RD Sharma solution class 7 chapter 3 Decimals Exercise 3.2

Exercise 3.2

Page-3.8

Question 1:

Find the product:
(i) 4.74 × 10
(ii) 0.45 × 10
(iii) 0.0215 × 10
(iv) 0.0054 × 10

Answer 1:

i) On dividing by 100, we get:

4.74 $\times$10 = $\frac{474}{100}\times 10 = \frac{474}{10}= 47.4$

ii) On dividing by 100, we get:

$\frac{45}{100}\times 10 = \frac{45 }{10}= 4.5$

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

$\frac{215}{10000}\times 10 = \frac{215}{1000}= 0.215$

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

$\frac{54}{10000}\times 10=\frac{54}{1000} = 0.054$

Question 2:

Find the product:
(i) 35.853 × 100
(ii) 42.5 × 100
(iii) 12.075 × 100
(iv) 100 × 0.005

Answer 2:

i) On dividing by 1,000, we get:

$\frac{35853}{1000}\times 100 = \frac{35853}{10}= 3585.3$

ii) On dividing by 10, we get:

 $\frac{425}{10}\times 100 =425 \times 10 = 4250$

iii) On dividing by 1,000, we get:

$\frac{12075}{1000}\times 100 = \frac{12075}{10 }= 1207.5$

iv) On dividing by 1,000, we get:

$100\times \frac{5}{1000}=\frac{5}{10}= 0.5$

Question 3:

Find the product:
(i) 2.506 × 1000
(ii) 20.708 × 1000
(iii) 0.0529 × 1000
(iv) 1000 × 0.1

Answer 3:

i) On dividing by 1000, we get:

$\frac{2506}{1000}\times 1000 = 2506$

ii) On dividing by 1000, we get:

$\frac{20708}{1000}\times 1000 = 20708$

iii) On dividing by 10,000, we get:

$\frac{529}{10000}\times 1000 = \frac{529}{10}=52.9$

iv) On dividing by 10, we get:

$1000 \times \frac{1}{10}= 100$

Question 4:

Find the product:
(i) 3.4 × 17
(ii) 0.745 × 12
(iii) 28.73 × 47
(iv) 0.0415 × 59

Answer 4:

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

$\frac{34}{10}\times 17 = \frac{578}{10}= 57.8$

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

$\frac{745}{1000}\times 12 = \frac{8940}{1000}= 8.94$

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

$\frac{2873}{100}\times 47= \frac{135031}{100}= 1350.31$

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

$\frac{415}{10000}\times 59 =\frac{24485}{10000} = 2.4485$

Question 5:

Find:
(i) 1.07 × 0.02
(ii) 211.9 × 1.13
(iii) 10.05 × 1.05
(iv) 13.01 × 5.01

Answer 5:

i)
   $$\begin{gathered} \frac{107}{100}\times \frac{2}{100} \\ =\frac{107\times 2}{10000} \end{gathered}$$
= 0.0214


ii) 
  $$\begin{gathered} \frac{2119}{10}\times \frac{113}{100} \\ =\frac{239447}{1000} \\ =239.447 \end{gathered}$$

iii)
   $$\begin{gathered} \frac{1005}{100}\times \frac{105}{100} \\ =\frac{105525}{10000} \\ =10.5525 \end{gathered}$$

iv)  

$$\begin{gathered} \frac{1301}{100}\times \frac{501}{100} \\ =\frac{651801}{10000} \\ =65.1801 \end{gathered}$$

Page-3.9

Question 6:

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

Answer 6:

Length of the rectangle = 5.5 m

Breadth of the rectangle = 3.4 m

We know:

Area of rectangle = Length $\times$ Breadth
                              = $5.5 \times 3.4 =\frac{55}{10}\times \frac{34}{10}=\frac{1870}{100}=18.7 meter square$

Thus, area of the rectangle = 18.7 m²

Question 7:

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

Answer 7:

Cost of one book = Rs. 25.75

∴ Cost of 24 books = Rs. 25.75 $\times$ 24
= $\frac{2575}{100}\times 24$
= $$\begin{gathered} \frac{103}{4}\times 24=103\times 6 \\ = 618 \end{gathered}$$

Hence, the cost of 24 books is Rs. 618.

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?

Answer 8:

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

∴ Distance travelled by the car in 15.5 litres of petrol = $14.75 \times 15.5$

= $\frac{1475}{100}\times \frac{155}{10}$
= $\frac{228625}{1000}$
= 228.625 km

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

Question 9:

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

Answer 9:

Price of 1 kg of rice = Rs. 42.65

Price of 18.25 kg of rice = Rs. 42.65 $\times$ 18.25
= $$\begin{gathered} \frac{4265}{100}\times \frac{1825}{100} \\ =\frac{7783625}{10000} \end{gathered}$$

= 778.3625

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

Question 10:

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

Answer 10:

Cost of 1 m of cloth = Rs. 152.50

$\therefore$ Cost of 10.75 m of cloth = Rs. 152.50 $\times$ 10.75

$$\begin{gathered} \frac{1525}{10}\times \frac{1075}{100} \\ =\frac{1639375}{1000} \end{gathered}$$
= 1639.375

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