RD SHARMA SOLUTION CHAPTER –3 Decimals | CLASS 7TH MATHEMATICS-EDUGROWN
Exercise 3.1
Question: 1
Write each of the following as decimals:
(i) 8/100
Solution:
(i) 8/100
Mark the decimal point two places from right to left
Mark the decimal point one place from right to left
9/10 = 0.9
4/100
Mark the decimal point two places from right to left
4/100
= 0.04
Convert 2/10 and 6/1000 into decimals
2/10
Mark the decimal point one place from right to left
2/10
= 0.2
6/1000
Mark the decimal point three places from right to left
6/1000
= 0.006
23, 0.2, 0.006 are unlike decimals. So we convert them into like decimals.
Question: 2
Convert each of the following into fractions in the lowest form:
(i) 0.04
(ii) 2.34
(iii) 0.342
(iv) 17.38
Solution:
(i) 0.04
= 0.04/1
= 4/100
= 1/25
(ii) 2.34
= 2.34/1
= 234/100
= 117/50
(iii) 0.342
= 0.342/1
= 342/1000
= 171/500
(iv) 17.38
=17.38/1
= 1738/100
= 869/50
Question: 3
Express the following fractions as decimals:
(i) 23/10
Solution:
(i) 23/10
= 23/10
= 2.3
Question: 4
Add the following:
(i) 41.8, 39.24, 5.01 and 62.6
(ii) 18.03, 146.3, 0.829 and 5.324
Solution:
(i) 148.65
(ii) 170.483
Question: 5
Find the value of:
(i) 9.756 – 6.28
(ii) 48.1- 0.37
(iii) 108.032 – 86.8
(iv) 100 – 26.32
Solution:
(i) 3.476
(ii) 47.73
(iii) 21.232
(iv) 73.68
Question: 6
Take out 3.547 from 7.2
Solution:
3.653
Question: 7
What is to be added to 36.85 to get 59.41?
Solution:
x + 36.85 = 59.41
x = 59.41-36.85
x = 22.56
Therefore 22.56 is added to 36.85 to get 59.41
Question: 8
What is to be subtracted from 17.1 to get 2.051?
Solution:
17.1- x = 2.051
17.1 = x + 2.051
x = 17.1 – 2.051
x = 15.049
Therefore 15.049 is subtracted from 17.1 to get 15.049
Question: 9
By how much should 34.79 be increased to get 70.15?
Solution:
34.79 + x = 70.15
x = 70.15 – 34.79
x = 35.36
Therefore 35.36 is increased to 70.15
Question: 10
By how much should 59.71 be decreased to get 34.58?
Solution:
59.71 – x = 34.58
59.71 – 34.58 = x
x = 25.13
Therefore 25.13 is decreased to get 34.58
Exercise 3.2
Question: 1
Find the product:
(i) 4.74 x 10
(ii) 0.45 x 10
(iii) 0.0215 x 10
(iv) 0.0054 x 100
Solution:
(i) 4.74 x 10
Shifting the decimal point by one place to the right
4.74 x 10 = 47.4
(ii) 0.45 x 10
Shifting the decimal point by one place to the right
0.45 × 10 = 4.5
(iii) 0.0215 x 10
Shifting the decimal point by one place to the right
0.0215 × 10 = 0.215
(iv) 0.0054 x 100
Shifting the decimal point by two places to the right
0.0054 × 100 = 0.054
Question: 2
Find the product:
(i) 35.853 x 100
(ii) 42.5 x 100
(iii) 12.075 x 100
(iv) 100 x 0.005
Solution:
(i) 35.853 x 100
Shifting the decimal point by two places to the right
35.853 = 3585.3
(ii) 42.5 x 100
Shifting the decimal point by two places to the right
42.5 × 100 = 4250
(iii) 12.075 x 100
Shifting the decimal point by two places to the right
12.075 × 100 = 1207.5
(iv) 100 x 0.005
Shifting the decimal point by two places to the right
0.005 × 100 = 0.5
Question: 3
Find the product:
(i) 2.506 x 1000
(ii) 20.708 x 1000
(iii) 0.0529 x 1000
(iv) 1000 x 0.1
Solution:
(i) 2.506 x 1000
Shifting the decimal point by three places to the right
2.506 × 1000 = 2506
(ii) 20.708 x 1000
Shifting the decimal point by three places to the right
20.708 × 1000 = 20708
(iii) 0.0529 x 1000
Shifting the decimal point by three places to the right
0.0529 × 1000 = 52.9
(iv) 1000 x 0.1
Shifting the decimal point by three places to the right
0.1 × 1000 = 100
Question: 4
Find the product:
(i) 3.4 x 17
(ii) 0.745 x 12
(iii) 28.73 x 47
(iv) 0.0415 x 59
Solution:
(i) 3.4 x 17
Multiply the number without looking into the decimal points
3.4 × 17 = 578
Mark the decimal point in the product to have one place of decimal as there in the given decimal
= 57.8
(ii) 0.745 x 12
Multiply the number without looking into the decimal points
745×12 = 8940
Mark the decimal point in the product to have three places of decimal as there in the given decimal
0.745 x 12= 8.940
(iii) 28.73 x 47
Multiply the number without looking into the decimal points
2873 × 47 = 135031
Mark the decimal point in the product to have two places of decimal as there in the given decimal
28.73 × 47 = 1350.31
(iv) 0.0415 x 59
Multiply the number without looking into the decimal points
415 × 59 = 24485
Mark the decimal point in the product to have two places of decimal as there in the given decimal
0.0415 × 59 = 2.4485
Question: 5
Find:
(i) 1.07 x 0.02
(ii) 211.9 x 1.13
(iii) 10.05 x 1.05
(iv) 13.01 x 5.01
Solution:
(i) 1.07 x 0.02
Multiply the number without looking into the decimal points
107× 2 = 214
Sum of the decimal places in the given decimals is 2 + 2 = 4
Mark the decimal point in the product to have four places of decimals
1.07 × 0.02 = 0.0214
(ii) 211.9 x 1.13
Multiply the number without looking into the decimal points
2119 × 113 = 239447
Sum of the decimal places in the given decimals is 1+ 2 = 3
Mark the decimal point in the product to have three places of decimals
211.9 × 1.13 = 239.447
(iii) 10.05 x 1.05
Multiply the number without looking into the decimal points
1005 × 105 = 105525
Sum of the decimal places in the given decimals is 2 + 2 = 4
Mark the decimal point in the product to have four places of decimals
10.05 × 1.05 = 10.5525
(iv) 13.01 x 5.01
Multiply the number without looking into the decimal points
1301 × 501 = 651801
Sum of the decimal places in the given decimals is 2+ 2 = 4
Mark the decimal point in the product to have four places of decimals
13.01 × 5.01 = 65.1801
Question: 6
Find the area of a rectangle whose length is 5.5 m and breadth is 3.4 m.
Solution:
We have
Length of rectangle = 5.5 m
Breadth of rectangle = 3.4 m
Area of rectangle = Length × Breadth
= 5.5 x 3.4
=18.7 m2
Question: 7
If the cost of a book is Rs 25.75, find the cost of 24 such books.
Solution:
Cost of one book = Rs.25.75
Therefore cost of 24 books = 25.75 x 24
= Rs.618.00
Question: 8
A car covers a distance of 14.75 km in one litre of petrol. How much distance will it cover in 15.5 litres of petrol?
Solution:
We have,
Distance covered in one litre of petrol = 14.75 km
Distance covered in 15.5 litres of petrol = 14.75 x 15.5
= 228.625 km
Question: 9
One kg of rice costs Rs 42.65. What will be the cost of 18.25 kg of rice?
Solution:
Cost of one kg rice = 42.65
Cost of 18.25kg = 42.65 x 18.25
= Rs.778.3625
Question: 10
One metre of cloth costs Rs 152.50. What is the cost of 10.75 metres of cloth?
Solution:
We have,
One metre of cloth cost = Rs.152.50
Cost of 10.75 metres =10.75 x 152.50
= Rs.1639.375
Exercise 3.3
Question: 1
Divide:
(i) 142.45 by 10
(ii) 54.25 by 10
(iii) 3.45 by 10
(iv) 0.57 by 10
(v) 0.043 by 10
(vi) 0.004 by 10
Solution:
(i) 142.45 by 10
Shifting the decimal point by one place to the left
142.45/10
= 14.245
(ii) 54.25 by 10
Shifting the decimal point by one place to the left
54.25/10
= 5.425
(iii) 3.45 by 10
Shifting the decimal point by one place to the left
3.45/10
0.345
(iv) 0.57 by 10
Shifting the decimal point by one place to the left
0.57/10
= 0.057
(v) 0.043 by 10
Shifting the decimal point by one place to the left
0.043/10
= 0.0043
(vi) 0.004 by 10
Shifting the decimal point by one place to the left
0.004/10
= 0.0004
Question: 2
Divide:
(i) 459.5 by 100
(ii) 74.3 by 100
(iii) 5.8 by 100
(iv) 0.7 by 100
(v) 0.48 by 100
(vi) 0.03 by 100
Solution:
(i) 459.5 by 100
Shifting the decimal point by two places to the left
459.5/100
= 4.595
(ii) 74.3 by 100
Shifting the decimal point by two places to the left
74.3/100
= 0.743
(iii) 5.8 by 100
Shifting the decimal point by two places to the left
5.8/100
= 0.058
(iv) 0.7 by 100
Shifting the decimal point by two places to the left
0.7/100
= 0.007
(v) 0.48 by 100
Shifting the decimal point by two places to the left
0.48/100
= 0.0048
(vi) 0.03 by 100
Shifting the decimal point by two places to the left
0.03/100
= 0.0003
Question: 3
Divide:
(i) 235.41 by 1000
(ii) 29.5 by 1000
(iii) 3.8 by 1000
(iv) 0.7 by 1000
Solution:
(i) 235.41 by 1000
Shifting the decimal point by three places to the left
235.41/1000
= 0.23541
(ii) 29.5 by 1000
Shifting the decimal point by three places to the left
29.51/000
= 0.0295
(iii) 3.8 by 1000
Shifting the decimal point by three places to the left
3.8/1000
= 0.0038
(iv) 0.7 by 1000
Shifting the decimal point by three places to the left
0.7/1000
= 0.007
Question: 4
Divide:
(i) 0.45 by 9
(ii) 217.44 by 18
(iii) 319.2 by 2.28
(iv) 40.32 by 9.6
(v) 0.765 by 0.9
(vi) 0.768 by 1.6
Solution:
(i) 0.45 by 9
= 0.45/9
= 0.05
(ii) 217.44 by 18
= 217.44/18
= 12.08
(iii) 319.2 by 2.28
= 319.2/2.28
(iv) 40.32 by 9.6
= 40.32/9.6
= 403.2/96
= 4.2
= 403.2/96 = 4.2
(v) 0.765 by 0.9
= 0.765/0.9
= 7.65/9
= 0.85
= 7.65/0.9 = 0.85
(vi) 0.768 by 1.6
= 0.768/1.6
= 7.68/16
= 0.48
Question: 5
Divide:
(i) 16.64 by 20
(ii) 0.192 by 12
(iii) 163.44 by 24
(iv) 403.2 by 96
(v) 16.344 by 12
(vi) 31.92 by 228
Solution:
(i) 16.64 by 20
= 16.64/20
= 1.664/2
= 0.832
(ii) 0.192 by 12
= 0.192/12
= 0.016
(iii) 163.44 by 24
= 163.44/24
= 6.81
(iv) 403.2 by 96
= 403.2/96
= 4.2
(v) 16.344 by 12
= 16.344/12
= 1.362
(vi) 31.92 by 228
= 31.92/228
= 0.14
Question: 6
Divide:
(i) 15.68 by 20
(ii) 164.6 by 200
(iii) 403.80 by 30
Solution:
(i) 15.68 by 20
=15.68/20
=1.568/2
= 0.784
(ii) 164.6 by 200
Question: 7
(i) 76 by 0.019
(ii) 88 by 0.08
(iii) 148 by 0.074
(iv) 7 by 0.014
(iii) 403.80 by 30
Solution:
(i) 76 by 0.019
= 76/0.019
= 76000/19
= 4000
(ii) 88 by 0.08
= 88/0.08
= 8800/8
=1100
(iii) 148 by 0.074
= 148/0.074
= 148000/74
= 2000
(iv) 7 by 0.014
= 70.014
= 7000/14
= 0.823
(iii) 403.80 by 30
= 403.80/30
Question: 8
Divide:
(i) 20 by 50
(ii) 8 by 100
(iii) 72 by 576
(iv) 144 by 15
Solution:
(i) 20 by 50
= 20/50
= 0.4
(ii) 8 by 100
= 8/100
By shifting the decimal point to the left
= 8/100
= 0.08
(iii) 72 by 576
= 72/576
= 0.125
(iv)144 by 15
= 144/15
= 9.6
Question: 9
A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it travel in 1 litre of petrol?
Solution:
Distance covered in 2.4 litres of petrol = 43.2 km
Distance covered in 1 litre of petrol = 43.2/2.4
= 18km
The distance travelled in 1 litre of petrol is 18 km
Question: 10
The total weight of some bags of wheat is 1743 kg. If each bag weights 49.8 kg, how many bags are there?
Solution:
Total weight of bags of wheat = 1743 kg
Each bag weight = 49.8 kg
No of bags = 1743/49.8
= 35
Therefore the total numbers of bags are 35
Question: 11
Shikha cuts 50 m of cloth into pieces of 1.25 m each. How many pieces does she get?
Solution:
Total length of cloth = 50 m
Length of each piece of cloth = 1.25 m
Number of pieces = 50/1.25
= 5000/125
= 40 pieces
Therefore Shikha got 40 pieces
Question: 12
Each side of a rectangular polygon is 2.5 cm in length. The perimeter of the polygon is 12.5 cm. How many sides does the polygon have?
Solution:
Length of each side of rectangular polygon = 5.2 cm
Perimeter of polygon = 12.5 cm
No of sides polygon has = 12.5 cm
No of sides polygon have = 12.5/2.5
= 5
Therefore the sides of the polygon is 5
Question: 13
The product of two decimals is 42.987. If one of them is 12.46, find the other.
Solution:
We have,
The product of the given decimals = 42.987
one decimal = 12.46
The other decimal = 42.987/12.46
= 3.45
The number is 3.45
Question: 14
The weight of 34 bags of sugar is 3483.3 kg. If all bags weigh equally, find the weight of each bag.
Solution:
Total weight of sugar = 3483.3kg
No of bags = 34
Weight of each bag = 3483.3/34
= 102.45 kg
Therefore weight of each bag is 102.45 kg
Question: 15
How many buckets of equal capacity can be filled from 586.5 litres of water, if each bucket has capacity of 8.5 litres?
Solution:
Capacity of each bucket = 805 litres
Total water available = 586.5 litres
Number of buckets = 805/586.5
= 69
Total number of buckets is 69
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