RD Sharma Solutions Class 7 Chapter 3 Decimals

Question 9: By how much should 34.79 be increased to get 70.15? 

Solution 9:

Let  be the unknown number

 + 34.79 = 70.15

 = 70.15 – 34.79

 = 35.36

35.36 should be increased to 34.79 to get 70.15

Question 10: By how much should 59.71 be decreased to get 34.58? 

Solution 10:

Let  be the unknown number

59.71 –  =34.58

59.71 – 34.58 =

 = 59.71 – 34.58

 = 25.13

25.13 should be decreased by 59.71 to get 34.58

Exercise 3.2

Question :1. Find the product:

(i) 4.74 × 10

(ii) 0.45 × 10

(iii) 0.0215 × 10

(iv) 0.0054 × 10 

Solution 1:

(i) 4.74 × 10

Now we’ve to do normal multiplication by shifting the decimal point by one place to the right

Therefore, 4.74 × 10 = 47.4

(ii) 0.45 × 10

Now we’ve to do normal multiplication by shifting the decimal point by one place to the right

Therefore, 0.45 × 10 = 4.5

(iii) 0.0215 × 10

Now we’ve to do normal multiplication by shifting the decimal point by one place to the right

Therefore, 0.0215 × 10 = 0.215

(iv) 0.0054 × 10

Now we’ve to do normal multiplication by shifting the decimal point by one place to the right

Therefore, 0.0054 × 10 = 0.054

Question :2. Find the product:

(i) 35.853 × 100

(ii) 42.5 × 100

(iii) 12.075 × 100

(iv) 100 × 0.005 

Solution 2:

(i) 35.853 × 100

Now we’ve to do normal multiplication by shifting the decimal point by two places to the right

Therefore, 35.853 × 100 = 3585.3

(ii) 42.5 × 100

Now we’ve to do normal multiplication by shifting the decimal point by two places to the right

Therefore, 42.5 × 100 = 4250

(iii) 12.075 × 100

Now we’ve to do normal multiplication by shifting the decimal point by two places to the right

Therefore, 12.075 × 100 = 1207.50

(iv) 100 × 0.005

Now we’ve to do normal multiplication by shifting the decimal point by two places to the right

Therefore, 100 × 0.005 = 0.5

Question :3. Find the product:

(i) 2.506 × 1000

(ii) 20.708 × 1000

(iii) 0.0529 × 1000

(iv) 1000 × 0.1 

Solution 3:

(i) 2.506 × 1000

Now we’ve to do normal multiplication by shifting the decimal point by three places to the right

Therefore 2.506 × 1000 = 2506

(ii) 20.708 × 1000

Now we’ve to do normal multiplication by shifting the decimal point by three places to the right

Therefore 20.708 × 1000 = 20708

(iii) 0.0529 × 1000

Now we’ve to do normal multiplication by shifting the decimal point by three places to the right

Therefore 0.0529 × 1000 = 52.9

(iv) 1000 × 0.1

Now we’ve to do normal multiplication by shifting the decimal point by three places to the right

Therefore 1000 × 0.1 = 100

Question :4. Find the product:

(i) 3.14 × 17

(ii) 0.745 × 12

(iii) 28.73 × 47

(iv) 0.0415 × 59 

Solution 4:

Question :5. Find:

(i) 1.07 × 0.02

(ii) 211.9 × 1.13

(iii) 10.05 × 1.05

(iv) 13.01 × 5.01 

Solution 5:

(i) 1.07 × 0.02

Multiply normally without observing at the decimal point

1.07 × 0.02 = 00214

Now put 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) 211.9 × 1.13

Multiply normally without observing at the decimal point

211.9 × 1.13 = 239447

Now put 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) 10.05 × 1.05

Multiply normally without observing at the decimal point

10.05 × 1.05 = 105525

Now put 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) 13.01 × 5.01

Multiply normally without observing at the decimal point

13.01 × 5.01 = 651801

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

13.01 × 5.01 = 65.1801

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

Solution 6:

According to the given information Length of rectangle = 5.5m

Breadth of rectangle = 3.4 m

Area of rectangle = length × breadth

= 5.5 × 3.4

= 18.7 m²

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

Solution 7:

According to the given information the cost of a book is Rs 25.57

The Cost of 24 books are = 25.57 × 24

= Rs 618.00 

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 4:

 

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 5:

 

Question :6. Divide:

(i) 15.68 by 20

(ii) 164.6 by 200

(iii) 403.80 by 30 

Solution 6:

 

Question :7. Divide:

(i) 76 by 0.019

(ii) 88 by 0.08

(iii) 148 by 0.074

(iv) 7 by 0.014 

Solution 7:

(i) 76 by 0.019 = 76/0.019

Multiply the fraction by 1000 then divide

= 76000/19

 

 

Question 8: Divide:

(i) 20 by 50

(ii) 8 by 100

(iii) 72 by 576

(iv) 144 by 15

 

Solution 8:

 

 

Question 9: A vehicle covers a distance 0f 43.2 km in 2.4 liters of petrol. How much distance will travel in 1 liter of petrol?

 

Solution 9:

 

Vehicle covered distance in 2.4 liters of petrol is = 43.2 km

Vehicle distance travel in 1 liter of petrol = 43.2/2.4

Multiply both by 10 then we get 432/24

On dividing

 

Hence, 18km can travel in 1litre of petrol.

 

 

Question 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 10:

 

Total weight of bags are 1743 kg

Each bag weighs are 49.8 kg

Number of bags are 1743/49.8

Multiply both by 10 then we get 17430/498

On dividing

 

 

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

 

Solution 11:

That total length of cloth is 50 m

Length of each piece is 1.25 m

Number of cloth piece are 50/1.25

Multiply both by 100 then we get 5000/125

On dividing

 

 

Question :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 12:

 

The length of each side of polygon is 2.5 cm

Perimeter of polygon is 12.5 cm

Number of sides is 12.5/2.5

Multiply both by 10 then we get 12.5/25

On dividing

 

 

 

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

 

Solution 13:

The product of two decimals  42.987

One of the numbers is 12.46

Another number is  42.987/12.46

Multiply both by 1000 then we get 42987/12460 

On dividing

 

Another 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 14:

The weight of 34 bags of sugar is = 3483.3 kg

Weight of each bag is 3483.3/34

Multiply both by 10 then we get 34833/34

On dividing

 

 

Each bag’s weight 102.45 kg

 

 

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

 

Solution 15:

 

The capacity of each bucket = 8.5 liters

Total water available = 586.5 liters

Number of buckets = 586.5/8.5

Multiply both by 10 then we get 5865/85

On dividing