## RD Sharma Solutions For Class 7 Maths Chapter 3 Decimals Free Online

## Exercise 3.1 Page No: 3.4

**1. Write each of the following as decimals:**

**(i) (8/100)**

**(ii) 20 + (9/10) + (4/100)**

**(iii) 23 + (2/10) + (6/1000)**

**Solution:**

(i) Given (8/100)

Mark the decimal point two places from right to left

(8/100) = 0.08

(ii) Given 20 + (9/10) + (4/100)

First convert the fractions (9/10) and (4/100) to decimals

Consider (9/10)

Mark the decimal point one place from right to left

(9/10) = 0.9

Now consider (4/100)

Mark the decimal point two places from right to left

(4/100) = 0.04

20 + (9/10) + (4/100) = 20 + 0.9 + 0.04

= 20.94

(iii) Given 23 + (2/10) + (6/1000)

First convert the fractions (2/10) and (6/1000) to decimals

Consider (2/10)

Mark the decimal point one place from right to left

(2/10) = 0.2

Now consider (6/1000)

Mark the decimal point three places from right to left

(6/1000) = 0.006

23 + (2/10) + (6/1000) = 23 + 0.2 + 0.006

= 23.206

**2. Convert each of the following fractions as decimals:**

**(i) 0.04**

**(ii) 2.34**

**(iii) 0.342**

**(iv) 17.38**

**Solution:**

(i) Given 0.04

Here we have to convert given decimals into fractions

0.04 can be written as (0.04/1)

Now multiply both numerator and denominator by 100 then we get

(0.04/1) = (0.04 × 100 /1 × 100)

= (4/100)

= (1/25)

(ii) Given 2.34

Here we have to convert given decimals into fractions

2.34 can be written as (2.34/1)

Now multiply both numerator and denominator by 100 then we get

(2.34/1) = (2.34 × 100 /1 × 100)

= (234/100)

= (117/50)

(iii) Given 0.342

Here we have to convert given decimals into fractions

0.342 can be written as (0.342/1)

Now multiply both numerator and denominator by 1000 then we get

(0.342/1) = (0.342 × 1000 /1 × 1000)

= (342/1000)

= (171/500)

(iv) Given 17.38

Here we have to convert given decimals into fractions

17.38 can be written as (17.38/1)

Now multiply both numerator and denominator by 100 then we get

(17.38/1) = (17.38 × 100 /1 × 100)

= (1738/100)

= (869/50)

**3. Express the following fractions as decimals:**

**(i) (23/10)**

**(ii) 25 (1/8)**

**(iii) 39 (7/35)**

**(iv) 15 (1/25)**

**Solution:**

(i) Given (23/10)

Divide 23 by 10 we get

(23/10) = 2.3

(ii) Given 25 (1/8)

25 (1/8) can be written as

25 (1/8) = 25 + (1/8)

Consider (1/8),

Now multiply both numerator and denominator by 125 to get 1000 as denominator

25 (1/8) = 25 + (1/8) = 25 + (1 × 125 /8 × 125)

= 25 + (125/1000)

= 25 + 0.125

= 25.125

(iii) Given 39 (7/35)

First convert given mixed fraction 39 (7/35) into improper fraction

39 (7/35) = 1372/35

By dividing we get

39 (7/35) = 39.2

(iv) Given 15 (1/25)

15 (1/25) can be written as

15 (1/25) = 15 + (1/25)

Consider (1/25),

Now multiply both numerator and denominator by 4 to get 100 as denominator

15 (1/25) = 15 + (1/25) = 15 + (1 × 4 /25 × 4)

= 15 + (4/100)

= 15 + 0.04

= 15.04

**4. Add the following:**

**(i) 41.8, 39.24, 5.01 and 62.6**

**(ii) 18.03, 146.3, .829 and 5.324**

**Solution:**

(i) Given 41.8, 39.24, 5.01 and 62.6

41.8

39.2

5.01

+ 62.6

148.65

(ii) Given 18.03, 146.3, 0.829 and 5.324

18.03

146.3

0.829

+ 5.324

170.483

**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) Given 9.756 – 6.28

9.756

– 6.28

3.476

(ii) Given 48.1 – 0.37

48.1

– 0.37

47.73

(iii) Given 108.032 – 86.8

108.032

– 86.8

21.232

(iv) Given 100 – 26.32

100.00

– 26.32

73.68

**6. Take out of 3.547 from 7.2**

**Solution:**

Given 3.547 from 7.2

7.2

– 3.547

3.653

**7. What is to be added to 36.85 to get 59.41?**

**Solution:**

Given 36.85 and 59.41

Let the unknown number be x

x + 36.85 = 59.41

x = 59.41 – 36.85

x = 22.56

Hence 22.56 is to be added to 36.85 to get 59.41

**8. What is to be subtracted from 17.1 to get 2.051?**

**Solution:**

Let the unknown number be x

Given that x is to be subtracted from 17.1 to get 2.051

17.1 – x = 2.051

17.1 – 2.051 = x

x = 17.1 – 2.051

x = 15.049

**9. By how much should 34.79 be increased to get 70.15?**

**Solution:**

Let x be the unknown number

x + 34.79 = 70.15

x = 70.15 – 34.79

x = 35.36

35.36 should be increased to 34.79 to get 70.15

**10. By how much should 59.71 be decreased to get 34.58?**

**Solution:**

Let x be the unknown number

59.71 – x =34.58

59.71 – 34.58 = x

x = 59.71 – 34.58

x = 25.13

25.13 should be decreased by 59.71 to get 34.58

## Exercise 3.2 Page No: 3.8

**1. Find the product:**

**(i) 4.74 × 10**

**(ii) 0.45 × 10**

**(iii) 0.0215 × 10**

**(iv) 0.0054 × 10**

**Solution:**

(i) Given 4.74 × 10

Here we have to do normal multiplication with shifting the decimal point by one place to the right

Therefore 4.74 × 10 = 47.4

(ii) Given 0.45 × 10

Here we have to do normal multiplication with shifting the decimal point by one place to the right

Therefore 0.45 × 10 = 4.5

(iii) Given 0.0215 × 10

Here we have to do normal multiplication with shifting the decimal point by one place to the right

Therefore 0.0215 × 10 = 0.215

(iv) Given 0.0054 × 10

Here we have to do normal multiplication with shifting the decimal point by one place to the right

Therefore 0.0054 × 10 = 0.054

**2. Find the product:**

**(i) 35.853 × 100**

**(ii) 42.5 × 100**

**(iii) 12.075 × 100**

**(iv) 100 × 0.005**

**Solution:**

(i) Given 35.853 × 100

Here we have to do normal multiplication with shifting the decimal point by two places to the right

Therefore 35.853 × 100 = 3585.3

(ii) Given 42.5 × 100

Here we have to do normal multiplication with shifting the decimal point by two places to the right

Therefore 42.5 × 100 = 4250

(iii) Given 12.075 × 100

Here we have to do normal multiplication with shifting the decimal point by two places to the right

Therefore 12.075 × 100 = 1207.50

(iv) Given 100 × 0.005

Here we have to do normal multiplication with shifting the decimal point by two places to the right

Therefore 100 × 0.005 = 0.5

**3. Find the product:**

**(i) 2.506 × 1000**

**(ii) 20.708 × 1000**

**(iii) 0.0529 × 1000**

**(iv) 1000 × 0.1**

**Solution:**

(i) Given 2.506 × 1000

Here we have to do normal multiplication with shifting the decimal point by three places to the right

Therefore 2.506 × 1000 = 2506

(ii) Given 20.708 × 1000

Here we have to do normal multiplication with shifting the decimal point by three places to the right

Therefore 20.708 × 1000 = 20708

(iii) Given 0.0529 × 1000

Here we have to do normal multiplication with shifting the decimal point by three places to the right

Therefore 0.0529 × 1000 = 52.9

(iv) Given 1000 × 0.1

Therefore 1000 × 0.1 = 100

**4. Find the product:**

**(i) 3.14 × 17**

**(ii) 0.745 × 12**

**(iii) 28.73 × 47**

**(iv) 0.0415 × 59**

**Solution:**

(i) Given 3.14 × 17

First multiply as usual without looking at the decimal point

3.14 × 17 = 578

Now mark the decimal point in the product to have one place of decimal as there in the given decimal

3.14 × 17 = 57.8

(ii) Given 0.745 × 12

First multiply as usual without looking at the decimal point

0.745 × 12 = 894

Now mark the decimal point in the product to have three places of decimal as there in the given decimal

0.745 × 12 = 8.94

(iii) Given 28.73 × 47

First multiply as usual without looking at the decimal point

28.73 × 47 = 135031

Now 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) Given 0.0415 × 59

First multiply as usual without looking at the decimal point

0.0415 × 59 = 24485

Now mark the decimal point in the product to have four places of decimal as there in the given decimal

0.0415 × 59 = 2.4485

**5. Find:**

**(i) 1.07 × 0.02**

**(ii) 211.9 × 1.13**

**(iii) 10.05 × 1.05**

**(iv) 13.01 × 5.01**

**Solution:**

(i) Given 1.07 × 0.02

First multiply as usual without looking at the decimal point

1.07 × 0.02 = 00214

Sum of the decimals is 4

Now mark the decimal point in the product to have four places of decimal as there in the given decimal

1.07 × 0.02 = 0.0214

(ii) Given 211.9 × 1.13

First multiply as usual without looking at the decimal point

211.9 × 1.13 = 239447

Sum of the decimals is 3

Now mark the decimal point in the product to have three places of decimal as there in the given decimal

211.9 × 1.13 = 239.447

(iii) Given 10.05 × 1.05

First multiply as usual without looking at the decimal point

10.05 × 1.05 = 105525

Sum of the decimals is 4

Now mark the decimal point in the product to have four places of decimal as there in the given decimal

10.05 × 1.05 = 10.5525

(iv) Given 13.01 × 5.01

First multiply as usual without looking at the decimal point

13.01 × 5.01 = 651801

Sum of the decimals is 4

13.01 × 5.01 = 65.1801

**6. Find the area of a rectangle whose length is 5.5m and breadth is 3.4m.**

**Solution:**

Given length of rectangle = 5.5m

Breadth of rectangle = 3.4 m

Area of rectangle = length × breadth

= 5.5 × 3.4

= 18.7 m2

**7. If the cost of a book is Rs 25.57, find the cost 0f 24 such books.**

**Solution:**

Given cost of a book is Rs 25.57

Cost of 24 books = 25.57 × 24

= Rs 618.00

**8. A car covers a distance of 14.75km in one liter of petrol. How much distance it will cover in 15.5 liters of petrol?**

**Solution:**

Given that distance covered by car in 1 liter of petrol = 14.75 km

Distance covered by car in 15.5 liters of petrol = 14.75 × 15.5

= 228.625 km

**9. One kg of rice costs Rs 42.65. What will be the cost of 18.25 kg of rice?**

**Solution:**

Given cost of 1kg of rice = 42.65

Cost of 18.25kg of rice = 42.65 × 18.25

= Rs 778.3625

**10. One meter of cloth costs Rs 152.50. What is the cost of 10.75 meters of cloth?**

**Solution:**

Given that cost of 1m cloth = Rs 152.50

Cost of 10.75 m of cloth = 152.50 × 10.75

= Rs 1639.375

## Exercise 3.3 Page No: 3.16

**1. Divide:**

**(i) 142.45 by 10**

**(ii) 54.25 by 10**

**(iii) 3.45 by 10**

**(iv) 0.57 by 10**

**(v) 0.0043 by 10**

**(vi) 0.004 by 10**

**Solution:**

(i) Given 142.45 by 10

Now shifting the decimal point by one place to the left we can get the result

142.45/10 = 14.245

(ii) Given 54.25 by 10

Now shifting the decimal point by one place to the left we can get the result

54.25/10 = 5.425

(iii) Given 3.45 by 10

Now shifting the decimal point by one place to the left we can get the result

3.45/10 = 0.345

(iv) Given 0.57 by 10

Now shifting the decimal point by one place to the left we can get the result

0.57/10 = 0.057

(v) Given 0.0043 by 10

Now shifting the decimal point by one place to the left we can get the result

0.0043/10 = 0.0043

(vi) Given 0.004 by 10

Now shifting the decimal point by one place to the left we can get the result

0.004/10 = 0.0004

**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) Given 459.5 by 100

Now shifting the decimal point by two places to the left we can get the result

459.5/100 = 4.595

(ii) Given 74.3 by 100

Now shifting the decimal point by two places to the left we can get the result

74.3/100 = 0.743

(iii) Given 5.8 by 100

Now shifting the decimal point by two places to the left we can get the result

5.8/100 = 0.058

(iv) Given 0.7 by 100

Now shifting the decimal point by two places to the left we can get the result

0.7/100 = 0.007

(v) Given 0.48 by 100

Now shifting the decimal point by two places to the left we can get the result

0.48/100 = 0.0048

(vi) Given 0.03 by 100

Now shifting the decimal point by two places to the left we can get the result

0.03 / 100 = 0.0003

**3. Divide:**

**(i) 235. 41 by 1000**

**(ii) 29.5 by 1000**

**(iii) 3.8 by 1000**

**(iv) 0.7 by 1000**

**Solution:**

(i) Given 235. 41 by 1000

Now shifting the decimal point by three places to the left we can get the result

235. 41/1000 = 0.23541

(ii) Given 29.5 by 1000

Now shifting the decimal point by three places to the left we can get the result

29.5/1000 = 0.0295

(iii) Given 3.8 by 1000

Now shifting the decimal point by three places to the left we can get the result

3.8 /1000 = 0.0038

(iv) Given 0.7 by 1000

Now shifting the decimal point by three places to the left we can get the result

0.7 /1000 = 0.0007

**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) Given 0.45 by 9

0.45 by 9 = 0.05

(ii) Given 217.44 by 18

217.44 by 18 = 12.08

3. Given 319.2 by 2.28

319.2 by 2.28 = 140

(iv) Given 40.32 by 9.6

40.32 by 9.6 = 4.2

(v) Given 0.765 by 0.9

0.765 by 0.9 = 0.85

(vi) Given 0.768 by 1.6

0.768 by 1.6 = 0.48

**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) Given 16.64 by 20

16.64 by 20 = 0.832

(ii) Given 0.192 by 12

0.192 by 12 = 0.016

(iii) Given 163.44 by 24

163.44 by 24 = 6.81

(iv) Given 403.2 by 96

403.2 by 96 = 4.2

(v) Given 16.344 by 12

16.344 by 12 = 1.362

(vi) Given 31.92 by 228

31.92 by 228 = 0.14

**6. Divide:**

**(i) 15.68 by 20**

**(ii) 164.6 by 200**

**(iii) 403.80 by 30**

**Solution:**

(i) Given 15.68 by 20

15.68 by 20 = 0.784

(ii) Given 164.6 by 200

164.6 by 200 = 0.823

(iii) Given 403.80 by 30

403.80 by 30 = 13.46

**7. Divide:**

**(i) 76 by 0.019**

**(ii) 88 by 0.08**

**(iii) 148 by 0.074**

**(iv) 7 by 0.014**

**Solution:**

(i) Given 76 by 0.019

Multiply both numerator and denominator by 1000 then divide

= 76000/19

76 by 0.019 = 4000

(ii) Given 88 by 0.08

Multiply both numerator and denominator by 100 then divide

= 8800/8

88 by 0.08 = 1100

(iii) Given 148 by 0.074

Multiply both numerator and denominator by 1000 then divide

= 14800/74

148 by 0.074 = 2000

(iv) Given 7 by 0.014

Multiply both numerator and denominator by 1000 then divide

= 7000/14

7 by 0.014 = 500

**8. Divide:**

**(i) 20 by 50**

**(ii) 8 by 100**

**(iii) 72 by 576**

**(iv) 144 by 15**

**Solution:**

(i) Given 20 by 50

20 by 50 = 0.4

(ii) Given 8 by 100

8 by 100 = 0.08

(iii) Given 72 by 576

72 by 576 = 0.125

(iv) Given 144 by 15

144 by 15 = 9.6

**9. A vehicle covers a distance 0f 43.2 km in 2.4 litres of petrol. How much distance will travel in 1 litre of petrol?**

**Solution:**

Given distance covered by vehicle in 2.4 litres of petrol is = 43.2 km

Distance travel by vehicle in 1 litre of petrol = 43.2/2.4

Multiply both numerator and denominator by 10 then we get 432/24

On dividing

Therefore 18km can travel in 1litre of petrol.

**10. The total weight of some bags of wheat is 1743 kg. If each bag weighs 49.8 kg, how many bags are there?**

**Solution:**

Given total weight of total bags = 1743 kg

Each bag weighs = 49.8 kg

Number of bags = 1743/49.8

Multiply both numerator and denominator by 10 then we get 17430/498

On dividing

Therefore number of bags are 35

**11. Shikha cuts 50 m of cloth into pieces 0f 1.25 m each. How many pieces does she get?**

**Solution:**

Given that total length of cloth = 50 m

Length of each piece = 1.25 m

Number of cloth piece = 50/1.25

Multiply both numerator and denominator by 100 then we get 5000/125

On dividing

Number of cloth piece = 40

**12. Each side of a rectangular polygon is 2.5cm in length. The perimeter of the polygon is 12.5 cm. How many sides does the polygon have?**

**Solution:**

Given that length of each side of polygon is = 2.5 cm

Perimeter of polygon = 12.5 cm

Number of sides = 12.5/2.5

Multiply both numerator and denominator by 10 then we get 125/25

On dividing

Number of sides of polygon is 5

**13. The product of two decimals is 42.987. If one of them is 12.46, find the other.**

**Solution:**

Given that product of two decimals = 42.987

One of the number is = 12.46

Another number is = 42.987/12.46

Multiply both numerator and denominator by 1000 then we get 42987/12460

On dividing

Another number is 3.45

**14. The weight of 34 bags of sugar is 3483.3 kg. If all bags weigh equally, find the weight of each bag.**

**Solution:**

Given that weight of 34 bags of sugar is = 3483.3 kg

Weight of each bag = 3483.3/34

Multiply both numerator and denominator by 10 then we get 34833/34

On dividing

Weight of each bag = 1o2.45 kg

**15. How many buckets of equal capacity can be filled from 586.5 litres of water, if each has capacity of 8.5 litres?**

**Solution:**

Given that capacity of each bucket = 8.5 litres

Total water available = 586.5 litres

Number of buckets = 586.5/8.5

Multiply both numerator and denominator by 10 then we get 5865/85

On dividing

Number of buckets = 69