balls in box B = 79

Estimated number of balls in box A = 50

Estimated number of balls in box B = 80

∴ Total estimated number of balls in both the boxes = (50 + 80) = 130

#### Page No 15:

#### Question 23:

*Estimate each difference to the nearest ten:*

(53 − 18)

#### Answer:

We have,

53 estimated to the nearest ten = 50

18 estimated to the nearest ten = 20

∴ The required estimation = (50 ‒ 20) = 30

#### Page No 15:

#### Question 24:

*Estimate each difference to the nearest ten:*

(97 − 38)

#### Answer:

100 estimated to the nearest ten = 100

38 estimated to the nearest ten = 40

∴ The required estimation = (100 ‒ 40) = 60

#### Page No 15:

#### Question 25:

*Estimate each difference to the nearest ten:*

(409 − 148)

#### Answer:

409 estimated to the nearest ten = 410

148 estimated to the nearest ten = 150

∴ The required estimation = (410 ‒ 150) = 260

#### Page No 15:

#### Question 26:

*Estimate each difference to the nearest hundred:*

(678 − 215)

#### Answer:

678 estimated to the nearest hundred = 700

215 estimated to the nearest hundred = 200

∴ The required estimation = (700 ‒ 200) = 500

#### Page No 15:

#### Question 27:

*Estimate each difference to the nearest hundred:*

(957 − 578)

#### Answer:

957 estimated to the nearest hundred = 1000

578 estimated to the nearest hundred = 600

∴ The required estimation = (1000 ‒ 600) = 400

#### Page No 15:

#### Question 28:

*Estimate each difference to the nearest hundred:*

(7258 − 2429)

#### Answer:

7258 estimated to the nearest hundred = 7300

2429 estimated to the nearest hundred = 2400

∴ The required estimation = (7300 ‒ 2400) = 4900

#### Page No 15:

#### Question 29:

*Estimate each difference to the nearest hundred:*

(5612 − 3095)

#### Answer:

5612 estimated to the nearest hundred = 5600

3095 estimated to the nearest hundred = 3100

∴ The required estimation = (5600 ‒ 3100) = 2500

#### Page No 15:

#### Question 30:

*Estimate each difference to the nearest thousand:*

(35863 − 27677)

#### Answer:

35863 estimated to the nearest thousand = 36000

27677 estimated to the nearest thousand = 28000

∴ The required estimation = (36000 ‒ 28000) = 8000

#### Page No 15:

#### Question 31:

*Estimate each difference to the nearest thousand:*

(47005 − 39488)

#### Answer:

47005 estimated to the nearest thousand = 47000

39488 estimated to the nearest thousand = 39000

∴ The required estimation = (47000 ‒ 39000) = 8000

#### Page No 15:

#### Question 1:

*Estimate each of the following products by rounding off each number to the nearest ten:*

38 × 63

#### Answer:

38 estimated to the nearest ten = 40

63 estimated to the nearest ten = 60

∴ The required estimation = (40 $\times $ 60) = 2400

#### Page No 15:

#### Question 2:

*Estimate each of the following products by rounding off each number to the nearest ten:*

54 × 47

#### Answer:

54 estimated to the nearest ten = 50

47 estimated to the nearest ten = 50

∴ The required estimation = (50 $\times $ 50) = 2500

#### Page No 15:

#### Question 3:

*Estimate each of the following products by rounding off each number to the nearest ten:*

28 × 63

#### Answer:

28 estimated to the nearest ten = 30

63 estimated to the nearest ten = 60

∴ The required estimation = (30 $\times $ 60) = 1800

#### Page No 15:

#### Question 4:

*Estimate each of the following products by rounding off each number to the nearest ten:*

42 × 75

#### Answer:

42 estimated to the nearest ten = 40

75 estimated to the nearest ten = 80

∴ The required estimation = (40 $\times $ 80) = 3200

#### Page No 15:

#### Question 5:

*Estimate each of the following products by rounding off each number to the nearest ten:*

64 × 58

#### Answer:

64 estimated to the nearest ten = 60

58 estimated to the nearest ten = 60

∴ The required estimation = (60 $\times $ 60) = 3600

#### Page No 15:

#### Question 6:

*Estimate each of the following products by rounding off each number to the nearest ten:*

15 × 34

#### Answer:

15 estimated to the nearest ten = 20

34 estimated to the nearest ten = 30

∴ The required estimation = (20 $\times $ 30) = 600

#### Page No 16:

#### Question 7:

*Estimate each of the following products by rounding off each number to the nearest hundred:*

376 × 123

#### Answer:

376 estimated to the nearest hundred = 400

123 estimated to the nearest hundred = 100

∴ The required estimation = (400 $\times $ 100) = 40000

#### Page No 16:

#### Question 8:

*Estimate each of the following products by rounding off each number to the nearest hundred:*

264 × 147

#### Answer:

264 estimated to the nearest hundred = 300

147 estimated to the nearest hundred = 100

∴ The required estimation = (300 $\times $ 100) = 30000

#### Page No 16:

#### Question 9:

*Estimate each of the following products by rounding off each number to the nearest hundred:*

423 × 158

#### Answer:

423 estimated to the nearest hundred = 400

158 estimated to the nearest hundred = 200

∴ The required estimation = (400 $\times $ 200) = 80000

#### Page No 16:

#### Question 10:

*Estimate each of the following products by rounding off each number to the nearest hundred:*

509 × 179

#### Answer:

509 estimated to the nearest hundred = 500

179 estimated to the nearest hundred = 200

∴ The required estimation = (500 $\times $ 200) = 100000

#### Page No 16:

#### Question 11:

*Estimate each of the following products by rounding off each number to the nearest hundred:*

392 × 138

#### Answer:

392 estimated to the nearest hundred = 400

138 estimated to the nearest hundred = 100

∴ The required estimation = (400 $\times $ 100) = 40000

#### Page No 16:

#### Question 12:

*Estimate each of the following products by rounding off each number to the nearest hundred:*

271 × 339

#### Answer:

271 estimated to the nearest hundred = 300

339 estimated to the nearest hundred = 300

∴ The required estimation = (300 $\times $ 300) = 90000

#### Page No 16:

#### Question 13:

*Estimate each of the following products by rounding off the first number upwards and the second number downwards:*

183 × 154

#### Answer:

183 estimated upwards = 200

154 estimated downwards = 100

∴ The required product = (200 $\times $ 100) = 20000

#### Page No 16:

#### Question 14:

*Estimate each of the following products by rounding off the first number upwards and the second number downwards:*

267 × 146

#### Answer:

267 estimated upwards = 300

146 estimated downwards = 100

∴ The required product = (300 $\times $ 100) = 30000

#### Page No 16:

#### Question 15:

*Estimate each of the following products by rounding off the first number upwards and the second number downwards:*

359 × 76

#### Answer:

359 estimated upwards = 400

76 estimated downwards = 70

∴ The required product = (400 $\times $ 70) =28000

#### Page No 16:

#### Question 16:

472 × 158

#### Answer:

472 estimated upwards = 500

158 estimated downwards = 100

∴ The required product = (500 $\times $ 100) = 50000

#### Page No 16:

#### Question 17:

680 × 164

#### Answer:

680 estimated upwards = 700

164 estimated downwards = 100

∴ The required product = (700 $\times $ 100) = 70000

#### Page No 16:

#### Question 18:

255 × 350

#### Answer:

255 estimated upwards = 300

350 estimated downwards = 300

∴ The required product = (300 $\times $ 300) = 90000

#### Page No 16:

#### Question 19:

*Estimate each of the following products by rounding off the first number downwards and the second number upwards:*

356 × 278

#### Answer:

356 estimated downwards = 300

278 estimated upwards = 300

∴ The required product = (300 $\times $ 300) = 90000

#### Page No 16:

#### Question 20:

*Estimate each of the following products by rounding off the first number downwards and the second number upwards:*

472 × 76

#### Answer:

472 estimated downwards = 400

76 estimated upwards = 80

∴ The required product = (400 $\times $ 80) = 32000

#### Page No 16:

#### Question 21:

*Estimate each of the following products by rounding off the first number downwards and the second number upwards:*

578 × 369

#### Answer:

578 estimated downwards = 500

369 estimated upwards = 400

∴ The required product = (500 $\times $ 400) = 200000

#### Page No 16:

#### Question 1:

*Find the estimated quotient for each of the following:*

87 ÷ 28

#### Answer:

87 ÷ 28 is approximately equal to 90 ÷ 30 = 3.

#### Page No 16:

#### Question 2:

*Find the estimated quotient for each of the following:*

83 ÷ 17

#### Answer:

The estimated quotient for 83 ÷ 17 is approximately equal to 80 ÷ 20 = 8 ÷ 2 = 4.

#### Page No 16:

#### Question 3:

*Find the estimated quotient for each of the following:*

75 ÷ 23

#### Answer:

The estimated quotient of 75 ÷ 23 is approximately equal to 80 ÷ 20 = 8 ÷ 2 = 4.

#### Page No 16:

#### Question 4:

*Find the estimated quotient for each of the following:*

193 ÷ 24

#### Answer:

The estimated quotient of 193 ÷ 24 is approximately equal to 200 ÷ 20 = 20 ÷ 2 = 10.

#### Page No 16:

#### Question 5:

*Find the estimated quotient for each of the following:*

725 ÷ 23

#### Answer:

The estimated quotient of 725 ÷ 23 is approximately equal to 700 ÷ 20 = 70 ÷ 2 = 35.

#### Page No 16:

#### Question 6:

*Find the estimated quotient for each of the following:*

275 ÷ 25

#### Answer:

The estimated quotient of 275 ÷ 25 is approximately equal to 300 ÷ 30 = 30 ÷ 3 = 10.

#### Page No 16:

#### Question 7:

*Find the estimated quotient for each of the following:*

633 ÷ 33

#### Answer:

The estimated quotient of 633 ÷ 33 is approximately equal to 600 ÷ 30 = 60 ÷ 3 = 20.

#### Page No 16:

#### Question 8:

*Find the estimated quotient for each of the following:*

729 ÷ 29

#### Answer:

729 ÷ 29 is approximately equal to 700 ÷ 30 or 70 ÷ 3, which is approximately equal to 23.

#### Page No 16:

#### Question 9:

*Find the estimated quotient for each of the following:*

858 ÷ 39

#### Answer:

858 ÷ 39 is approximately equal to 900 ÷ 40 or 90 ÷ 4, which is approximately equal to 23.

#### Page No 16:

#### Question 10:

*Find the estimated quotient for each of the following:*

868 ÷ 38

#### Answer:

868 ÷ 38 is approximately equal to 900 ÷ 40 or 90 ÷ 4, which is approximately equal to 23.

#### Page No 19:

#### Question 1:

Express each of the following as a Roman numeral:

(i) 2

(ii) 8

(iii) 14

(iv) 29

(v) 36

(vi) 43

(vii) 54

(viii) 61

(ix) 73

(x) 81

(xi) 91

(xii) 95

(xiii) 99

(xiv) 105

(xv) 114

#### Answer:

We may write these numbers as given below:

(i) 2 = II

(ii) 8 = (5 + 3) = VIII

(iii) 14 = (10 + 4) = XIV

(iv) 29 = ( 10 + 10 + 9 ) = XXIX

(v) 36 = (10 + 10 + 10 + 6) = XXXVI

(vi) 43 = (50 - 10) + 3 = XLIII

(vii) 54 = (50 + 4) = LIV

(viii) 61= (50 + 10 + 1) = LXI

(ix) 73 = ( 50 + 10 + 10 + 3) = LXXIII

(x) 81 = (50 + 10 + 10 + 10 + 1) = LXXXI

(xi) 91 =(100 - 10) + 1 = XCI

(xii) 95 = (100 - 10) + 5 = XCV

(xiii) 99 = (100 - 10) + 9 = XCIX

(xiv) 105 = (100 + 5) = CV

(xv) 114 = (100 + 10) + 4 = CXIV

#### Page No 19:

#### Question 2:

Express each of the following as a Roman numeral:

(i) 164

(ii) 195

(iii) 226

(iv) 341

(v) 475

(vi) 596

(vii) 611

(viii) 759

#### Answer:

We may write these numbers in Roman numerals as follows:

(i) 164 = (100 + 50 + 10 + 4) = CLXIV

(ii) 195 = 100 + (100 - 10) + 5 = CXCV

(iii) 226 = (100 + 100 + 10 + 10 + 6) = CCXXVI

(iv) 341= 100 + 100+ 100 + (50 -10) + 1 = CCCXLI

(v) 475 = (500 - 100) + 50 + 10 + 10 + 5 = CDLXXV

(vi) 596 = 500 + (100 - 10) + 6 = DXCVI

(vii) 611= 500 + 100 + 11 = DCXI

(viii) 759 = 500 + 100 + 100 + 50 + 9 = DCCLIX

#### Page No 19:

#### Question 3:

Write each of the following as a Hindu-Arabic numeral:

(i) XXVII

(ii) XXXIV

(iii) XLV

(iv) LIV

(v) LXXIV

(vi) XCI

(vii) XCVI

(viii) CXI

(ix) CLIV

(x) CCXXIV

(xi) CCCLXV

(xii) CDXIV

(xiii) CDLXIV

(xiv) DVI

(xv) DCCLXVI

#### Answer:

We can write the given Roman numerals in Hindu-Arabic numerals as follows:

(i) XXVII = 10 + 10 + 7 = 27

(ii) XXXIV = 10 + 10 + 10 + 4 = 34

(iii) XLV = (50 − 10 ) + 5 = 45

(iv) LIV = 50 + 4 = 54

(v) LXXIV = 50 + 10 + 10 + 4 = 74

(vi) XCI = (100 − 10) + 1 = 91

(vii) XCVI = (100 − 10) + 6 = 96

(viii) CXI = 100 + 10 + 1= 111

(ix) CLIV = 100 + 50 + 4 = 154

(x) CCXXIV = 100 + 100 + 10 + 10 + 4 = 224

(xi) CCCLXV = 100 + 100 + 100 + 50 + 10 + 5 = 365

(xii) CDXIV = (500 − 100) + 10 + 4 = 414

(xiii) CDLXIV = (500 − 100) + 50 + 10 + 4 = 464

(xiv) DVI = 500 + 6= 506

(xv) DCCLXVI = 500 + 100 + 100 + 50 + 10 + 6 = 766

#### Page No 19:

#### Question 4:

Show that each of the following is meaningless. Give reason in each case.

(i) VC

(ii) IL

(iii) VVII

(iv) IXX

#### Answer:

(i) VC is wrong because V, L and D are never subtracted.

(ii) IL is wrong because I can be subtracted from V and X only.

(iii) VVII is wrong because V, L and D are never repeated.

(iv) IXX is wrong because X (ten) must be placed before IX (nine).

#### Page No 20:

#### Question 1:

**Mark against the correct answer**

The place value of 6 in the numeral 48632950 is

(a) 6

(b) 632950

(c) 600000

(d) 486

#### Answer:

Option c is correct.

Place value of 6 = 6 lakhs = (6 $\times $ 100000) = 600000

#### Page No 20:

#### Question 2:

**Mark against the correct answer**

The face value of 4 in the numeral 89247605 is

(a) 4

(b) 40000

(c) 47605

(d) 8924

#### Answer:

Option a is correct.

The face value of a digit remains as it is irrespective of the place it occupies in the place value chart.

Thus, the face value of 4 is always 4 irrespective of where it may be.

#### Page No 20:

#### Question 3:

**Mark against the correct answer**

The difference between the place value and the face value of 5 in the numeral 78653421 is

(a) 53416

(b) 4995

(c) 49995

(d) none of these

#### Answer:

Option c is correct.

Place value of 5 = 5 $\times $ 10000 = 50000

Face value of 5 = 5

∴ Required difference = 50000 − 5 = 49995

#### Page No 20:

#### Question 4:

**Mark against the correct answer**

The smallest counting number is

(a) 0

(b) 1

(c) 10

(d) none of these

#### Answer:

Option b is correct.

The smallest counting number is 1.

#### Page No 20:

#### Question 5:

**Mark against the correct answer**

How many 4-digit numbers are there?

(a) 8999

(b) 9000

(c) 8000

(d) none of these

#### Answer:

Option b is correct.

The largest four-digit number = 9999

The smallest four-digit number = 1000

Total number of all four-digit numbers = (9999 − 1000) + 1

= 8999 + 1

= 9000

#### Page No 20:

#### Question 6:

**Mark against the correct answer**

How many 7-digit numbers are there?

(a) 8999999

(b) 9000000

(c) 10000000

(d) none of these

#### Answer:

Option b is correct.

The largest seven-digit number = 9999999

The smallest seven-digit number = 1000000

Total number of seven-digit numbers = (9999999 − 1000000) + 1

= 8999999 + 1

= 9000000

#### Page No 20:

#### Question 7:

**Mark against the correct answer**

How many 8-digit numbers are there?

(a) 99999999

(b) 89999999

(c) 90000000

(d) none of these

#### Answer:

Option c is correct.

The largest eight-digit number = 99999999

The smallest eight-digit number = 10000000

Total number of eight-digit numbers = (99999999 − 10000000) + 1

= 89999999 + 1

= 90000000

#### Page No 20:

#### Question 8:

**Mark against the correct answer**

What comes just before 1000000?

(a) 99999

(b) 999999

(c) 9999999

(d) none of these

#### Answer:

Option b is correct.

The number just before 1000000 is 999999 (i.e., 1000000 − 1).

#### Page No 20:

#### Question 9:

**Mark against the correct answer**

Which of the following is not meaningful?

(a) VX

(b) XV

(c) XXV

(d) XXXV

#### Answer:

Option a is correct.

V, L and D are never subtracted. Thus, VX is wrong.

#### Page No 20:

#### Question 10:

**Mark against the correct answer**

Which of the following is not meaningful?

(a) CI

(b) CII

(c) IC

(d) XC

#### Answer:

Option c is correct.

I can be subtracted from V and X only. Thus, IC is wrong.

#### Page No 20:

#### Question 11:

**Mark against the correct answer**

Which of the following is not meaningful?

(a) XIV

(b) XVV

(c) XIII

(d) XXII

#### Answer:

Option b is correct.

V, L and D are never repeated. Thus, XVV is meaningless.

#### Page No 21:

#### Question 1:

Write each of the following numerals in words:

(i) 16, 06, 23, 708

(ii) 14, 23, 08, 915

#### Answer:

(i) Sixteen crore six lakh twenty-three thousand seven hundred eight

(ii) Fourteen crore twenty-three lakh eight thousand nine hundred fifteen

#### Page No 21:

#### Question 2:

Write each of the following numerals in words:

(i) 80, 060, 409

(ii) 234, 150, 319

#### Answer:

(i) Eighty million sixty thousand four hundred nine

(ii) Two hundred thirty-four million one hundred fifty thousand three hundred nineteen

#### Page No 21:

#### Question 3:

Arrange the following numbers in ascending order:

3903216, 19430124, 864572, 6940513, 16531079

#### Answer:

We have,

864572 is a 6-digit number.

3903216 and 6940513 are seven-digit numbers.

At the ten lakhs place, one number has 3, while the second number has 6.

Clearly, 3 < 6

∴ 3903216 < 6940513

16531079 and 19430124 are eight-digit numbers.

At the crores place, both the numbers have the same digit, namely 1.

At the ten lakhs place, one number has 6, while the second number has 9.

Clearly, 6 < 9

∴ 16531079 < 19430124

The given numbers in ascending order are:

864572 < 3903216 < 6940513 < 16531079 < 19430124

#### Page No 21:

#### Question 4:

Arrange the following numbers in descending order:

54796203, 4675238, 63240613, 5125648, 589623

#### Answer:

63240613 and 54796203 are both eight-digit numbers.

At the crores place, one number has 6, while the second number has 5.

Clearly, 5 < 6

∴ 63240613 > 54796203

5125648 and 4675238 are both seven-digit numbers.

However, at the ten lakhs place, one number has 5, while the second number has 4.

Clearly, 4 < 5

∴ 5125648 > 4675238

589623 is a six-digit number.

The given numbers in descending order are:

63240613 > 54796203 > 5125648 > 4675238 > 589623

#### Page No 21:

#### Question 5:

How many 7-digit numbers are there in all?

#### Answer:

The largest seven-digit number = 9999999

The smallest seven-digit number = 1000000

Number of all seven-digits numbers = (9999999 − 1000000) + 1

= 899999 + 1

= 9000000

Hence, there is a total of ninety lakh 7-digit numbers.

#### Page No 21:

#### Question 6:

Write the largest and smallest numbes using each of the digits 1, 4, 6, 8, 0 only once and find their difference.

#### Answer:

The largest number using each of the digits: 1, 4, 6, 8 and 0, is 86410.

The smallest number using each of the digits: 1, 4, 6, 8 and 0, is 10468.

∴ Required difference = 86410 − 10468

= 75942

#### Page No 21:

#### Question 7:

Write the Hindu-Arabic numeral for each of the following:

(i) CCXLII

(ii) CDLXV

(iii) LXXVI

(iv) DCCXLI

(v) XCIV

(vi) CXCIX

#### Answer:

(i) CCXLII = 100 + 100 + (50 − 10) + 2 = 242

(ii) CDLXV = (500 − 100) + 50 + 10 + 5 = 465

(iii) LXXVI = 50 + 10 + 10 + 6 = 76

(iv) DCCXLI = 500 + 100 + 100 + ( 50 − 10) + 1 = 741

(v) XCIV = (100 − 10) + 4 = 94

(vi) CXCIX = 100 + (100 − 10) + 9 = 199

#### Page No 21:

#### Question 8:

Write the Roman numeral for each of the following:

(i) 84

(ii) 99

(iii) 145

(iv) 406

(v) 519

#### Answer:

(i) 84 = 50 + 30 + 4 = LXXXIV

(ii) 99 = 90 + 9 = XCIX

(iii) 145 = 100 + (50 − 10) + 5 = CXLV

(iv) 406 = 400 + 6 = CDVI

(v) 519 = 500 +10 + 9 = DXIX

#### Page No 21:

#### Question 9:

Write the successor and predecessor of 999999 and find their difference.

#### Answer:

Successor of 999999 = 999999 + 1 = 1000000

Predecessor of 999999 = 999999 − 1 = 999998

∴ Required difference = 1000000 − 999998

= 2

#### Page No 21:

#### Question 10:

Round off each of the following to the nearest thousand:

(i) 1046

(ii) 973

(iii) 5624

(iv) 4368

#### Answer:

(i) The number is 1046. Its digit at the hundreds place is 0 < 5.

So, the given number is rounded off to the nearest thousand as 1000.

(ii) The number is 973. Its digit at the hundreds place is 9 > 5.

So, the given number is rounded off to the nearest thousand as 1000.

(iii) The number is 5624. Its digit at the hundreds place is 6 > 5.

So, the given number is rounded off to the nearest thousand as 6000.

(iv) The number is 4368. Its digit at the hundreds place is 3 < 5.

So, the given number is rounded off to the nearest thousand as 4000.

#### Page No 21:

#### Question 11:

Which of the following Roman numerals is correct?

(a) XC

(b) XD

(c) DM

(d) VL

#### Answer:

Option (a) is correct.

X can be subtracted from L and C only.

i.e., XC = ( 100 − 10 ) = 90

#### Page No 21:

#### Question 12:

1 Lakh = ...... thousands.

(a) 10

(b) 100

(c) 1000

(d) none of these

#### Answer:

Option (b) is correct.

One lakh (100000) is equal to one hundred thousand (100,000).

#### Page No 21:

#### Question 13:

No Roman numeral can be repeated more than ..... times.

(a) two

(b) three

(c) four

(d) none of these

#### Answer:

Option (b) is correct.

No Roman numeral can be repeated more than **three** times.

#### Page No 21:

#### Question 14:

How many times does the digit 9 occur between 1 and 100?

(a) 11

(b) 15

(c) 18

(d) 20

#### Answer:

Option (d) is correct.

Between 1 and 100, the digit 9 occurs in 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 and 99.

∴ The digit occurs 20 times between 1 and 100.

#### Page No 21:

#### Question 15:

(7268 − 2427) estimated to the nearest hundred is

(a) 4900

(b) 4800

(c) 4841

(d) 5000

#### Answer:

Option (a) is correct.

7268 will be rounded off to the nearest hundred as 7300.

2427 will be rounded of to the nearest hundred as 2400.

∴ 7300 − 2400 = 4900

#### Page No 21:

#### Question 16:

One million = ...... .

(a) 1 lakh

(b) 10 lakh

(c) 100 lakh

(d) 1 crore

#### Answer:

Option (b) is correct.

1 million (1,000,000) = 10 lakh (10 $\times $ 1,00,000)

#### Page No 21:

#### Question 17:

1512 when round off to the nearest hundred is

(a) 1600

(b) 1500

(c) 1510

(d) none of these

#### Answer:

Option (b) is correct.

The number is 1512. Its digit at the tens place is 1 < 5.

So, the given number is rounded off to the nearest hundred as 1500.

#### Page No 21:

#### Question 18:

Which of the symbols are never repeated?

(a) V, X and C

(b) V, X and D

(c) V, L and D

(d) L, K and C

#### Answer:

Option (c) is correct.

In Roman numerals, V, L and D are never repeated and never subtracted.

#### Page No 21:

#### Question 19:

Write 86324805 separating periods in HIndu-Arabic system.

#### Answer:

**Periods:** Crores Lakhs Thousands Hundreds Tens Ones

**Digits:** 8 63 24 8 0 5

Using commas, we write the given number as 8,63,24,805.

#### Page No 21:

#### Question 20:

**Fill in the blanks:**

(i) 1 crore = ...... lakh

(ii) 1 crore = ...... million

(iii) 564 when estimated to the nearest hundred is ...... .

(iv) The smallest 4-digit number with four different digits is ...... .

#### Answer:

(i) 1 crore = __100__ lakh

(ii) 1 crore = __10__ million

(iii) 564 when estimated to the nearest hundred is __600.__

(iv) The smallest 4-digit number with four different digits is __1023.__

#### Page No 22:

#### Question 21:

*Write 'T' for true and 'F' for false*

The difference in the face value and the place value of 5 in 85419 is 85414.

#### Answer:

F

Place value of 5 in 85419 = 5000

Face value of 5 in 85419 = 5

∴ Their difference = 5000 − 5 = 4995

#### Page No 22:

#### Question 22:

*Write 'T' for true and 'F' for false*

In Roman numerals V, L and D are never subtracted.

#### Answer:

T

In Roman numerals, V, L and D are never repeated and never subtracted.

#### Page No 22:

#### Question 23:

*Write 'T' for true and 'F' for false*

The successor of the greatest 5-digit number is 100000.

#### Answer:

T

Greatest five-digit number = 99999

Successor of 99999 = 99999 + 1 = 100000

#### Page No 22:

#### Question 24:

*Write 'T' for true and 'F' for false*

The estimated value of 46,530 to the nearest hundred is 46500.

#### Answer:

T

The number is 46,530. Its digit at the tens place is 3 < 5.

So, the number 46,530 is rounded off to the nearest hundred as 46,500.

#### Page No 22:

#### Question 25:

*Write 'T' for true and 'F' for false*

100 lakhs make a million.

#### Answer:

F

10 lakhs = 1 million

View NCERT Solutions for all chapters of Class 6