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#### Page No 5:

#### Question 1:

#### 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:

(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

#### 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:

(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

#### 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:

(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)

#### 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:

(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

#### 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 â€’ 900) = 8999100

#### Page No 6:

#### Question 6:

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 â€’ 900) = 8999100

#### 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 â€’ 7) = 69,99,993

#### Page No 6:

#### Question 7:

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

The face value of 7 in 27650934 = 7

$\therefore $ Required difference = (7000000 â€’ 7) = 69,99,993

#### Answer:

The largest 6-digit number = 999999

The smallest 6-digit number = 100000

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

= 899999 + 1

= 900000

= 9 lakhs

#### Page No 6:

#### Question 8:

The largest 6-digit number = 999999

The smallest 6-digit number = 100000

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

= 899999 + 1

= 900000

= 9 lakhs

#### 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:

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

#### 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:

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

Thus, one hundred thousands make a lakh.

#### 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:

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

Thus, 10,000 thousands make a crore.

#### Answer:

The given number is 738.

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

∴ Required difference = 837 â€’ 738 = 99

#### Page No 6:

#### Question 12:

The given number is 738.

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

∴ Required difference = 837 â€’ 738 = 99

#### Answer:

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

#### Page No 6:

#### Question 13:

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

#### Answer:

The number just before 9900000 is 9900000 â€’ 1 = 9899999.

#### Page No 6:

#### Question 14:

The number just before 9900000 is 9900000 â€’ 1 = 9899999.

#### Answer:

The number just before 10000000 is 10000000 â€’ 1 = 9999999.

#### Page No 6:

#### Question 15:

The number just before 10000000 is 10000000 â€’ 1 = 9999999.

#### 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:

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

#### 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:

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

#### Answer:

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

#### Page No 6:

#### Question 18:

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

#### 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:

**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

#### 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:

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 |

#### 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:

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.

#### 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:

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.

#### 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:

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

#### 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:

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

#### 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:

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.

#### 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:

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

#### 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:

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

#### 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:

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

#### 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:

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

#### 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:

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

#### 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:

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

#### 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:

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

#### 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:

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

#### 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:

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

#### 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:

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

#### 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:

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

#### Answer:

New number = Sum of 37684955 and 3615045

= 37684955 + 3615045

= 41300000

#### Page No 11:

#### Question 4:

New number = Sum of 37684955 and 3615045

= 37684955 + 3615045

= 41300000

#### 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:

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

#### 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:

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

#### 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:

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

#### 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:

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

#### Answer:

Total population of the city = 28756304

Number of males in the city = 16987059

∴ Number of females in the city = 28756304 â€’ 16987059

= 11769245

#### Page No 12:

#### Question 9:

Total population of the city = 28756304

Number of males in the city = 16987059

∴ Number of females in the city = 28756304 â€’ 16987059

= 11769245

#### Answer:

Required number = 13246510 â€’ 4658642 = 8587868

∴ 13246510 is larger than 4658642 by 8587868.

#### Page No 12:

#### Question 10:

Required number = 13246510 â€’ 4658642 = 8587868

∴ 13246510 is larger than 4658642 by 8587868.

#### Answer:

Required number = 1 crore â€’ 564387

= 10000000 â€’ 5643879

= 4356121

∴ 5643879 is smaller than one crore by 4356121.

#### Page No 12:

#### Question 11:

Required number = 1 crore â€’ 564387

= 10000000 â€’ 5643879

= 4356121

∴ 5643879 is smaller than one crore by 4356121.

#### Answer:

11010101 â€’ required number = 2635967

Thus, required number = 11010101 â€’ 2635967

= 8374134

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

#### Page No 12:

#### Question 12:

11010101 â€’ required number = 2635967

Thus, required number = 11010101 â€’ 2635967

= 8374134

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

#### Answer:

Sum of the two numbers = 10750308

One of the number = 8967519

∴ The other number = 10750308 â€’ 8967519

= 1782789

#### Page No 12:

#### Question 13:

Sum of the two numbers = 10750308

One of the number = 8967519

∴ The other number = 10750308 â€’ 8967519

= 1782789

#### Answer:

Initial amount with the man = Rs 20000000

Amount spent on buying a school building = Rs 13607085

∴ Amount left with the man = Rs 20000000 â€’ Rs 13607085

= Rs 6392915

#### Page No 12:

#### Question 14:

Initial amount with the man = Rs 20000000

Amount spent on buying a school building = Rs 13607085

∴ Amount left with the man = Rs 20000000 â€’ Rs 13607085

= Rs 6392915

#### 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 â€’ (Rs 7253840 + Rs 5675450 + Rs 2937680)

= Rs 18536000 â€’ Rs 15866970

= Rs 2669030

#### Page No 12:

#### Question 15:

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 â€’ (Rs 7253840 + Rs 5675450 + Rs 2937680)

= Rs 18536000 â€’ Rs 15866970

= Rs 2669030

#### 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 â€’ (Rs 4836980 + Rs 3964790)

= Rs 10672540 â€’ Rs 8801770

= Rs 1870770

#### Page No 12:

#### Question 16:

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 â€’ (Rs 4836980 + Rs 3964790)

= Rs 10672540 â€’ Rs 8801770

= Rs 1870770

#### 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:

Cost of one chair = Rs 1485

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

= Rs 696465

∴ Cost of 469 chairs is Rs 696465.

#### 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:

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.

#### 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:

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.

#### 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:

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.

#### 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:

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.

#### 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:

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.

#### Answer:

Product of two numbers = 13421408

One of the number = 364

∴ The other number = 13421408 ÷ 364

= 36872

#### Page No 12:

#### Question 23:

Product of two numbers = 13421408

One of the number = 364

∴ The other number = 13421408 ÷ 364

= 36872

#### 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:

Cost of 36 flats = Rs 68251500

Cost of one flat = Rs 68251500 ÷ 36

= Rs 1895875

∴ Each flat costs Rs 1895875.

#### 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 â€’ 14.48 kg

= 15.77 kg = 15 kg 770 g

#### Page No 12:

#### Question 25:

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 â€’ 14.48 kg

= 15.77 kg = 15 kg 770 g

#### 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 â€’ 2.85 m

= 2.15 m = 2 m 15 cm

#### Page No 12:

#### Question 26:

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 â€’ 2.85 m

= 2.15 m = 2 m 15 cm

#### 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:

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.

#### 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:

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.

#### 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:

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

#### 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:

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

#### 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 [âˆµ 1 m = 100 cm]

#### Page No 14:

#### Question 1:

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 [âˆµ 1 m = 100 cm]

#### 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:

(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

#### 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:

(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

#### 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:

(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

#### 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:

(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

#### 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:

57 estimated to the nearest ten = 60

34 estimated to the nearest ten = 30

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

#### 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:

43 estimated to the nearest ten = 40

78 estimated to the nearest ten = 80

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

#### 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:

14 estimated to the nearest ten = 10

69 estimated to the nearest ten = 70

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

#### 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:

86 estimated to the nearest ten = 90

19 estimated to the nearest ten = 20

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

#### 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:

95 estimated to the nearest ten = 100

58 estimated to the nearest ten = 60

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

#### 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:

77 estimated to the nearest ten = 80

63 estimated to the nearest ten = 60

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

#### 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:

356 estimated to the nearest ten = 360

275 estimated to the nearest ten = 280

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

#### 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:

463 estimated to the nearest ten = 460

182 estimated to the nearest ten = 180

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

#### 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:

538 estimated to the nearest ten = 540

276 estimated to the nearest ten = 280

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

#### 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:

236 estimated to the nearest hundred = 200

689 estimated to the nearest hundred = 700

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

#### 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:

458 estimated to the nearest hundred = 500

324 estimated to the nearest hundred = 300

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

#### 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:

170 estimated to the nearest hundred = 200

395 estimated to the nearest hundred = 400

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

#### 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:

3280 estimated to the nearest hundred = 3300

4395 estimated to the nearest hundred = 4400

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

#### 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:

5130 estimated to the nearest hundred = 5100

1410 estimated to the nearest hundred = 1400

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

#### 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:

10083 estimated to the nearest hundred = 10100

29380 estimated to the nearest hundred = 29400

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

#### 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:

32836 estimated to the nearest thousand = 33000

16466 estimated to the nearest thousand = 16000

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

#### 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:

46703 estimated to the nearest thousand = 47000

11375 estimated to the nearest thousand = 11000

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

#### 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:

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

#### Answer:

We have,

53 estimated to the nearest ten = 50

18 estimated to the nearest ten = 20

∴ The required estimation = (50 â€’ 20) = 30

#### Page No 15:

#### Question 24:

We have,

53 estimated to the nearest ten = 50

18 estimated to the nearest ten = 20

∴ The required estimation = (50 â€’ 20) = 30

#### Answer:

100 estimated to the nearest ten = 100

38 estimated to the nearest ten = 40

∴ The required estimation = (100 â€’ 40) = 60

#### Page No 15:

#### Question 25:

100 estimated to the nearest ten = 100

38 estimated to the nearest ten = 40

∴ The required estimation = (100 â€’ 40) = 60

#### Answer:

409 estimated to the nearest ten = 410

148 estimated to the nearest ten = 150

∴ The required estimation = (410 â€’ 150) = 260

#### Page No 15:

#### Question 26:

409 estimated to the nearest ten = 410

148 estimated to the nearest ten = 150

∴ The required estimation = (410 â€’ 150) = 260

#### Answer:

678 estimated to the nearest hundred = 700

215 estimated to the nearest hundred = 200

∴ The required estimation = (700 â€’ 200) = 500

#### Page No 15:

#### Question 27:

678 estimated to the nearest hundred = 700

215 estimated to the nearest hundred = 200

∴ The required estimation = (700 â€’ 200) = 500

#### Answer:

957 estimated to the nearest hundred = 1000

578 estimated to the nearest hundred = 600

∴ The required estimation = (1000 â€’ 600) = 400

#### Page No 15:

#### Question 28:

957 estimated to the nearest hundred = 1000

578 estimated to the nearest hundred = 600

∴ The required estimation = (1000 â€’ 600) = 400

#### Answer:

7258 estimated to the nearest hundred = 7300

2429 estimated to the nearest hundred = 2400

∴ The required estimation = (7300 â€’ 2400) = 4900

#### Page No 15:

#### Question 29:

7258 estimated to the nearest hundred = 7300

2429 estimated to the nearest hundred = 2400

∴ The required estimation = (7300 â€’ 2400) = 4900

#### Answer:

5612 estimated to the nearest hundred = 5600

3095 estimated to the nearest hundred = 3100

∴ The required estimation = (5600 â€’ 3100) = 2500

#### Page No 15:

#### Question 30:

5612 estimated to the nearest hundred = 5600

3095 estimated to the nearest hundred = 3100

∴ The required estimation = (5600 â€’ 3100) = 2500

#### Answer:

35863 estimated to the nearest thousand = 36000

27677 estimated to the nearest thousand = 28000

∴ The required estimation = (36000 â€’ 28000) = 8000

#### Page No 15:

#### Question 31:

35863 estimated to the nearest thousand = 36000

27677 estimated to the nearest thousand = 28000

∴ The required estimation = (36000 â€’ 28000) = 8000

#### Answer:

47005 estimated to the nearest thousand = 47000

39488 estimated to the nearest thousand = 39000

∴ The required estimation = (47000 â€’ 39000) = 8000

#### Page No 15:

#### Question 1:

47005 estimated to the nearest thousand = 47000

39488 estimated to the nearest thousand = 39000

∴ The required estimation = (47000 â€’ 39000) = 8000

#### 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:

38 estimated to the nearest ten = 40

63 estimated to the nearest ten = 60

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

#### 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:

54 estimated to the nearest ten = 50

47 estimated to the nearest ten = 50

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

#### 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:

28 estimated to the nearest ten = 30

63 estimated to the nearest ten = 60

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

#### 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:

42 estimated to the nearest ten = 40

75 estimated to the nearest ten = 80

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

#### 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:

64 estimated to the nearest ten = 60

58 estimated to the nearest ten = 60

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

#### 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:

15 estimated to the nearest ten = 20

34 estimated to the nearest ten = 30

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

#### 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:

376 estimated to the nearest hundred = 400

123 estimated to the nearest hundred = 100

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

#### 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:

264 estimated to the nearest hundred = 300

147 estimated to the nearest hundred = 100

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

#### 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:

423 estimated to the nearest hundred = 400

158 estimated to the nearest hundred = 200

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

#### 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:

509 estimated to the nearest hundred = 500

179 estimated to the nearest hundred = 200

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

#### 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:

392 estimated to the nearest hundred = 400

138 estimated to the nearest hundred = 100

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

#### 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:

271 estimated to the nearest hundred = 300

339 estimated to the nearest hundred = 300

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

#### Answer:

183 estimated upwards = 200

154 estimated downwards = 100

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

#### Page No 16:

#### Question 14:

183 estimated upwards = 200

154 estimated downwards = 100

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

#### Answer:

267 estimated upwards = 300

146 estimated downwards = 100

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

#### Page No 16:

#### Question 15:

267 estimated upwards = 300

146 estimated downwards = 100

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

#### Answer:

359 estimated upwards = 400

76 estimated downwards = 70

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

#### Page No 16:

#### Question 16:

359 estimated upwards = 400

76 estimated downwards = 70

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

#### Answer:

472 estimated upwards = 500

158 estimated downwards = 100

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

#### Page No 16:

#### Question 17:

472 estimated upwards = 500

158 estimated downwards = 100

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

#### Answer:

680 estimated upwards = 700

164 estimated downwards = 100

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

#### Page No 16:

#### Question 18:

680 estimated upwards = 700

164 estimated downwards = 100

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

#### Answer:

255 estimated upwards = 300

350 estimated downwards = 300

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

#### Page No 16:

#### Question 19:

255 estimated upwards = 300

350 estimated downwards = 300

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

#### Answer:

356 estimated downwards = 300

278 estimated upwards = 300

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

#### Page No 16:

#### Question 20:

356 estimated downwards = 300

278 estimated upwards = 300

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

#### Answer:

472 estimated downwards = 400

76 estimated upwards = 80

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

#### Page No 16:

#### Question 21:

472 estimated downwards = 400

76 estimated upwards = 80

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

#### Answer:

578 estimated downwards = 500

369 estimated upwards = 400

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

#### Page No 16:

#### Question 1:

578 estimated downwards = 500

369 estimated upwards = 400

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

#### Answer:

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

#### Page No 16:

#### Question 2:

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

#### Answer:

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

#### Page No 16:

#### Question 3:

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

#### Answer:

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

#### Page No 16:

#### Question 4:

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

#### Answer:

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

#### Page No 16:

#### Question 5:

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

#### Answer:

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

#### Page No 16:

#### Question 6:

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

#### Answer:

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

#### Page No 16:

#### Question 7:

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

#### Answer:

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

#### Page No 16:

#### Question 8:

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

#### Answer:

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

#### Page No 16:

#### Question 9:

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

#### Answer:

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

#### Page No 16:

#### Question 10:

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

#### Answer:

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

#### Page No 19:

#### Question 1:

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

#### 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:

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

#### 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:

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

#### 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:

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

#### 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:

(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).

#### Answer:

Option c is correct.

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

#### Page No 20:

#### Question 2:

Option c is correct.

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

#### 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:

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.

#### 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:

Option c is correct.

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

Face value of 5 = 5

∴ Required difference = 50000 − 5 = 49995

#### Answer:

Option b is correct.

The smallest counting number is 1.

#### Page No 20:

#### Question 5:

Option b is correct.

The smallest counting number is 1.

#### 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:

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

#### 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:

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

#### 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:

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

#### Answer:

Option b is correct.

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

#### Page No 20:

#### Question 9:

Option b is correct.

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

#### Answer:

Option a is correct.

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

#### Page No 20:

#### Question 10:

Option a is correct.

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

#### Answer:

Option c is correct.

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

#### Page No 20:

#### Question 11:

Option c is correct.

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

#### Answer:

Option b is correct.

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

#### Page No 21:

#### Question 1:

Option b is correct.

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

#### 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:

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

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

#### 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:

(i) Eighty million sixty thousand four hundred nine

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

#### 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:

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

#### 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:

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

#### 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:

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.

#### 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:

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

#### 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:

(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

#### 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:

(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

#### Answer:

Successor of 999999 = 999999 + 1 = 1000000

Predecessor of 999999 = 999999 − 1 = 999998

∴ Required difference = 1000000 − 999998

= 2

#### Page No 21:

#### Question 10:

Successor of 999999 = 999999 + 1 = 1000000

Predecessor of 999999 = 999999 − 1 = 999998

∴ Required difference = 1000000 − 999998

= 2

#### 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:

(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.

#### 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:

Option (a) is correct.

X can be subtracted from L and C only.

i.e., XC = ( 100 − 10 ) = 90

#### Answer:

Option (b) is correct.

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

#### Page No 21:

#### Question 13:

Option (b) is correct.

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

#### Answer:

Option (b) is correct.

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

#### Page No 21:

#### Question 14:

Option (b) is correct.

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

#### 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:

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.

#### 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:

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

#### Answer:

Option (b) is correct.

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

#### Page No 21:

#### Question 17:

Option (b) is correct.

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

#### 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:

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.

#### Answer:

Option (c) is correct.

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

#### Page No 21:

#### Question 19:

Option (c) is correct.

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

#### 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:

**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.

#### 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:

(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.__

#### 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:

F

Place value of 5 in 85419 = 5000

Face value of 5 in 85419 = 5

∴ Their difference = 5000 − 5 = 4995

#### Answer:

T

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

#### Page No 22:

#### Question 23:

T

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

#### Answer:

T

Greatest five-digit number = 99999

Successor of 99999 = 99999 + 1 = 100000

#### Page No 22:

#### Question 24:

T

Greatest five-digit number = 99999

Successor of 99999 = 99999 + 1 = 100000

#### 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:

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.

#### Answer:

F

10 lakhs = 1 million

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