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#### 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 eitht
(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

(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

#### 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

(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

#### 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

(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)

#### 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

(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

#### Question 5:

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

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

#### Question 6:

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

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

#### Question 7:

How many 6-digit numbers are there in all?

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

#### Question 8:

How many 7-digit numbers are there in all?

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

#### Question 9:

How many thousands make a lakh?

One lakh (1,00,000) is equal to one hundred thousand (100 $×$ 1000).
Thus, one hundred thousands make a lakh.

#### Question 10:

How many thousands make a crore?

One crore (1,00,00,000) is equal to one hundred lakh (10,000 $×$ 1,000).
Thus, 10,000 thousands make a crore.

#### Question 11:

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

The given number is 738.
On reversing the digits of this number, we get 837.
∴ Required difference = 837 ‒ 738 = 99

#### Question 12:

What comes just after 9547999?

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

#### Question 13:

What comes just before 9900000?

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

#### Question 14:

What comes just before 10000000?

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

#### Question 15:

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

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

#### Question 16:

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

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

#### Question 17:

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

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

#### 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

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

#### 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

 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

#### Question 1:

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

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.

#### Question 2:

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

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.

#### Question 3:

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

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

#### Question 4:

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

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

#### Question 5:

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

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.

#### Question 6:

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

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

#### Question 7:

Arrange the following numbers in descending order:
63521047, 7354206, 63514759, 7355014, 102345680

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

#### Question 8:

Arrange the following numbers in descending order:
5032786, 23794206, 5032790, 23756819, 987876

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

#### Question 9:

Arrange the following numbers in descending order:
190909, 1808088, 16060666, 16007777, 181888, 1808090

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

#### Question 10:

Arrange the following numbers in descending order:
199988, 1704382, 200175, 1702497, 201200, 1712040

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

#### Question 11:

Arrange the following numbers in ascending order:
9873426, 24615019, 990357, 9874012, 24620010

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

#### Question 12:

Arrange the following numbers in ascending order:
56943201, 5694437, 56944000, 5695440, 56943300

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

#### Question 13:

Arrange the following numbers in ascending order:
700087, 8014257, 8015032, 10012458, 8014306

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

#### Question 14:

Arrange the following numbers in ascending order:
1020304, 893245, 980134, 1021403, 893425, 1020216

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

#### 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?

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

#### 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?

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

#### Question 3:

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

New number = Sum of 37684955 and 3615045
= 37684955 + 3615045
= 41300000

#### 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.

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

#### 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.

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

#### 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?

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

#### 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?

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

#### 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.

Total population of the city = 28756304
Number of males in the city = 16987059
∴ Number of females in the city =  28756304 ‒ 16987059
= 11769245

#### Question 9:

By how much is 13246510 larger than 4658642?

Required number = 13246510 ‒ 4658642 = 8587868
∴ 13246510 is larger than 4658642 by 8587868.

#### Question 10:

By how much is 5643879 smaller than one crore?

Required number = 1 crore ‒ 564387
= 10000000 ‒ 5643879
= 4356121

∴ 5643879 is smaller than one crore by 4356121.

#### Question 11:

What number must be subtracted from 11010101 to get 2635967?

11010101 ‒ required number = 2635967

Thus, required number = 11010101 ‒ 2635967
= 8374134

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

#### Question 12:

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

Sum of the two numbers = 10750308
One of the number = 8967519

∴ The other number = 10750308 ‒ 8967519
= 1782789

#### 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?

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

#### 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?

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

#### 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?

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

#### Question 16:

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

Cost of one chair = Rs 1485
Cost of 469 chairs = Rs 1485 $×$ 469
= Rs 696465

∴ Cost of 469 chairs is Rs 696465.

#### Question 17:

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

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.

#### Question 18:

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

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.

#### Question 19:

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

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 $×$ 156 = Rs 1365936

∴ Mr Bhaskar will save Rs 1365936 in 13 years.

#### Question 20:

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

Cost of one scooter = Rs 36725
Cost of 487 scooter = Rs 36725 $×$ 487
= Rs 17885075

∴ The cost of 487 scooters will be Rs 17885075.

#### Question 21:

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

Distance covered by the aeroplane in one hour = 1485 km
Distance covered in 72 hours = 1485 km $×$ 72 = 106920 km

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

#### Question 22:

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

Product of two numbers = 13421408
One of the number = 364

∴ The other number = 13421408 ÷ 364
= 36872

#### Question 23:

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

Cost of 36 flats = Rs 68251500
Cost of one flat = Rs 68251500 ÷ 36
= Rs 1895875

∴ Each flat costs Rs 1895875.

#### 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?

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

#### 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?

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

#### 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?

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 $×$ 16
= 2.75 m $×$ 16
= 44 m

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

#### 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?

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.

#### Question 28:

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

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 $×$ 14
= 2.75 kg $×$ 14
= 38.5 kg = 38 kg 500 g

#### 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?

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

#### 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?

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]

#### Question 1:

Round each of the following numbers to the nearest ten:
(a) 36
(b) 173
(c) 3869
(d) 16378

(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

#### Question 2:

Round each of the following numbers to the nearest hundred:
(a) 814
(b) 1254
(c) 43126
(d) 98165

(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

#### Question 3:

Round each of the following numbers to the nearest thousand:
(a) 793
(b) 4826
(c) 16719
(d) 28394

(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

#### Question 4:

Round each of the following numbers to the nearest ten thousand:
(a) 17514
(b) 26340
(c) 34890
(d) 272685

(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

#### Question 5:

Estimate each sum to the nearest ten:
(57 + 34)

57 estimated to the nearest ten = 60
34 estimated to the nearest ten = 30

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

#### Question 6:

Estimate each sum to the nearest ten:
(43 + 78)

43 estimated to the nearest ten = 40
78 estimated to the nearest ten = 80
∴ The required estimation = (40 + 80) = 120

#### Question 7:

Estimate each sum to the nearest ten:
(14 + 69)

14 estimated to the nearest ten = 10
69 estimated to the nearest ten = 70
∴ The required estimation = (10 + 70) = 80

#### Question 8:

Estimate each sum to the nearest ten:
(86 + 19)

86 estimated to the nearest ten = 90
19 estimated to the nearest ten = 20
∴ The required estimation = (90 + 20) = 110

#### Question 9:

Estimate each sum to the nearest ten:
(95 + 58)

95 estimated to the nearest ten = 100
58 estimated to the nearest ten = 60
∴ The required estimation = (100 + 60) = 160

#### Question 10:

Estimate each sum to the nearest ten:
(77 + 63)

77 estimated to the nearest ten = 80
63 estimated to the nearest ten = 60
∴ The required estimation = (80 + 60) = 140

#### Question 11:

Estimate each sum to the nearest ten:
(356 + 275)

356 estimated to the nearest ten = 360
275 estimated to the nearest ten = 280
∴ The required estimation = (360 + 280) = 640

#### Question 12:

Estimate each sum to the nearest ten:
(463 + 182)

463 estimated to the nearest ten = 460
182 estimated to the nearest ten = 180
∴ The required estimation = (460 + 180) = 640

#### Question 13:

Estimate each sum to the nearest ten:
(538 + 276)

538 estimated to the nearest ten = 540
276 estimated to the nearest ten = 280
∴ The required estimation = (540 + 280) = 820

#### Question 14:

Estimate each sum to the nearest hundred:
(236 + 689)

236 estimated to the nearest hundred = 200
689 estimated to the nearest hundred = 700
∴ The required estimation = (200 + 700) = 900

#### Question 15:

Estimate each sum to the nearest hundred:
(458 + 324)

458 estimated to the nearest hundred = 500
324 estimated to the nearest hundred = 300
∴ The required estimation = (500 + 300) = 800

#### Question 16:

Estimate each sum to the nearest hundred:
(170 + 395)

170 estimated to the nearest hundred = 200
395 estimated to the nearest hundred = 400
∴ The required estimation = (200 + 400) = 600

#### Question 17:

Estimate each sum to the nearest hundred:
(3280 + 4395)

3280 estimated to the nearest hundred = 3300
4395 estimated to the nearest hundred = 4400
∴ The required estimation = (3300 + 4400) = 7700

#### Question 18:

Estimate each sum to the nearest hundred:
(5130 + 1410)

5130 estimated to the nearest hundred = 5100
1410 estimated to the nearest hundred = 1400
∴ The required estimation = (5100 + 1400) = 6500

#### Question 19:

Estimate each sum to the nearest hundred:
(10083 + 29380)

10083 estimated to the nearest hundred = 10100
29380 estimated to the nearest hundred = 29400
∴ The required estimation = (10100 + 29400) = 39500

#### Question 20:

Estimate each sum to the nearest thousand:
(32836 + 16466)

32836 estimated to the nearest thousand = 33000
16466 estimated to the nearest thousand = 16000
∴ The required estimation = (33000 + 16000) = 49000

#### Question 21:

Estimate each sum to the nearest thousand:
(46703 + 11375)

46703 estimated to the nearest thousand = 47000
11375 estimated to the nearest thousand = 11000
∴ The required estimation = (47000 + 11000) = 58000

#### 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.

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

#### Question 23:

Estimate each difference to the nearest ten:
(53 − 18)

We have,
53 estimated to the nearest ten = 50
18 estimated to the nearest ten = 20
∴ The required estimation = (50 ‒ 20) = 30

#### Question 24:

Estimate each difference to the nearest ten:
(97 − 38)

100 estimated to the nearest ten = 100
38 estimated to the nearest ten = 40
∴ The required estimation = (100 ‒ 40) = 60

#### Question 25:

Estimate each difference to the nearest ten:
(409 − 148)

409 estimated to the nearest ten = 410
148 estimated to the nearest ten = 150
∴ The required estimation = (410 ‒ 150) = 260

#### Question 26:

Estimate each difference to the nearest hundred:
(678 − 215)

678 estimated to the nearest hundred = 700
215 estimated to the nearest hundred = 200
∴ The required estimation = (700 ‒ 200) = 500

#### Question 27:

Estimate each difference to the nearest hundred:
(957 − 578)

957 estimated to the nearest hundred = 1000
578 estimated to the nearest hundred = 600
∴ The required estimation = (1000 ‒ 600) = 400

#### Question 28:

Estimate each difference to the nearest hundred:
(7258 − 2429)

7258 estimated to the nearest hundred = 7300
2429 estimated to the nearest  hundred = 2400
∴ The required estimation = (7300 ‒ 2400) = 4900

#### Question 29:

Estimate each difference to the nearest hundred:
(5612 − 3095)

5612 estimated to the nearest hundred = 5600
3095 estimated to the nearest hundred = 3100
∴ The required estimation = (5600 ‒ 3100) = 2500

#### Question 30:

Estimate each difference to the nearest thousand:
(35863 − 27677)

35863 estimated to the nearest thousand = 36000
27677 estimated to the nearest  thousand = 28000
∴ The required estimation = (36000 ‒ 28000) = 8000

#### Question 31:

Estimate each difference to the nearest thousand:
(47005 − 39488)

47005 estimated to the nearest thousand = 47000
39488 estimated to the nearest  thousand = 39000
∴ The required estimation = (47000 ‒ 39000) = 8000

#### Question 1:

Estimate each of the following products by rounding off each number to the nearest ten:
38 × 63

38 estimated to the nearest ten = 40
63 estimated to the nearest ten = 60
∴ The required estimation = (40 $×$ 60) = 2400

#### Question 2:

Estimate each of the following products by rounding off each number to the nearest ten:
54 × 47

54 estimated to the nearest ten = 50
47 estimated to the nearest ten = 50
∴ The required estimation = (50 $×$ 50) = 2500

#### Question 3:

Estimate each of the following products by rounding off each number to the nearest ten:
28 × 63

28 estimated to the nearest ten = 30
63 estimated to the nearest ten = 60
∴ The required estimation = (30 $×$ 60) = 1800

#### Question 4:

Estimate each of the following products by rounding off each number to the nearest ten:
42 × 75

42 estimated to the nearest ten = 40
75 estimated to the nearest ten = 80
∴ The required estimation = (40 $×$ 80) = 3200

#### Question 5:

Estimate each of the following products by rounding off each number to the nearest ten:
64 × 58

64 estimated to the nearest ten = 60
58 estimated to the nearest ten = 60
∴ The required estimation = (60 $×$ 60) = 3600

#### Question 6:

Estimate each of the following products by rounding off each number to the nearest ten:
15 × 34

15 estimated to the nearest ten = 20
34 estimated to the nearest ten = 30
∴ The required estimation = (20 $×$ 30) = 600

#### Question 7:

Estimate each of the following products by rounding off each number to the nearest hundred:
376 × 123

376 estimated to the nearest hundred = 400
123 estimated to the nearest hundred = 100
∴ The required estimation = (400 $×$ 100) = 40000

#### Question 8:

Estimate each of the following products by rounding off each number to the nearest hundred:
264 × 147

264 estimated to the nearest hundred = 300
147 estimated to the nearest hundred = 100
∴ The required estimation = (300 $×$ 100) = 30000

#### Question 9:

Estimate each of the following products by rounding off each number to the nearest hundred:
423 × 158

423 estimated to the nearest hundred = 400
158 estimated to the nearest hundred = 200
∴ The required estimation = (400 $×$ 200) = 80000

#### Question 10:

Estimate each of the following products by rounding off each number to the nearest hundred:
509 × 179

509 estimated to the nearest hundred = 500
179 estimated to the nearest hundred = 200
∴ The required estimation = (500 $×$ 200) = 100000

#### Question 11:

Estimate each of the following products by rounding off each number to the nearest hundred:
392 × 138

392 estimated to the nearest hundred = 400
138 estimated to the nearest hundred = 100
∴ The required estimation = (400 $×$ 100) = 40000

#### Question 12:

Estimate each of the following products by rounding off each number to the nearest hundred:
271 × 339

271 estimated to the nearest hundred = 300
339 estimated to the nearest hundred = 300
∴ The required estimation = (300 $×$ 300) = 90000

#### Question 13:

Estimate each of the following products by rounding off the first number upwards and the second number downwards:
183 × 154

183 estimated upwards = 200
154 estimated downwards = 100
∴ The required product = (200 $×$ 100) = 20000

#### Question 14:

Estimate each of the following products by rounding off the first number upwards and the second number downwards:
267 × 146

267 estimated upwards = 300
146 estimated downwards = 100
∴ The required product = (300 $×$ 100) = 30000

#### Question 15:

Estimate each of the following products by rounding off the first number upwards and the second number downwards:
359 × 76

359 estimated upwards = 400
76 estimated downwards = 70
∴ The required product = (400 $×$ 70) =28000

#### Question 16:

Estimate each of the following products by rounding off the first number upwards and the second number downwards:
472 × 158

472 estimated upwards = 500
158 estimated downwards = 100
∴ The required product = (500 $×$ 100) = 50000

#### Question 17:

Estimate each of the following products by rounding off the first number upwards and the second number downwards:
680 × 164

680 estimated upwards = 700
164 estimated downwards = 100
∴ The required product = (700 $×$ 100) = 70000

#### Question 18:

Estimate each of the following products by rounding off the first number upwards and the second number downwards:
255 × 350

255 estimated upwards = 300
350 estimated downwards = 300
∴ The required product = (300 $×$ 300) = 90000

#### Question 19:

Estimate each of the following products by rounding off the first number downwards and the second number upwards:
356 × 278

356 estimated downwards = 300
278 estimated upwards = 300
∴ The required product = (300 $×$ 300) = 90000

#### Question 20:

Estimate each of the following products by rounding off the first number downwards and the second number upwards:
472 × 76

472 estimated downwards = 400
76 estimated upwards = 80
∴ The required product = (400 $×$ 80) = 32000

#### Question 21:

Estimate each of the following products by rounding off the first number downwards and the second number upwards:
578 × 369

578 estimated downwards = 500
369 estimated upwards = 400
∴  The required product = (500 $×$ 400) = 200000

#### Question 1:

Find the estimated quotient for each of the following:
87 ÷ 28

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

#### Question 2:

Find the estimated quotient for each of the following:
83 ÷ 17

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

#### Question 3:

Find the estimated quotient for each of the following:
75 ÷ 23

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

#### Question 4:

Find the estimated quotient for each of the following:
193 ÷ 24

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

#### Question 5:

Find the estimated quotient for each of the following:
725 ÷ 23

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

#### Question 6:

Find the estimated quotient for each of the following:
275 ÷ 25

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

#### Question 7:

Find the estimated quotient for each of the following:
633 ÷ 33

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

#### Question 8:

Find the estimated quotient for each of the following:
729 ÷ 29

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

#### Question 9:

Find the estimated quotient for each of the following:
858 ÷ 39

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

#### Question 10:

Find the estimated quotient for each of the following:
868 ÷ 38

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

#### 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

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

#### 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

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

#### 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

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

#### Question 4:

Show that each of the following is meaningless. Give reason in each case.
(i) VC
(ii) IL
(iii) VVII
(iv) IXX

(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).

#### Question 1:

The place value of 6 in the numeral 48632950 is
(a) 6
(b) 632950
(c) 600000
(d) 486

Option c is correct.

Place value of 6 = 6 lakhs = (6 $×$ 100000) = 600000

#### Question 2:

The face value of 4 in the numeral 89247605 is
(a) 4
(b) 40000
(c) 47605
(d) 8924

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.

#### Question 3:

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

Option c is correct.

Place value of 5 = 5 $×$ 10000 = 50000
Face value of 5 = 5

∴ Required difference = 50000 − 5 = 49995

#### Question 4:

The smallest counting number is
(a) 0
(b) 1
(c) 10
(d) none of these

Option b is correct.

The smallest counting number is 1.

#### Question 5:

How many 4-digit numbers are there?
(a) 8999
(b) 9000
(c) 8000
(d) none of these

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

#### Question 6:

How many 7-digit numbers are there?
(a) 8999999
(b) 9000000
(c) 10000000
(d) none of these

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

#### Question 7:

How many 8-digit numbers are there?
(a) 99999999
(b) 89999999
(c) 90000000
(d) none of these

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

#### Question 8:

What comes just before 1000000?
(a) 99999
(b) 999999
(c) 9999999
(d) none of these

Option b is correct.

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

#### Question 9:

Which of the following is not meaningful?
(a) VX
(b) XV
(c) XXV
(d) XXXV

Option a is correct.

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

#### Question 10:

Which of the following is not meaningful?
(a) CI
(b) CII
(c) IC
(d) XC

Option c is correct.

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

#### Question 11:

Which of the following is not meaningful?
(a) XIV
(b) XVV
(c) XIII
(d) XXII

Option b is correct.

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

#### Question 1:

Write each of the following numerals in words:
(i) 16, 06, 23, 708
(ii) 14, 23, 08, 915

(i) Sixteen crore six lakh twenty-three thousand seven hundred eight
(ii) Fourteen crore twenty-three lakh eight thousand nine hundred fifteen

#### Question 2:

Write each of the following numerals in words:
(i) 80, 060, 409
(ii) 234, 150, 319

(i) Eighty million sixty thousand four hundred nine
(ii) Two hundred thirty-four million one hundred fifty thousand three hundred nineteen

#### Question 3:

Arrange the following numbers in ascending order:
3903216, 19430124, 864572, 6940513, 16531079

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

#### Question 4:

Arrange the following numbers in descending order:
54796203, 4675238, 63240613, 5125648, 589623

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

#### Question 5:

How many 7-digit numbers are there in all?

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.

#### Question 6:

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

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

#### Question 7:

Write the Hindu-Arabic numeral for each of the following:
(i) CCXLII
(ii) CDLXV
(iii) LXXVI
(iv) DCCXLI
(v) XCIV
(vi) CXCIX

(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

#### Question 8:

Write the Roman numeral for each of the following:
(i) 84
(ii) 99
(iii) 145
(iv) 406
(v) 519

(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

#### Question 9:

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

Successor of 999999 = 999999 + 1 = 1000000
Predecessor of 999999 = 999999 − 1 = 999998
∴ Required difference = 1000000 − 999998
= 2

#### Question 10:

Round off each of the following to the nearest thousand:
(i) 1046
(ii) 973
(iii) 5624
(iv) 4368

(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.

#### Question 11:

Which of the  following Roman numerals is correct?
(a) XC
(b) XD
(c) DM
(d) VL

Option (a) is correct.

X can be subtracted from L and C only.
i.e., XC = ( 100 − 10 ) = 90

#### Question 12:

1 Lakh = ...... thousands.
(a) 10
(b) 100
(c) 1000
(d) none of these

Option (b) is correct.

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

#### Question 13:

No Roman numeral can be repeated more than ..... times.
(a) two
(b) three
(c) four
(d) none of these

Option (b) is correct.

No Roman numeral can be repeated more than three times.

#### Question 14:

How many times does the digit 9 occur between 1 and 100?
(a) 11
(b) 15
(c) 18
(d) 20

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.

#### Question 15:

(7268 − 2427) estimated to the nearest hundred is
(a) 4900
(b) 4800
(c) 4841
(d) 5000

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

#### Question 16:

One million = ...... .
(a) 1 lakh
(b) 10 lakh
(c) 100 lakh
(d) 1 crore

Option (b) is correct.

1 million (1,000,000) = 10 lakh (10 $×$ 1,00,000)

#### Question 17:

1512 when round off to the nearest hundred is
(a) 1600
(b) 1500
(c) 1510
(d) none of these

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.

#### 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

Option (c) is correct.

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

#### Question 19:

Write 86324805 separating periods in HIndu-Arabic system.

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.

#### 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 ...... .

(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.

#### 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.

F

Place value of 5 in 85419 = 5000
Face value of 5 in 85419 = 5
∴ Their difference = 5000 − 5 = 4995

#### Question 22:

Write 'T' for true and 'F' for false
In Roman numerals V, L and D are never subtracted.

T

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

#### Question 23:

Write 'T' for true and 'F' for false
The successor of the greatest 5-digit number is 100000.

T
Greatest five-digit number = 99999
Successor of 99999 = 99999 + 1 = 100000

#### Question 24:

Write 'T' for true and 'F' for false
The estimated value of 46,530 to the nearest hundred is 46500.

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.

#### Question 25:

Write 'T' for true and 'F' for false
100 lakhs make a million.