Table of Contents
Exercise 1A
Question 1:
Write the numeral for each of the following numbers:
(i) Nine thousand eighteen
(ii) Fifty-four thousand seventy-three
(iii) Three lakh two thousand five hundred six
(iv) Twenty lakh ten thousand eight
(v) Six crore five lakh fifty-seven
(vi) Two crore two lakh two thousand two hundred two
(vii) Twelve crore twelve lakh twelve thousand twelve
(viii) Fifteen crore fifty lakh twenty thousand sixty-eight
ANSWER:
(i) Nine thousand eighteen = 9018
(ii) Fifty-four thousand seventy-three = 54073
(iii) Three lakh two thousand five hundred six = 302506
(iv) Twenty lakh ten thousand eight = 2010008
(v) Six crore five lakh fifty-seven = 60500057
(vi) Two crore two lakh two thousand two hundred two = 20202202
(vii) Twelve crore twelve lakh twelve thousand twelve = 121212012
(viii) Fifteen crore fifty lakh twenty thousand sixty-eight = 155020068
Page No 5:
Question 2:
Write each of the following numbers in words:
(i) 63,005
(ii) 7,07,075
(iii) 34,20,019
(iv) 3,05,09,012
(v) 5,10,03,604
(vi) 6,18,05,008
(vii) 19,09,09,900
(viii) 6,15,30,807
(ix) 6,60,60,060
ANSWER:
(i) 63,005 = Sixty-three thousand five
(ii) 7,07,075 = Seven lakh seven thousand seventy-five
(iii) 34,20,019 = Thirty-four lakh twenty thousand nineteen
(iv) 3,05,09,012 = Three crore five lakh nine thousand twelve
(v) 5,10,03,604 = Five crore ten lakh three thousand six hundred four
(vi) 6,18,05,008 = Six crore eighteen lakh five thousand eight
(vii) 19,09,09,900 = Nineteen crore nine lakh nine thousand nine hundred
(viii) 6,15,30,807 = Six crore fifteen lakh thirty thousand eight hundred seven
(ix) 6,60,60,060 = Six crore sixty lakh sixty thousand sixty
Page No 5:
Question 3:
Write each of the following numbers in expanded form:
(i) 15,768
(ii) 3,08,927
(iii) 24,05,609
(iv) 5,36,18,493
(v) 6,06,06,006
(iv) 9,10,10,510
ANSWER:
(i) 15,768 = (1 x 10000) + (5 x 1000) + (7 x 100) + (6 x 10) + (8 x 1)
(ii) 3,08,927 = (3 x 100000) + (8 x 1000) + (9 x 100) + (2 x 10) + (7 x 1)
(iii) 24,05,609 = (2 x 1000000) + (4 x 100000) + (5 x 1000) + (6 x 100) + (9 x 1)
(iv) 5,36,18,493 = (5 x 10000000) + (3 x 1000000) + (6 x 100000) + (1 x 10000) + (8 x 1000) + (4 x 100) + (9 x 10) + (3 x 1)
(v) 6,06,06,006 = (6 x 10000000) + (6 x 100000) + (6 x 1000) + (6 x 1)
(iv) 9,10,10,510 = (9 x 10000000) + (1 x 1000000) + (1 x 10000) + (5 x 100) + (1 x 10)
Page No 6:
Question 4:
Write the corresponding numeral for each of the following:
(i) 6 × 10000 + 2 × 1000 + 5 × 100 + 8 × 10 + 1
(ii) 5 × 100000 + 8 × 10000 + 1 × 1000 + 6 × 100 + 2 × 10 + 3 × 1
(iii) 2 × 10000000 + 5 × 100000 + 7 × 1000 + 9 × 100 + 5 × 1
(iv) 3 × 1000000 + 4 × 100000 + 6 × 1000 + 5 × 100 + 7 × 1
ANSWER:
(i) 6 × 10000 + 2 × 1000 + 5 × 100 + 8 × 10 + 4 x 1 = 62,584
(ii) 5 × 100000 + 8 × 10000 + 1 × 1000 + 6 × 100 + 2 × 10 + 3 × 1 = 5,81,623
(iii) 2 × 10000000 + 5 × 100000 + 7 × 1000 + 9 × 100 + 5 × 1 = 2,05,07,905
(iv) 3 × 1000000 + 4 × 100000 + 6 × 1000 + 5 × 100 + 7 × 1 = 34,06,507
Page No 6:
Question 5:
Find the difference between the place values of the two nines in 79520986.
ANSWER:
The place value of 9 at ten lakhs place = 90 lakhs = 9000000
The place value of 9 at hundreds place = 9 hundreds = 900
∴∴ Required difference = (9000000 ‒ 900) = 8999100
Page No 6:
Question 6:
Find the difference between the place value and the face value of 7 in 27650934.
ANSWER:
The place value of 7 in 27650934 = 70 lakhs = 70,00,000
The face value of 7 in 27650934 = 7
∴∴ Required difference = (7000000 ‒ 7) = 69,99,993
Page No 6:
Question 7:
How many 6-digit numbers are there in all?
ANSWER:
The largest 6-digit number = 999999
The smallest 6-digit number = 100000
∴∴ Total number of 6-digit numbers = (999999 ‒ 100000) + 1
= 899999 + 1
= 900000
= 9 lakhs
Page No 6:
Question 8:
How many 7-digit numbers are there in all?
ANSWER:
The largest 7-digit number = 9999999
The smallest 7-digit number = 1000000
∴ Total number of 7-digit numbers = (9999999 – 1000000) + 1
= 8999999 + 1
= 9000000
= Ninety lakhs
Page No 6:
Question 9:
How many thousands make a lakh?
ANSWER:
One lakh (1,00,000) is equal to one hundred thousand (100 ×× 1000).
Thus, one hundred thousands make a lakh.
Page No 6:
Question 10:
How many thousands make a crore?
ANSWER:
One crore (1,00,00,000) is equal to one hundred lakh (10,000 ×× 1,000).
Thus, 10,000 thousands make a crore.
Page No 6:
Question 11:
Find the difference between the number 738 and that obtained on reversing its digits.
ANSWER:
The given number is 738.
On reversing the digits of this number, we get 837.
∴ Required difference = 837 ‒ 738 = 99
Page No 6:
Question 12:
What comes just after 9547999?
ANSWER:
The number just after 9547999 is 9547999 + 1 = 9548000.
Page No 6:
Question 13:
What comes just before 9900000?
ANSWER:
The number just before 9900000 is 9900000 ‒ 1 = 9899999.
Page No 6:
Question 14:
What comes just before 10000000?
ANSWER:
The number just before 10000000 is 10000000 ‒ 1 = 9999999.
Page No 6:
Question 15:
Write all 3-digit numbers using 2, 3, 4, taking each digit only once.
ANSWER:
The 3-digit numbers formed by 2, 3 and 4 by taking each digit only once are 234, 324, 243, 342, 423 and 432.
Page No 6:
Question 16:
Write the smallest number of different digits formed by using the digits 3, 1, 0, 5 and 7.
ANSWER:
The smallest number formed by using each of the given digits (i.e, 3,1,0,5 and 7) only once is 10357.
Page No 6:
Question 17:
Write the largest number of different digits formed by using the digits 2, 4, 0, 3, 6 and 9.
ANSWER:
The largest number formed by using each of the given digits only once is 964320.
Page No 6:
Question 18:
Rewrite each of the following numerals with proper commas, using the international place-value chart. Also, write the number name of each in the international system.
(i) 735821
(ii) 6057894
(iii) 56943821
(iv) 37502093
(v) 89350064
(vi) 90703006
ANSWER:
Representation of the numbers on the international place-value chart:
| Periods | Millions | Thousands | Ones | ||||||
| Place | Hundred millions | Ten millions | Millions | Hundred thousands | Ten thousands | Thousands | Hundreds | Tens | Ones |
| HM | TM | M | H Th | T Th | Th | H | T | O | |
| (i) | 7 | 3 | 5 | 8 | 2 | 1 | |||
| (ii) | 6 | 0 | 5 | 7 | 8 | 9 | 4 | ||
| (iii) | 5 | 6 | 9 | 4 | 3 | 8 | 2 | 1 | |
| (iv) | 3 | 7 | 5 | 0 | 2 | 0 | 9 | 3 | |
| (v) | 8 | 9 | 3 | 5 | 0 | 0 | 6 | 4 | |
| (vi) | 9 | 0 | 7 | 0 | 3 | 0 | 0 | 6 | |
| Crore | Ten lakhs | Lakhs | Ten Thousand | Thousand | Hundred | Tens | Ones |
The number names of the given numbers in the international system:
(i) 735,821 = Seven hundred thirty-five thousand eight hundred twenty-one
(ii) 6,057,894 = Six million fifty-seven thousand eight hundred ninety-four
(iii) 56,943,821 = Fifty-six million nine hundred forty-three thousand eight hundred twenty-one
(iv) 37,502,093 = Thirty-seven million five hundred two thousand ninety-three
(v) 89,350,064 = Eighty-nine millions three hundred fifty thousand sixty-four
(vi) 90,703,006 = Ninety million seven hundred three thousand and six
Page No 6:
Question 19:
Write each of the following in figures in the international place-value chart:
(i) Thirty million one hundred five thousand sixty-three
(ii) Fifty-two million two hundred five thousand six
(iii) Five million five thousand five
ANSWER:
| Periods | Millions | Thousands | Ones | ||||||
| Place | Hundred millions | Ten millions | Millions | Hundred thousands | Ten thousands | Thousands | Hundreds | Tens | Ones |
| HM | TM | M | H Th | T Th | Th | H | T | O | |
| (i) | 3 | 0 | 1 | 0 | 5 | 0 | 6 | 3 | |
| (ii) | 5 | 2 | 2 | 0 | 5 | 0 | 0 | 6 | |
| (iii) | 5 | 0 | 0 | 5 | 0 | 0 | 5 |
Page No 8:
Question 1:
Fill in each of the following boxes with the correct symbol > or <:
1003467 9879651003467 987965
ANSWER:
1003467 >> 987965
We know that a 7-digit number is always greater than a 6-digit number. Since 1003467 is a 7-digit number and 987965 is a 6-digit number, 1003467 is greater than 987965.
Page No 8:
Question 2:
Fill in each of the following boxes with the correct symbol > or <:
3572014 102354013572014 10235401
ANSWER:
3572014 << 10235401
We know that a 7-digit number is always less than an 8-digit number. Since 3572014 is a 7-digit number and 10235401 is an 8-digit number, 3572014 is less than 10235401.
Page No 8:
Question 3:
Fill in each of the following boxes with the correct symbol > or <:
3254790 32601523254790 3260152
ANSWER:
Both the numbers have the digit 3 at the ten lakhs places.
Also, both the numbers have the digit 2 at the lakhs places.
However, the digits at the ten thousands place in 3254790 and 3260152 are 5 and 6, respectively.
Clearly, 5 < 6
∴ 3254790 < 3260152
Page No 8:
Question 4:
Fill in each of the following boxes with the correct symbol > or <:
10357690 1124356710357690 11243567
ANSWER:
Both have the digit 1 at the crores places.
However, the digits at the ten lakhs places in 10357690 and 11243567 are 0 and 1, respectively.
Clearly, 0 < 1
∴ 10357690 < 11243567
Page No 8:
Question 5:
Fill in each of the following boxes with the correct symbol > or <:
27596381 796541227596381 7965412
ANSWER:
27596381 > 7965412
We know that an 8-digit number is always greater than a 7-digit number. Since 7965412 is a 7-digit number and 27596381 is an 8-digit number, 27596381 is greater than 7965412.
Page No 8:
Question 6:
Fill in each of the following boxes with the correct symbol > or <:
47893501 4789402147893501 47894021
ANSWER:
Both the numbers have the same digits, namely 4, 7, 8 and 9, at the crores, ten lakhs, lakhs and ten thousands places, respectively.
However, the digits at the thousands place in 47893501 and 47894021 are 3 and 4, respectively.
Clearly, 3 < 4
∴ 47893501 < 47894021
Page No 8:
Question 7:
Arrange the following numbers in descending order:
63521047, 7354206, 63514759, 7355014, 102345680
ANSWER:
102345680 is a 9-digit number.
63521047 and 63514759 are both 8-digit numbers.
Both the numbers have the same digits, namely 6, 3 and 5, at the crores, ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in 63521047 and 63514759 are 2 and 1, respectively.
Clearly, 2 > 1
∴ 63521047 > 63514759
7355014 and 7354206 are both 7-digit numbers.
Both the numbers have the same digits, namely 7, 3 and 5 at the crores, ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in 7355014 and 7354206 are 5 and 4, respectively.
Clearly, 5> 4
∴ 7355014 > 7354206
The given numbers in descending order are:
102345680 > 63521047 > 63514759 > 7355014 > 7354206
Page No 8:
Question 8:
Arrange the following numbers in descending order:
5032786, 23794206, 5032790, 23756819, 987876
ANSWER:
23794206 and 23756819 are both 8-digit numbers.
Both the numbers have the same digits, namely 2, 3 and 7 at the crores, ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in 23794206 and 23756819 are 9 and 5, respectively.
Clearly, 9 > 5
∴ 23794206 > 23756819
5032790 and 5032786 are both 7-digit numbers.
Both the numbers have the same digits, namely 5, 0, 3, 2 and 7, at the ten lakhs, lakhs, ten thousands, thousands and hundreds places, respectively.
However, the digits at the tens place in 5032790 and 5032786 are 9 and 8, respectively.
Clearly, 9 > 8
∴ 5032790 > 5032786
987876 is a 6-digit number.
The given numbers in descending order are:
23794206 > 23756819 > 5032790 > 5032786 > 987876
Page No 8:
Question 9:
Arrange the following numbers in descending order:
190909, 1808088, 16060666, 16007777, 181888, 1808090
ANSWER:
16060666 and 16007777 are both 8-digit numbers.
Both the numbers have the same digits, namely 1, 6 and 0, at the crores, ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in 16060666 and 16007777 are 6 and 0, respectively.
Clearly, 6 > 0
∴ 16060666 > 16007777
1808090 and 1808088 are both 7-digit numbers.
Both the numbers have the same digits , namely 1, 8, 0, 8 and 0, at the ten lakhs, lakhs, ten thousands, thousands and hundreds places, respectively.
However, the digits at the tens place in 1808090 and 1808088 are 9 and 8, respectively.
Clearly, 9 > 8
∴ 1808090 > 1808088
190909 and 181888 are both 6-digit numbers.
Both the numbers have the same digit, 1, at the lakhs place.
However, the digits at the ten thousands place in 190909 and 181888 are 9 and 8, respectively.
Clearly, 9 > 8
∴ 190909 > 181888
Thus, the given numbers in descending order are:
16060666 > 16007777 > 1808090 > 1808088 >190909 > 181888
Page No 8:
Question 10:
Arrange the following numbers in descending order:
199988, 1704382, 200175, 1702497, 201200, 1712040
ANSWER:
1712040, 1704382 and 1702497 are all 7-digit numbers.
The three numbers have the same digits, namely 1 and 7, at the ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in 1712040, 1704382 and 1702497 are 1, 0 and 0.
∴ 1712040 is the largest.
Of the other two numbers, the respective digits at the thousands place are 4 and 2.
Clearly, 4 > 2
∴ 1704382 > 1702497
201200, 200175 and 199988 are all 6-digit numbers.
At the lakhs place, we have 2 > 1.
So, 199988 is the smallest of the three numbers.
The other two numbers have the same digits, namely 2 and 0, at the lakhs and ten thousands places, respectively.
However, the digits at the thousands place in 201200 and 200175 are 1 and 0, respectively.
Clearly, 1 > 0
∴ 201200 > 200175
The given numbers in descending order are:
1712040 > 1704382 > 1702497 > 201200 > 200175 > 199988
Page No 8:
Question 11:
Arrange the following numbers in ascending order:
9873426, 24615019, 990357, 9874012, 24620010
ANSWER:
990357 is 6 digit number.
9873426 and 9874012 are both 7-digit numbers.
Both the numbers have the same digits, namely 9, 8 and 7, at the ten lakhs, lakhs and ten thousands places, respectively.
However, the digits at the thousands place in 9873426 and 9874012 are 3 and 4, respectively.
Clearly, 4 < 7
∴ 9873426 < 9874012
24615019 and 24620010 are both 8-digit numbers.
Both the numbers have the same digits, namely 2, 4 and 6, at the crores, ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in 24615019 and 24620010 are 2 and 1, respectively.
Clearly, 1 < 2
∴ 24615019 < 24620010
The given numbers in ascending order are:
990357 < 9873426 < 9874012 < 24615019 < 24620010
Page No 8:
Question 12:
Arrange the following numbers in ascending order:
56943201, 5694437, 56944000, 5695440, 56943300
ANSWER:
5694437 and 5695440 are both 7-digit numbers.
Both have the same digit, i.e., 5 at the ten lakhs place.
Both have the same digit, i.e., 6 at the lakhs place.
Both have the same digit, i.e., 9 at the ten thousands place.
However, the digits at the thousand place in 5694437 and 5695440 are 4 and 5, respectively.
Clearly, 4 < 5
∴ 5694437 < 5695440
56943201, 56943300 and 56944000 are all 8-digit numbers.
They have the same digit, i.e., 5 at the crores place.
They have the same digit, i.e., 6 at the ten lakhs place.
They have the same digit, i.e., 9 at the lakhs place.
They have the same digit, i.e., 4 at the ten thousands place.
However, at the thousands place, one number has 4 while the others have 3 .
∴ 56944000 is the largest.
The other two numbers have 3 and 2 at their hundreds places.
Clearly, 2 <3
∴ 56943201 < 56943300
The given numbers in ascending order are:
5694437 < 5695440 < 56943201 < 56943300 < 56944000
Page No 8:
Question 13:
Arrange the following numbers in ascending order:
700087, 8014257, 8015032, 10012458, 8014306
ANSWER:
700087 is 6-digit number.
8014257, 8014306 and 8015032 are all 7-digit numbers.
They have the same digits, namely 8, 0 and 1, at the ten lakhs, lakhs and ten thousands places, respectively.
But, at the thousands place, one number has 5 while the other two numbers have 4.
Here, 801503 is the largest.
The other two numbers have 2 and 3 at their hundreds places.
Clearly, 2 < 3
∴ 8014306 < 8015032
10012458 is an 8-digit number.
The given numbers in ascending order are:
700087 < 8014257 < 8014306 < 8015032 < 10012458
Page No 8:
Question 14:
Arrange the following numbers in ascending order:
1020304, 893245, 980134, 1021403, 893425, 1020216
ANSWER:
893245, 893425 and 980134 are all 6-digit numbers.
Among the three, 980134 is the largest.
The other two numbers have the same digits, namely 8, 9 and 3, at the lakhs, ten thousands and thousands places, respectively.
However, the digits at the hundreds place in 893245 and 893425 are 2 and 4, respectively.
Clearly, 2 < 4
∴ 893245 < 893425
1020216, 1020304 and 1021403 are all 7-digit numbers.
They have the same digits, namely 1, 0 and 2, at the ten lakhs, lakhs and ten thousands places, respectively.
At the thousands place, 1021403 has 1.
The other two numbers have the digits 2 and 3 at their hundreds places.
Clearly, 2 < 3
∴ 1020216 < 1020304
The given numbers in ascending order are:
893245 < 893425 < 980134 < 1020216 < 1020304 < 1021403
Exercise 1B
Question 1:
The number of persons who visited the holy shrine of Mata Vaishno Devi during last two consecutive years was 13789509 and 12976498 respectively. How many persons visited the shrine during these two years?
ANSWER:
Number of persons who visited the holy shrine in the first year = 13789509
Number of persons who visited the holy shrine in the second year = 12976498
∴ Number of persons who visited the holy shrine during these two years = 13789509 + 12976498 = 26766007
Page No 11:
Question 2:
Last year, three sugar factories in a town produced 24809565 bags, 18738576 bags and 9564568 bags of sugar respectively. How many bags were produced by all the three factories during last year?
ANSWER:
Bags of sugar produced by the first factory in last year = 24809565
Bags of sugar produced by the second factory in last year = 18738576
Bags of sugar produced by the third sugar factory in last year = 9564568
∴ Total number of bags of sugar were produced by the three factories during last year = 24809565 + 18738576 + 9564568
= 53112709
Page No 11:
Question 3:
A number exceeds 37684955 by 3615045. What is that number?
ANSWER:
New number = Sum of 37684955 and 3615045
= 37684955 + 3615045
= 41300000
Page No 11:
Question 4:
There were three candidates in an election. They received 687905 votes, 495086 votes and 93756 votes respectively. The number of invalid votes was 13849. If 25467 persons did not vote, find how many votes were registered.
ANSWER:
Total number of votes received by the three candidates = 687905 + 495086 + 93756 = 1276747
Number of invalid votes = 13849
Number of persons who did not vote = 25467
∴ Total number of registered voters = 1276747 + 13849 + 25467
= 1316063
Page No 11:
Question 5:
A survey conducted on an Indian state shows that 1623546 people have only primary education; 9768678 people have secondary education; 6837954 people have higher education and 2684536 people are illiterate. If the number of children below the age of school admission is 698781, find the total population of the state.
ANSWER:
People who had only primary education = 1623546
People who had secondary education = 9768678
People who had higher education = 6837954
Illiterate people in the state = 2684536
Children below the age of school admission = 698781
∴ Total population of the state = 1623546 + 9768678 + 6837954 + 2684536 + 698781
= 21613495
Page No 11:
Question 6:
In a particular year a company produced 8765435 bicycles. Next year, the number of bicycles produced was 1378689 more than those produced in the preceding year.
How many bicycles were produced during the second year?
How many bicycles were produced during these two years?
ANSWER:
Bicycles produced by the company in the first year = 8765435
Bicycles produced by the company in the second year = 8765435 + 1378689
= 10144124
∴ Total number of bicycles produced during these two years = 8765435 + 10144124
= 18909559
Page No 11:
Question 7:
The sale receipt of a company during a year was Rs 20956480. Next year, it increased by Rs 6709570. What was the total sale receipt of the company during these two years?
ANSWER:
Sale receipts of a company during the first year = Rs 20956480
Sale receipts of the company during the second year = Rs 20956480 + Rs 6709570
= Rs 27666050
∴ Total number of sale receipts of the company during these two years = Rs 20956480 + Rs 27666050
= Rs 48622530
Page No 11:
Question 8:
The total population of a city is 28756304. If the number of males is 16987059, find the number of females in the city.
ANSWER:
Total population of the city = 28756304
Number of males in the city = 16987059
∴ Number of females in the city = 28756304 ‒ 16987059
= 11769245
Page No 12:
Question 9:
By how much is 13246510 larger than 4658642?
ANSWER:
Required number = 13246510 ‒ 4658642 = 8587868
∴ 13246510 is larger than 4658642 by 8587868.
Page No 12:
Question 10:
By how much is 5643879 smaller than one crore?
ANSWER:
Required number = 1 crore ‒ 564387
= 10000000 ‒ 5643879
= 4356121
∴ 5643879 is smaller than one crore by 4356121.
Page No 12:
Question 11:
What number must be subtracted from 11010101 to get 2635967?
ANSWER:
11010101 ‒ required number = 2635967
Thus, required number = 11010101 ‒ 2635967
= 8374134
∴ The number 8374134 must be subtracted from 11010101 to get 2635967.
Page No 12:
Question 12:
The sum of two numbers is 10750308. If one of them is 8967519, what is the other number?
ANSWER:
Sum of the two numbers = 10750308
One of the number = 8967519
∴ The other number = 10750308 ‒ 8967519
= 1782789
Page No 12:
Question 13:
A man had Rs 20000000 with him. He spent Rs 13607085 on buying a school building. How much money is left with him?
ANSWER:
Initial amount with the man = Rs 20000000
Amount spent on buying a school building = Rs 13607085
∴ Amount left with the man = Rs 20000000 ‒ Rs 13607085
= Rs 6392915
Page No 12:
Question 14:
A society needed Rs 18536000 to buy a property. It collected Rs 7253840 as membership fee, took a loan of Rs 5675450 from a bank and collected Rs 2937680 as donation. How much is the society still short of?
ANSWER:
Money need by the society to buy the property = Rs 18536000
Amount collected as membership fee = Rs 7253840
Amount taken on loan from the bank = Rs 5675450
Amount collected as donation = Rs 2937680
∴ Amount of money short = Rs 18536000 ‒ (Rs 7253840 + Rs 5675450 + Rs 2937680)
= Rs 18536000 ‒ Rs 15866970
= Rs 2669030
Page No 12:
Question 15:
A man had Rs 10672540 with him. He gave Rs 4836980 to his wife, Rs 3964790 to his son and the rest to his daughter. How much money was received by the daughter?
ANSWER:
Initial amount with the man = Rs 10672540
Amount given to his wife = Rs 4836980
Amount given to his son = Rs 3964790
∴ Amount received by his daughter = Rs 10672540 ‒ (Rs 4836980 + Rs 3964790)
= Rs 10672540 ‒ Rs 8801770
= Rs 1870770
Page No 12:
Question 16:
The cost of a chair is Rs 1485. How much will 469 such chairs cost?
ANSWER:
Cost of one chair = Rs 1485
Cost of 469 chairs = Rs 1485 ×× 469
= Rs 696465
∴ Cost of 469 chairs is Rs 696465.
Page No 12:
Question 17:
How much money was collected from 1786 students of a school for a charity show if each student contributed Rs 625?
ANSWER:
Contribution from one student for the charity program = Rs 625
Contribution from 1786 students = Rs 625 x 1786 = Rs 1116250
∴ Rs 1116250 was collected from 1786 students for the charity program.
Page No 12:
Question 18:
A factory produces 6985 screws per day. How many screws will it produce in 358 days?
ANSWER:
Number of screws produced by the factory in one day = 6985
Number of screws produced in 358 days = 6985 x 358
= 2500630
∴ The factory will produce 2500630 screws in 358 days.
Page No 12:
Question 19:
Mr Bhaskar saves Rs 8756 every month. How much money will he save in 13 years?
ANSWER:
We know that
1 year = 12 months
13 years = 13 x 12 = 156 months
Now, we have:
Amount saved by Mr Bhaskar in one month = Rs 8756
Amount saved in 156 months = Rs 8756 ×× 156 = Rs 1365936
∴ Mr Bhaskar will save Rs 1365936 in 13 years.
Page No 12:
Question 20:
A scooter costs Rs 36725. How much will 487 such scooters cost?
ANSWER:
Cost of one scooter = Rs 36725
Cost of 487 scooter = Rs 36725 ×× 487
= Rs 17885075
∴ The cost of 487 scooters will be Rs 17885075.
Page No 12:
Question 21:
An aeroplane covers 1485 km in 1 hour. How much distance will it cover in 72 hours?
ANSWER:
Distance covered by the aeroplane in one hour = 1485 km
Distance covered in 72 hours = 1485 km ×× 72 = 106920 km
∴ The distance covered by the aeroplane in 72 hours will be 106920 km.
Page No 12:
Question 22:
The product of two numbers is 13421408. If one of the numbers is 364, find the other.
ANSWER:
Product of two numbers = 13421408
One of the number = 364
∴ The other number = 13421408 ÷ 364
= 36872
Page No 12:
Question 23:
If 36 flats cost Rs 68251500, what is the cost of each such flat?
ANSWER:
Cost of 36 flats = Rs 68251500
Cost of one flat = Rs 68251500 ÷ 36
= Rs 1895875
∴ Each flat costs Rs 1895875.
Page No 12:
Question 24:
The mass of a cylinder filled with gas is 30 kg 250 g and the mass of the empty cylinder is 14 kg 480 g. How much is the mass of the gas contained in it?
ANSWER:
We know that 1 kg = 1000 g
Now, mass of the gas-filled cylinder = 30 kg 250 g = 30.25 kg
Mass of an empty cylinder = 14 kg 480 g = 14.48 kg
∴ Mass of the gas contained in the cylinder = 30.25 kg ‒ 14.48 kg
= 15.77 kg = 15 kg 770 g
Page No 12:
Question 25:
From a cloth 5 m long, a piece of length 2 m 85 cm is cut off. What is the length of the remaining piece?
ANSWER:
We know that 1 m = 100 cm
Length of the cloth = 5 m
Length of the piece cut off from the cloth = 2 m 85 cm
∴ Length of the remaining piece of cloth = 5 m ‒ 2.85 m
= 2.15 m = 2 m 15 cm
Page No 12:
Question 26:
In order to make a shirt, a length of 2 m 75 cm of cloth is needed. How much length of the cloth will be required for 16 such shirts?
ANSWER:
We know that 1 m = 100 cm
Now, length of the cloth required to make one shirt = 2 m 75 cm
Length of the cloth required to make 16 such shirts = 2 m 75 cm ×× 16
= 2.75 m ×× 16
= 44 m
∴ The length of the cloth required to make 16 shirts will be 44 m.
Page No 12:
Question 27:
For making 8 trousers of the same size, 14 m 80 cm of cloth is needed. How much cloth will be required for each such trouser?
ANSWER:
We know that 1 m = 100 cm
Cloth needed for making 8 trousers = 14 m 80 cm
Cloth needed for making 1 trousers = 14 m 80 cm ÷ 8
= 14 .8 m ÷ 8
= 1.85 m = 1 m 85 cm
∴ 1 m 85 cm of cloth will be required to make one shirt.
Page No 12:
Question 28:
The mass of a brick is 2 kg 750 g. What is the total mass of 14 such bricks?
ANSWER:
We know that 1 kg = 1000 g
Now, mass of one brick = 2 kg 750 g
∴ Mass of 14 such bricks = 2 kg 750 g ×× 14
= 2.75 kg ×× 14
= 38.5 kg = 38 kg 500 g
Page No 12:
Question 29:
The total mass of 8 packets, each of the same size, is 10 kg 600 g. What is the mass of each such packet?
ANSWER:
We know that 1 kg = 1000 g
Now, total mass of 8 packets of the same size = 10 kg 600 g
∴ Mass of one such packet = 10 kg 600 g ÷ 8
= 10.6 kg ÷ 8
= 1.325 kg = 1 kg 325 g
Page No 12:
Question 30:
A rope of length 10 m has been divided into 8 pieces of the same length. What is the length of each piece?
ANSWER:
Length of the rope divided into 8 equal pieces = 10 m
Length of one piece = 10 m ÷ 8
= 1.25 m = 1 m 25 cm [∵ 1 m = 100 cm]
Page No 14:
Exercise 1C
Question 1:
Round each of the following numbers to the nearest ten:
(a) 36
(b) 173
(c) 3869
(d) 16378
ANSWER:
(i) In 36, the ones digit is 6 > 5.
∴ The required rounded number = 40
(ii) In 173, the ones digit is 3 < 5.
∴ The required rounded number = 170
(iii) In 3869, the ones digit is 9 > 5.
∴ The required rounded number = 3870
(iv) In 16378, the ones digit is 8 > 5.
∴ The required rounded number = 16380
Page No 14:
Question 2:
Round each of the following numbers to the nearest hundred:
(a) 814
(b) 1254
(c) 43126
(d) 98165
ANSWER:
(i) In 814, the tens digit is 1 < 5.
∴ The required rounded number = 800
(ii) In 1254, the tens digit is 5 = 5
∴ The required rounded number = 1300
(iii) In 43126, the tens digit is 2 < 5
∴ The required rounded number = 43100
(iv) In 98165, the tens digit is 6 > 5
∴ The required rounded number = 98200
Page No 14:
Question 3:
Round each of the following numbers to the nearest thousand:
(a) 793
(b) 4826
(c) 16719
(d) 28394
ANSWER:
(i) In 793, the hundreds digit is 7 > 5
∴ The required rounded number = 1000
(ii) In 4826, the hundreds digit is 8 > 5
∴ The required rounded number = 5000
(iii) In 16719, the hundreds digit is 7 > 5
∴ The required rounded number = 17000
(iv) In 28394, the hundreds digit is 3 < 5
∴ The required rounded number = 28000
Page No 14:
Question 4:
Round each of the following numbers to the nearest ten thousand:
(a) 17514
(b) 26340
(c) 34890
(d) 272685
ANSWER:
(i) In 17514, the thousands digit is 7 > 5
∴ The required rounded number = 20000
(ii) In 26340, the thousands digit is 6 > 5
∴ The required rounded number = 30000
(iii) In 34890, the thousands digit is 4 < 5
∴ The required rounded number = 30000
(iv) In 272685, the thousands digit is 2 < 5
∴ The required rounded number = 270000
Page No 14:
Question 5:
Estimate each sum to the nearest ten:
(57 + 34)
ANSWER:
57 estimated to the nearest ten = 60
34 estimated to the nearest ten = 30
∴ The required estimation = (60 + 30) = 90
Page No 14:
Question 6:
Estimate each sum to the nearest ten:
(43 + 78)
ANSWER:
43 estimated to the nearest ten = 40
78 estimated to the nearest ten = 80
∴ The required estimation = (40 + 80) = 120
Page No 14:
Question 7:
Estimate each sum to the nearest ten:
(14 + 69)
ANSWER:
14 estimated to the nearest ten = 10
69 estimated to the nearest ten = 70
∴ The required estimation = (10 + 70) = 80
Page No 14:
Question 8:
Estimate each sum to the nearest ten:
(86 + 19)
ANSWER:
86 estimated to the nearest ten = 90
19 estimated to the nearest ten = 20
∴ The required estimation = (90 + 20) = 110
Page No 14:
Question 9:
Estimate each sum to the nearest ten:
(95 + 58)
ANSWER:
95 estimated to the nearest ten = 100
58 estimated to the nearest ten = 60
∴ The required estimation = (100 + 60) = 160
Page No 14:
Question 10:
Estimate each sum to the nearest ten:
(77 + 63)
ANSWER:
77 estimated to the nearest ten = 80
63 estimated to the nearest ten = 60
∴ The required estimation = (80 + 60) = 140
Page No 14:
Question 11:
Estimate each sum to the nearest ten:
(356 + 275)
ANSWER:
356 estimated to the nearest ten = 360
275 estimated to the nearest ten = 280
∴ The required estimation = (360 + 280) = 640
Page No 14:
Question 12:
Estimate each sum to the nearest ten:
(463 + 182)
ANSWER:
463 estimated to the nearest ten = 460
182 estimated to the nearest ten = 180
∴ The required estimation = (460 + 180) = 640
Page No 14:
Question 13:
Estimate each sum to the nearest ten:
(538 + 276)
ANSWER:
538 estimated to the nearest ten = 540
276 estimated to the nearest ten = 280
∴ The required estimation = (540 + 280) = 820
Page No 14:
Question 14:
Estimate each sum to the nearest hundred:
(236 + 689)
ANSWER:
236 estimated to the nearest hundred = 200
689 estimated to the nearest hundred = 700
∴ The required estimation = (200 + 700) = 900
Page No 14:
Question 15:
Estimate each sum to the nearest hundred:
(458 + 324)
ANSWER:
458 estimated to the nearest hundred = 500
324 estimated to the nearest hundred = 300
∴ The required estimation = (500 + 300) = 800
Page No 14:
Question 16:
Estimate each sum to the nearest hundred:
(170 + 395)
ANSWER:
170 estimated to the nearest hundred = 200
395 estimated to the nearest hundred = 400
∴ The required estimation = (200 + 400) = 600
Page No 15:
Question 17:
Estimate each sum to the nearest hundred:
(3280 + 4395)
ANSWER:
3280 estimated to the nearest hundred = 3300
4395 estimated to the nearest hundred = 4400
∴ The required estimation = (3300 + 4400) = 7700
Page No 15:
Question 18:
Estimate each sum to the nearest hundred:
(5130 + 1410)
ANSWER:
5130 estimated to the nearest hundred = 5100
1410 estimated to the nearest hundred = 1400
∴ The required estimation = (5100 + 1400) = 6500
Page No 15:
Question 19:
Estimate each sum to the nearest hundred:
(10083 + 29380)
ANSWER:
10083 estimated to the nearest hundred = 10100
29380 estimated to the nearest hundred = 29400
∴ The required estimation = (10100 + 29400) = 39500
Page No 15:
Question 20:
Estimate each sum to the nearest thousand:
(32836 + 16466)
ANSWER:
32836 estimated to the nearest thousand = 33000
16466 estimated to the nearest thousand = 16000
∴ The required estimation = (33000 + 16000) = 49000
Page No 15:
Question 21:
Estimate each sum to the nearest thousand:
(46703 + 11375)
ANSWER:
46703 estimated to the nearest thousand = 47000
11375 estimated to the nearest thousand = 11000
∴ The required estimation = (47000 + 11000) = 58000
Page No 15:
Question 22:
Estimate each sum to the nearest thousand:
There are 54 balls in box A and 79 balls in box B. Estimate the total number of balls in both the boxes taken together.
ANSWER:
Number of balls in box A = 54
Number of balls in box B = 79
Estimated number of balls in box A = 50
Estimated number of balls in box B = 80
∴ Total estimated number of balls in both the boxes = (50 + 80) = 130
Page No 15:
Question 23:
Estimate each difference to the nearest ten:
(53 − 18)
ANSWER:
We have,
53 estimated to the nearest ten = 50
18 estimated to the nearest ten = 20
∴ The required estimation = (50 ‒ 20) = 30
Page No 15:
Question 24:
Estimate each difference to the nearest ten:
(97 − 38)
ANSWER:
100 estimated to the nearest ten = 100
38 estimated to the nearest ten = 40
∴ The required estimation = (100 ‒ 40) = 60
Page No 15:
Question 25:
Estimate each difference to the nearest ten:
(409 − 148)
ANSWER:
409 estimated to the nearest ten = 410
148 estimated to the nearest ten = 150
∴ The required estimation = (410 ‒ 150) = 260
Page No 15:
Question 26:
Estimate each difference to the nearest hundred:
(678 − 215)
ANSWER:
678 estimated to the nearest hundred = 700
215 estimated to the nearest hundred = 200
∴ The required estimation = (700 ‒ 200) = 500
Page No 15:
Question 27:
Estimate each difference to the nearest hundred:
(957 − 578)
ANSWER:
957 estimated to the nearest hundred = 1000
578 estimated to the nearest hundred = 600
∴ The required estimation = (1000 ‒ 600) = 400
Page No 15:
Question 28:
Estimate each difference to the nearest hundred:
(7258 − 2429)
ANSWER:
7258 estimated to the nearest hundred = 7300
2429 estimated to the nearest hundred = 2400
∴ The required estimation = (7300 ‒ 2400) = 4900
Page No 15:
Question 29:
Estimate each difference to the nearest hundred:
(5612 − 3095)
ANSWER:
5612 estimated to the nearest hundred = 5600
3095 estimated to the nearest hundred = 3100
∴ The required estimation = (5600 ‒ 3100) = 2500
Page No 15:
Question 30:
Estimate each difference to the nearest thousand:
(35863 − 27677)
ANSWER:
35863 estimated to the nearest thousand = 36000
27677 estimated to the nearest thousand = 28000
∴ The required estimation = (36000 ‒ 28000) = 8000
Page No 15:
Question 31:
Estimate each difference to the nearest thousand:
(47005 − 39488)
ANSWER:
47005 estimated to the nearest thousand = 47000
39488 estimated to the nearest thousand = 39000
∴ The required estimation = (47000 ‒ 39000) = 8000
Page No 15:
Exercise 1D
Question 1:
Estimate each of the following products by rounding off each number to the nearest ten:
38 × 63
ANSWER:
38 estimated to the nearest ten = 40
63 estimated to the nearest ten = 60
∴ The required estimation = (40 ×× 60) = 2400
Page No 15:
Question 2:
Estimate each of the following products by rounding off each number to the nearest ten:
54 × 47
ANSWER:
54 estimated to the nearest ten = 50
47 estimated to the nearest ten = 50
∴ The required estimation = (50 ×× 50) = 2500
Page No 15:
Question 3:
Estimate each of the following products by rounding off each number to the nearest ten:
28 × 63
ANSWER:
28 estimated to the nearest ten = 30
63 estimated to the nearest ten = 60
∴ The required estimation = (30 ×× 60) = 1800
Page No 15:
Question 4:
Estimate each of the following products by rounding off each number to the nearest ten:
42 × 75
ANSWER:
42 estimated to the nearest ten = 40
75 estimated to the nearest ten = 80
∴ The required estimation = (40 ×× 80) = 3200
Page No 15:
Question 5:
Estimate each of the following products by rounding off each number to the nearest ten:
64 × 58
ANSWER:
64 estimated to the nearest ten = 60
58 estimated to the nearest ten = 60
∴ The required estimation = (60 ×× 60) = 3600
Page No 15:
Question 6:
Estimate each of the following products by rounding off each number to the nearest ten:
15 × 34
ANSWER:
15 estimated to the nearest ten = 20
34 estimated to the nearest ten = 30
∴ The required estimation = (20 ×× 30) = 600
Page No 16:
Question 7:
Estimate each of the following products by rounding off each number to the nearest hundred:
376 × 123
ANSWER:
376 estimated to the nearest hundred = 400
123 estimated to the nearest hundred = 100
∴ The required estimation = (400 ×× 100) = 40000
Page No 16:
Question 8:
Estimate each of the following products by rounding off each number to the nearest hundred:
264 × 147
ANSWER:
264 estimated to the nearest hundred = 300
147 estimated to the nearest hundred = 100
∴ The required estimation = (300 ×× 100) = 30000
Page No 16:
Question 9:
Estimate each of the following products by rounding off each number to the nearest hundred:
423 × 158
ANSWER:
423 estimated to the nearest hundred = 400
158 estimated to the nearest hundred = 200
∴ The required estimation = (400 ×× 200) = 80000
Page No 16:
Question 10:
Estimate each of the following products by rounding off each number to the nearest hundred:
509 × 179
ANSWER:
509 estimated to the nearest hundred = 500
179 estimated to the nearest hundred = 200
∴ The required estimation = (500 ×× 200) = 100000
Page No 16:
Question 11:
Estimate each of the following products by rounding off each number to the nearest hundred:
392 × 138
ANSWER:
392 estimated to the nearest hundred = 400
138 estimated to the nearest hundred = 100
∴ The required estimation = (400 ×× 100) = 40000
Page No 16:
Question 12:
Estimate each of the following products by rounding off each number to the nearest hundred:
271 × 339
ANSWER:
271 estimated to the nearest hundred = 300
339 estimated to the nearest hundred = 300
∴ The required estimation = (300 ×× 300) = 90000
Page No 16:
Question 13:
Estimate each of the following products by rounding off the first number upwards and the second number downwards:
183 × 154
ANSWER:
183 estimated upwards = 200
154 estimated downwards = 100
∴ The required product = (200 ×× 100) = 20000
Page No 16:
Question 14:
Estimate each of the following products by rounding off the first number upwards and the second number downwards:
267 × 146
ANSWER:
267 estimated upwards = 300
146 estimated downwards = 100
∴ The required product = (300 ×× 100) = 30000
Page No 16:
Question 15:
Estimate each of the following products by rounding off the first number upwards and the second number downwards:
359 × 76
ANSWER:
359 estimated upwards = 400
76 estimated downwards = 70
∴ The required product = (400 ×× 70) =28000
Page No 16:
Question 16:
Estimate each of the following products by rounding off the first number upwards and the second number downwards:
472 × 158
ANSWER:
472 estimated upwards = 500
158 estimated downwards = 100
∴ The required product = (500 ×× 100) = 50000
Page No 16:
Question 17:
Estimate each of the following products by rounding off the first number upwards and the second number downwards:
680 × 164
ANSWER:
680 estimated upwards = 700
164 estimated downwards = 100
∴ The required product = (700 ×× 100) = 70000
Page No 16:
Question 18:
Estimate each of the following products by rounding off the first number upwards and the second number downwards:
255 × 350
ANSWER:
255 estimated upwards = 300
350 estimated downwards = 300
∴ The required product = (300 ×× 300) = 90000
Page No 16:
Question 19:
Estimate each of the following products by rounding off the first number downwards and the second number upwards:
356 × 278
ANSWER:
356 estimated downwards = 300
278 estimated upwards = 300
∴ The required product = (300 ×× 300) = 90000
Page No 16:
Question 20:
Estimate each of the following products by rounding off the first number downwards and the second number upwards:
472 × 76
ANSWER:
472 estimated downwards = 400
76 estimated upwards = 80
∴ The required product = (400 ×× 80) = 32000
Page No 16:
Question 21:
Estimate each of the following products by rounding off the first number downwards and the second number upwards:
578 × 369
ANSWER:
578 estimated downwards = 500
369 estimated upwards = 400
∴ The required product = (500 ×× 400) = 200000
Page No 16:
Exercise 1E
Question 1:
Find the estimated quotient for each of the following:
87 ÷ 28
ANSWER:
87 ÷ 28 is approximately equal to 90 ÷ 30 = 3.
Page No 16:
Question 2:
Find the estimated quotient for each of the following:
83 ÷ 17
ANSWER:
The estimated quotient for 83 ÷ 17 is approximately equal to 80 ÷ 20 = 8 ÷ 2 = 4.
Page No 16:
Question 3:
Find the estimated quotient for each of the following:
75 ÷ 23
ANSWER:
The estimated quotient of 75 ÷ 23 is approximately equal to 80 ÷ 20 = 8 ÷ 2 = 4.
Page No 16:
Question 4:
Find the estimated quotient for each of the following:
193 ÷ 24
ANSWER:
The estimated quotient of 193 ÷ 24 is approximately equal to 200 ÷ 20 = 20 ÷ 2 = 10.
Page No 16:
Question 5:
Find the estimated quotient for each of the following:
725 ÷ 23
ANSWER:
The estimated quotient of 725 ÷ 23 is approximately equal to 700 ÷ 20 = 70 ÷ 2 = 35.
Page No 16:
Question 6:
Find the estimated quotient for each of the following:
275 ÷ 25
ANSWER:
The estimated quotient of 275 ÷ 25 is approximately equal to 300 ÷ 30 = 30 ÷ 3 = 10.
Page No 16:
Question 7:
Find the estimated quotient for each of the following:
633 ÷ 33
ANSWER:
The estimated quotient of 633 ÷ 33 is approximately equal to 600 ÷ 30 = 60 ÷ 3 = 20.
Page No 16:
Question 8:
Find the estimated quotient for each of the following:
729 ÷ 29
ANSWER:
729 ÷ 29 is approximately equal to 700 ÷ 30 or 70 ÷ 3, which is approximately equal to 23.
Page No 16:
Question 9:
Find the estimated quotient for each of the following:
858 ÷ 39
ANSWER:
858 ÷ 39 is approximately equal to 900 ÷ 40 or 90 ÷ 4, which is approximately equal to 23.
Page No 16:
Question 10:
Find the estimated quotient for each of the following:
868 ÷ 38
ANSWER:
868 ÷ 38 is approximately equal to 900 ÷ 40 or 90 ÷ 4, which is approximately equal to 23.
Page No 19:
Exercise 1F
Question 1:
Express each of the following as a Roman numeral:
(i) 2
(ii) 8
(iii) 14
(iv) 29
(v) 36
(vi) 43
(vii) 54
(viii) 61
(ix) 73
(x) 81
(xi) 91
(xii) 95
(xiii) 99
(xiv) 105
(xv) 114
ANSWER:
We may write these numbers as given below:
(i) 2 = II
(ii) 8 = (5 + 3) = VIII
(iii) 14 = (10 + 4) = XIV
(iv) 29 = ( 10 + 10 + 9 ) = XXIX
(v) 36 = (10 + 10 + 10 + 6) = XXXVI
(vi) 43 = (50 – 10) + 3 = XLIII
(vii) 54 = (50 + 4) = LIV
(viii) 61= (50 + 10 + 1) = LXI
(ix) 73 = ( 50 + 10 + 10 + 3) = LXXIII
(x) 81 = (50 + 10 + 10 + 10 + 1) = LXXXI
(xi) 91 =(100 – 10) + 1 = XCI
(xii) 95 = (100 – 10) + 5 = XCV
(xiii) 99 = (100 – 10) + 9 = XCIX
(xiv) 105 = (100 + 5) = CV
(xv) 114 = (100 + 10) + 4 = CXIV
Page No 19:
Question 2:
Express each of the following as a Roman numeral:
(i) 164
(ii) 195
(iii) 226
(iv) 341
(v) 475
(vi) 596
(vii) 611
(viii) 759
ANSWER:
We may write these numbers in Roman numerals as follows:
(i) 164 = (100 + 50 + 10 + 4) = CLXIV
(ii) 195 = 100 + (100 – 10) + 5 = CXCV
(iii) 226 = (100 + 100 + 10 + 10 + 6) = CCXXVI
(iv) 341= 100 + 100+ 100 + (50 -10) + 1 = CCCXLI
(v) 475 = (500 – 100) + 50 + 10 + 10 + 5 = CDLXXV
(vi) 596 = 500 + (100 – 10) + 6 = DXCVI
(vii) 611= 500 + 100 + 11 = DCXI
(viii) 759 = 500 + 100 + 100 + 50 + 9 = DCCLIX
Page No 19:
Question 3:
Write each of the following as a Hindu-Arabic numeral:
(i) XXVII
(ii) XXXIV
(iii) XLV
(iv) LIV
(v) LXXIV
(vi) XCI
(vii) XCVI
(viii) CXI
(ix) CLIV
(x) CCXXIV
(xi) CCCLXV
(xii) CDXIV
(xiii) CDLXIV
(xiv) DVI
(xv) DCCLXVI
ANSWER:
We can write the given Roman numerals in Hindu-Arabic numerals as follows:
(i) XXVII = 10 + 10 + 7 = 27
(ii) XXXIV = 10 + 10 + 10 + 4 = 34
(iii) XLV = (50 − 10 ) + 5 = 45
(iv) LIV = 50 + 4 = 54
(v) LXXIV = 50 + 10 + 10 + 4 = 74
(vi) XCI = (100 − 10) + 1 = 91
(vii) XCVI = (100 − 10) + 6 = 96
(viii) CXI = 100 + 10 + 1= 111
(ix) CLIV = 100 + 50 + 4 = 154
(x) CCXXIV = 100 + 100 + 10 + 10 + 4 = 224
(xi) CCCLXV = 100 + 100 + 100 + 50 + 10 + 5 = 365
(xii) CDXIV = (500 − 100) + 10 + 4 = 414
(xiii) CDLXIV = (500 − 100) + 50 + 10 + 4 = 464
(xiv) DVI = 500 + 6= 506
(xv) DCCLXVI = 500 + 100 + 100 + 50 + 10 + 6 = 766
Page No 19:
Question 4:
Show that each of the following is meaningless. Give reason in each case.
(i) VC
(ii) IL
(iii) VVII
(iv) IXX
ANSWER:
(i) VC is wrong because V, L and D are never subtracted.
(ii) IL is wrong because I can be subtracted from V and X only.
(iii) VVII is wrong because V, L and D are never repeated.
(iv) IXX is wrong because X (ten) must be placed before IX (nine).
Page No 20:
Exercise 1G
Question 1:
Mark against the correct answer
The place value of 6 in the numeral 48632950 is
(a) 6
(b) 632950
(c) 600000
(d) 486
ANSWER:
Option c is correct.
Place value of 6 = 6 lakhs = (6 ×× 100000) = 600000
Page No 20:
Question 2:
Mark against the correct answer
The face value of 4 in the numeral 89247605 is
(a) 4
(b) 40000
(c) 47605
(d) 8924
ANSWER:
Option a is correct.
The face value of a digit remains as it is irrespective of the place it occupies in the place value chart.
Thus, the face value of 4 is always 4 irrespective of where it may be.
Page No 20:
Question 3:
Mark against the correct answer
The difference between the place value and the face value of 5 in the numeral 78653421 is
(a) 53416
(b) 4995
(c) 49995
(d) none of these
ANSWER:
Option c is correct.
Place value of 5 = 5 ×× 10000 = 50000
Face value of 5 = 5
∴ Required difference = 50000 − 5 = 49995
Page No 20:
Question 4:
Mark against the correct answer
The smallest counting number is
(a) 0
(b) 1
(c) 10
(d) none of these
ANSWER:
Option b is correct.
The smallest counting number is 1.
Page No 20:
Question 5:
Mark against the correct answer
How many 4-digit numbers are there?
(a) 8999
(b) 9000
(c) 8000
(d) none of these
ANSWER:
Option b is correct.
The largest four-digit number = 9999
The smallest four-digit number = 1000
Total number of all four-digit numbers = (9999 − 1000) + 1
= 8999 + 1
= 9000
Page No 20:
Question 6:
Mark against the correct answer
How many 7-digit numbers are there?
(a) 8999999
(b) 9000000
(c) 10000000
(d) none of these
ANSWER:
Option b is correct.
The largest seven-digit number = 9999999
The smallest seven-digit number = 1000000
Total number of seven-digit numbers = (9999999 − 1000000) + 1
= 8999999 + 1
= 9000000
Page No 20:
Question 7:
Mark against the correct answer
How many 8-digit numbers are there?
(a) 99999999
(b) 89999999
(c) 90000000
(d) none of these
ANSWER:
Option c is correct.
The largest eight-digit number = 99999999
The smallest eight-digit number = 10000000
Total number of eight-digit numbers = (99999999 − 10000000) + 1
= 89999999 + 1
= 90000000
Page No 20:
Question 8:
Mark against the correct answer
What comes just before 1000000?
(a) 99999
(b) 999999
(c) 9999999
(d) none of these
ANSWER:
Option b is correct.
The number just before 1000000 is 999999 (i.e., 1000000 − 1).
Page No 20:
Question 9:
Mark against the correct answer
Which of the following is not meaningful?
(a) VX
(b) XV
(c) XXV
(d) XXXV
ANSWER:
Option a is correct.
V, L and D are never subtracted. Thus, VX is wrong.
Page No 20:
Question 10:
Mark against the correct answer
Which of the following is not meaningful?
(a) CI
(b) CII
(c) IC
(d) XC
ANSWER:
Option c is correct.
I can be subtracted from V and X only. Thus, IC is wrong.
Page No 20:
Question 11:
Mark against the correct answer
Which of the following is not meaningful?
(a) XIV
(b) XVV
(c) XIII
(d) XXII
ANSWER:
Option b is correct.
V, L and D are never repeated. Thus, XVV is meaningless.
Page No 21:
Exercise 1G
Question 1:
Write each of the following numerals in words:
(i) 16, 06, 23, 708
(ii) 14, 23, 08, 915
ANSWER:
(i) Sixteen crore six lakh twenty-three thousand seven hundred eight
(ii) Fourteen crore twenty-three lakh eight thousand nine hundred fifteen
Page No 21:
Question 2:
Write each of the following numerals in words:
(i) 80, 060, 409
(ii) 234, 150, 319
ANSWER:
(i) Eighty million sixty thousand four hundred nine
(ii) Two hundred thirty-four million one hundred fifty thousand three hundred nineteen
Page No 21:
Question 3:
Arrange the following numbers in ascending order:
3903216, 19430124, 864572, 6940513, 16531079
ANSWER:
We have,
864572 is a 6-digit number.
3903216 and 6940513 are seven-digit numbers.
At the ten lakhs place, one number has 3, while the second number has 6.
Clearly, 3 < 6
∴ 3903216 < 6940513
16531079 and 19430124 are eight-digit numbers.
At the crores place, both the numbers have the same digit, namely 1.
At the ten lakhs place, one number has 6, while the second number has 9.
Clearly, 6 < 9
∴ 16531079 < 19430124
The given numbers in ascending order are:
864572 < 3903216 < 6940513 < 16531079 < 19430124
Page No 21:
Question 4:
Arrange the following numbers in descending order:
54796203, 4675238, 63240613, 5125648, 589623
ANSWER:
63240613 and 54796203 are both eight-digit numbers.
At the crores place, one number has 6, while the second number has 5.
Clearly, 5 < 6
∴ 63240613 > 54796203
5125648 and 4675238 are both seven-digit numbers.
However, at the ten lakhs place, one number has 5, while the second number has 4.
Clearly, 4 < 5
∴ 5125648 > 4675238
589623 is a six-digit number.
The given numbers in descending order are:
63240613 > 54796203 > 5125648 > 4675238 > 589623
Page No 21:
Question 5:
How many 7-digit numbers are there in all?
ANSWER:
The largest seven-digit number = 9999999
The smallest seven-digit number = 1000000
Number of all seven-digits numbers = (9999999 − 1000000) + 1
= 899999 + 1
= 9000000
Hence, there is a total of ninety lakh 7-digit numbers.
Page No 21:
Question 6:
Write the largest and smallest numbes using each of the digits 1, 4, 6, 8, 0 only once and find their difference.
ANSWER:
The largest number using each of the digits: 1, 4, 6, 8 and 0, is 86410.
The smallest number using each of the digits: 1, 4, 6, 8 and 0, is 10468.
∴ Required difference = 86410 − 10468
= 75942
Page No 21:
Question 7:
Write the Hindu-Arabic numeral for each of the following:
(i) CCXLII
(ii) CDLXV
(iii) LXXVI
(iv) DCCXLI
(v) XCIV
(vi) CXCIX
ANSWER:
(i) CCXLII = 100 + 100 + (50 − 10) + 2 = 242
(ii) CDLXV = (500 − 100) + 50 + 10 + 5 = 465
(iii) LXXVI = 50 + 10 + 10 + 6 = 76
(iv) DCCXLI = 500 + 100 + 100 + ( 50 − 10) + 1 = 741
(v) XCIV = (100 − 10) + 4 = 94
(vi) CXCIX = 100 + (100 − 10) + 9 = 199
Page No 21:
Question 8:
Write the Roman numeral for each of the following:
(i) 84
(ii) 99
(iii) 145
(iv) 406
(v) 519
ANSWER:
(i) 84 = 50 + 30 + 4 = LXXXIV
(ii) 99 = 90 + 9 = XCIX
(iii) 145 = 100 + (50 − 10) + 5 = CXLV
(iv) 406 = 400 + 6 = CDVI
(v) 519 = 500 +10 + 9 = DXIX
Page No 21:
Question 9:
Write the successor and predecessor of 999999 and find their difference.
ANSWER:
Successor of 999999 = 999999 + 1 = 1000000
Predecessor of 999999 = 999999 − 1 = 999998
∴ Required difference = 1000000 − 999998
= 2
Page No 21:
Question 10:
Round off each of the following to the nearest thousand:
(i) 1046
(ii) 973
(iii) 5624
(iv) 4368
ANSWER:
(i) The number is 1046. Its digit at the hundreds place is 0 < 5.
So, the given number is rounded off to the nearest thousand as 1000.
(ii) The number is 973. Its digit at the hundreds place is 9 > 5.
So, the given number is rounded off to the nearest thousand as 1000.
(iii) The number is 5624. Its digit at the hundreds place is 6 > 5.
So, the given number is rounded off to the nearest thousand as 6000.
(iv) The number is 4368. Its digit at the hundreds place is 3 < 5.
So, the given number is rounded off to the nearest thousand as 4000.
Page No 21:
Question 11:
Which of the following Roman numerals is correct?
(a) XC
(b) XD
(c) DM
(d) VL
ANSWER:
Option (a) is correct.
X can be subtracted from L and C only.
i.e., XC = ( 100 − 10 ) = 90
Page No 21:
Question 12:
1 Lakh = …… thousands.
(a) 10
(b) 100
(c) 1000
(d) none of these
ANSWER:
Option (b) is correct.
One lakh (100000) is equal to one hundred thousand (100,000).
Page No 21:
Question 13:
No Roman numeral can be repeated more than ….. times.
(a) two
(b) three
(c) four
(d) none of these
ANSWER:
Option (b) is correct.
No Roman numeral can be repeated more than three times.
Page No 21:
Question 14:
How many times does the digit 9 occur between 1 and 100?
(a) 11
(b) 15
(c) 18
(d) 20
ANSWER:
Option (d) is correct.
Between 1 and 100, the digit 9 occurs in 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 and 99.
∴ The digit occurs 20 times between 1 and 100.
Page No 21:
Question 15:
(7268 − 2427) estimated to the nearest hundred is
(a) 4900
(b) 4800
(c) 4841
(d) 5000
ANSWER:
Option (a) is correct.
7268 will be rounded off to the nearest hundred as 7300.
2427 will be rounded of to the nearest hundred as 2400.
∴ 7300 − 2400 = 4900
Page No 21:
Question 16:
One million = …… .
(a) 1 lakh
(b) 10 lakh
(c) 100 lakh
(d) 1 crore
ANSWER:
Option (b) is correct.
1 million (1,000,000) = 10 lakh (10 ×× 1,00,000)
Page No 21:
Question 17:
1512 when round off to the nearest hundred is
(a) 1600
(b) 1500
(c) 1510
(d) none of these
ANSWER:
Option (b) is correct.
The number is 1512. Its digit at the tens place is 1 < 5.
So, the given number is rounded off to the nearest hundred as 1500.
Page No 21:
Question 18:
Which of the symbols are never repeated?
(a) V, X and C
(b) V, X and D
(c) V, L and D
(d) L, K and C
ANSWER:
Option (c) is correct.
In Roman numerals, V, L and D are never repeated and never subtracted.
Page No 21:
Question 19:
Write 86324805 separating periods in HIndu-Arabic system.
ANSWER:
Periods: Crores Lakhs Thousands Hundreds Tens Ones
Digits: 8 63 24 8 0 5
Using commas, we write the given number as 8,63,24,805.
Page No 21:
Question 20:
Fill in the blanks:
(i) 1 crore = …… lakh
(ii) 1 crore = …… million
(iii) 564 when estimated to the nearest hundred is …… .
(iv) The smallest 4-digit number with four different digits is …… .
ANSWER:
(i) 1 crore = 100 lakh
(ii) 1 crore = 10 million
(iii) 564 when estimated to the nearest hundred is 600.
(iv) The smallest 4-digit number with four different digits is 1023.
Page No 22:
Question 21:
Write ‘T’ for true and ‘F’ for false
The difference in the face value and the place value of 5 in 85419 is 85414.
ANSWER:
F
Place value of 5 in 85419 = 5000
Face value of 5 in 85419 = 5
∴ Their difference = 5000 − 5 = 4995
Page No 22:
Question 22:
Write ‘T’ for true and ‘F’ for false
In Roman numerals V, L and D are never subtracted.
ANSWER:
T
In Roman numerals, V, L and D are never repeated and never subtracted.
Page No 22:
Question 23:
Write ‘T’ for true and ‘F’ for false
The successor of the greatest 5-digit number is 100000.
ANSWER:
T
Greatest five-digit number = 99999
Successor of 99999 = 99999 + 1 = 100000
Page No 22:
Question 24:
Write ‘T’ for true and ‘F’ for false
The estimated value of 46,530 to the nearest hundred is 46500.
ANSWER:
T
The number is 46,530. Its digit at the tens place is 3 < 5.
So, the number 46,530 is rounded off to the nearest hundred as 46,500.
Page No 22:
Question 25:
Write ‘T’ for true and ‘F’ for false
100 lakhs make a million.
ANSWER:
F
10 lakhs = 1 million
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