Decimals (Exercise 3.2) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

Q.1. Find the product:

(i) 4.74 × 10

(ii) 0.45 × 10

(iii) 0.0215 × 10

(iv) 0.0054 × 10

Ans: 

(i) On dividing by 100, we get:

4.74 ×10 = × 10 = = 47.4

(ii) On dividing by 100, we get:

×10 = = 4.5

(iii) Because the decimal is after 4 places from the right, we will divide by 10,000. We get: 

×10 = = 0.215

(iv) Because the decimal is after 4 places from the right, we will divide by 10,000. We get:

×10 = = 0.054

Q.2. Find the product:

(i) 35.853 × 100

(ii) 42.5 × 100

(iii) 12.075 × 100

(iv) 100 × 0.005

Ans: 

(i) On dividing by 1,000, we get:

× 100 = = 3585.3

(ii) On dividing by 10, we get:

× 100 =425 ×10 = 4250

(iii) On dividing by 1,000, we get:

× 100 =  = 1207.5

(iv) On dividing by 1,000, we get:

100 ×== 0.5

Q.3. Find the product:

(i) 2.506 × 1000

(ii) 20.708 × 1000

(iii) 0.0529 × 1000

(iv) 1000 × 0.1

Ans: 

(i) On dividing by 1000, we get:

×1000 = 2506

(ii) On dividing by 1000, we get:

× 1000 = 20708

(iii) On dividing by 10,000, we get:

×1000 = = 52.9

(iv) On dividing by 10, we get:

1000 ×= 100

Q.4. Find the product:

(i) 3.4 × 17

(ii) 0.745 × 12

(iii) 28.73 × 47

(iv) 0.0415 × 59

Ans: 

(i) On dividing the decimal by 10 and multiplying the numbers, we get:

 = 57.8

(ii) On dividing the decimal by 1000 and multiplying the numbers, we get:

 = 8.94

(iii) On dividing the decimal by 100 and multiplying the numbers, we get:

 = 1350.31

(iv) On dividing the decimal by 10000 and multiplying the numbers, we get:

 = 2.4485

Q.5. Find:

(i) 1.07 × 0.02

(ii) 211.9 × 1.13

(iii) 10.05 × 1.05

(iv) 13.01 × 5.01

Ans: 

(i)

=

= 0.0214

(ii)

=

= 239.447

(iii)

=

= 10.5525

(iv)

=

= 65.1801

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

Ans: Length of the rectangle = 5.5 m

Breadth of the rectangle = 3.4 m

We know:

Area of rectangle = Length × Breadth

= 5.5 × 3.4 == 18.7 meter square

Thus, area of the rectangle = 18.7 m²

Q.7. If the cost of a book is Rs 25.75, find the cost of 24 such books.

Ans: Cost of one book = Rs. 25.75

∴ Cost of 24 books = Rs. 25.75 × 24

=

=

= 103 × 6 

= 618

Q.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?

Ans: Distance travelled by the car in 1 litre of petrol = 14.75 km

∴ Distance travelled by the car in 15.5 litres of petrol = 14.75 × 15.5

=

=

= 228.625 km

Thus, the car travelled 228.625 km in 15.5 litres of petrol.

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

Ans: Price of 1 kg of rice = Rs. 42.65

Price of 18.25 kg of rice = Rs. 42.65 × 18.25

=

=

= 778.3625

Thus, 18.25 kg of rice will cost Rs. 778.36.

Q.10. One metre of cloth costs Rs 152.50. What is the cost of 10.75 metres of cloth?

Ans: Cost of 1 m of cloth = Rs. 152.50

∴ Cost of 10.75 m of cloth = Rs. 152.50 × 10.75

=

= 1639.375

Thus, 10.75 m of cloth will cost Rs. 1639.375.