RD Sharma solution class 7 chapter 3 Decimals Exercise 3.3

Exercise 3.3

Page-3.16

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

Answer 1:

(i)
  $$\begin{gathered} \frac{142.45}{10}=\frac{14245}{100 \times 10} \\ =\frac{14245}{1000} \\ =14.245 \end{gathered}$$


(ii)
  $$\begin{gathered} \frac{54.25}{10}= \frac{5425}{100\times 10} \\ =\frac{5425}{1000} \\ =5.425 \end{gathered}$$


(iii)
   $$\begin{gathered} \frac{3.45}{10}=\frac{345}{100\times 10} \\ =\frac{345}{1000} \\ =0.345 \end{gathered}$$

(iv)   
   $$\begin{gathered} \frac{0.57}{10}=\frac{57}{1000} \\ =0.057 \end{gathered}$$

(v)
   $$\begin{gathered} \frac{0.043}{10}=\frac{43}{10\times 1000} \\ =0.0043 \end{gathered}$$

(vi)
   $$\begin{gathered} \frac{0.004}{10}=\frac{4}{10\times 1000} \\ =0.0004 \end{gathered}$$

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

Answer 2:

(i)  $$\begin{gathered} \frac{459.5}{100}=\frac{4595}{1000} \\ =4.595 \end{gathered}$$

(ii) $$\begin{gathered} \frac{74.3}{100}=\frac{743}{1000} \\ =0.743 \end{gathered}$$

(iii)   $$\begin{gathered} \frac{5.8}{100}=\frac{58}{1000} \\ =0.058 \end{gathered}$$

(iv)  $$\begin{gathered} \frac{0.7}{100}=\frac{7}{1000} \\ =0.007 \end{gathered}$$

(v)  $$\begin{gathered} \frac{0.48}{100}=\frac{48}{100\times 100} \\ =0.0048 \end{gathered}$$

(vi)  $$\begin{gathered} \frac{0.03}{100}=\frac{3}{100\times 100} \\ =0.0003 \end{gathered}$$

Question 3:

Divide:
(i) 235.41 by 1000
(ii) 29.5 by 1000
(iii) 3.8 by 1000
(iv) 0.7 by 1000

Answer 3:

(i)  $$\begin{gathered} \frac{235.41}{1000}=\frac{23541}{1000\times 100} \\ =0.23451 \end{gathered}$$

(ii) $$\begin{gathered} \frac{29.5}{1000}=\frac{295}{1000\times 10} \\ =0.0295 \end{gathered}$$

(iii)   $$\begin{gathered} \frac{3.8}{1000}=\frac{38}{1000\times 10} \\ =0.0038 \end{gathered}$$

(iv)  $$\begin{gathered} \frac{0.7}{1000}=\frac{7}{1000\times 10} \\ =0.0007 \end{gathered}$$

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

Answer 4:

(i) 
  $$\begin{gathered} \frac{0.45}{9}=\frac{45}{9\times 100} \\ =\frac{5}{100} \\ =0.05 \end{gathered}$$

(ii)
   $$\begin{gathered} \frac{217.44}{18}=\frac{21744}{18\times 100} \\ =12.08 \end{gathered}$$

(iii) 
   $$\begin{gathered} \frac{319.2}{2.28}=\frac{3192\times 100}{228\times 10} \\ =140 \end{gathered}$$

(iv) 
    $$\begin{gathered} \frac{40.32}{9.6}=\frac{4032\times 10}{96\times 100} \\ =4.2 \end{gathered}$$

(v)  
   $$\begin{gathered} \frac{0.765}{0.9}=\frac{765\times 10}{9\times 1000} \\ =\frac{7650}{9000} \\ =0.85 \end{gathered}$$

(vi) 
    $$\begin{gathered} \frac{0.768}{1.6}=\frac{768\times 10}{16\times 1000} \\ =\frac{7680}{16000} \\ =0.48 \end{gathered}$$

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

Answer 5:

(i) 
  $$\begin{gathered} \frac{16.64}{20}=\frac{1664}{20\times 100} \\ =0.832 \end{gathered}$$

(ii) 
   $$\begin{gathered} \frac{0.192}{12}=\frac{192}{12\times 1000} \\ =0.016 \end{gathered}$$

(iii) 
   $$\begin{gathered} \frac{163.44}{24}=\frac{16344}{24\times 100} \\ =6.81 \end{gathered}$$

(iv) 
   $$\begin{gathered} \frac{403.2}{96}=\frac{4032}{960} \\ =4.2 \end{gathered}$$

(v)  
  $$\begin{gathered} \frac{16.344}{12}=\frac{16344}{12\times 1000} \\ =\frac{1362}{1000} \\ =1.362 \end{gathered}$$

(vi) 
    $$\begin{gathered} \frac{31.92}{228}=\frac{3192}{228\times 100} \\ =\frac{14}{100} \\ =0.14 \end{gathered}$$

Question 6:

Divide:
(i) 15.68 by 20
(ii) 164.6 by 200
(iii) 403.80 by 30

Answer 6:

(i) 

$\frac{15.68}{20}$
 $$\begin{gathered} =\frac{1568}{20\times 100} \\ =0.784 \end{gathered}$$

(ii) 

$\frac{164.6}{200}$
$$\begin{gathered} \frac{1646}{200\times 10} \\ =\frac{1646}{2000} \\ =0.823 \end{gathered}$$


(iii) 

$\frac{403.8}{30}$
$$\begin{gathered} =\frac{4038}{30\times 10} \\ =\frac{4038}{300} \\ =13.46 \end{gathered}$$

Page-3.17

Question 7:

Divide:
(i) 76 by 0.019
(ii) 88 by 0.08
(iii) 148 by 0.074
(iv) 7 by 0.014

Answer 7:

(i)  
$$\begin{gathered} \frac{76}{0.019}=\frac{76\times 1000}{19} \\ =4000 \end{gathered}$$

(ii) 
  $$\begin{gathered} \frac{88}{0.08}=\frac{88\times 100}{8} \\ =1100 \end{gathered}$$

(iii) 
$$\begin{gathered} \frac{148}{0.074}=\frac{148\times 1000}{74} \\ =2000 \end{gathered}$$

(iv) 
$$\begin{gathered} \frac{7}{0.014}=\frac{7\times 1000}{14} \\ =500 \end{gathered}$$

Question 8:

Divide:
(i) 20 by 50
(ii) 8 by 100
(iii) 72 by 576
(iv) 144 by 15

Answer 8:

(i)

$$\begin{gathered} \frac{20}{50} \\ =\frac{2}{5} \\ =0.4 \end{gathered}$$


(ii)

$$\begin{gathered} \frac{8}{100} \\ =0.08 \end{gathered}$$

(iii) 

$$\begin{gathered} \frac{72}{576} \\ =\frac{18}{144} \\ =\frac{3}{24} \\ =0.125 \end{gathered}$$

(iv)

$$\begin{gathered} \frac{144}{15} \\ =\frac{48}{5} \\ =9.6 \end{gathered}$$

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?

Answer 9:

Distance travelled by the vehicle in 2.4 litres of petrol = 43.2 km

$\therefore$ Distance travelled in 1 litre of petrol will be:

$$\begin{gathered} \frac{43.2}{2.4} \\ =\frac{432}{24} \\ =18 \end{gathered}$$

Thus, the vehicle will travel 18 km in 1 litre of petrol.

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?

Answer 10:

Let the number of bags of wheat be x.

Given:

Weight of x bags = 1,743 kg

Weight of one bag = 49.8 kg

Therefore, 49.8 $\times$ x = 1,743
x = $$\begin{gathered} \frac{1743}{49.8} \\ =\frac{1743 \times 10}{498} \end{gathered}$$
       = 35

Thus, there are 35 bags of wheat.

Question 11:

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

Answer 11:

Length of cloth = 50 m

Length of one piece of cloth = 1.25 m

Let the number of pieces be x.

$\therefore$ Number of pieces​ of cloth $\times$ Length of each piece of cloth = Total length of cloth

x $\times$1.25 = 50
x = $\frac{50}{1.25}$
   = $$\begin{gathered} \frac{50 \times 100}{125} \\ =40 \end{gathered}$$

Thus, she gets 40 pieces of 1.25 m cloth from a total of 50 m.

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?

Answer 12:

Length of each side of the polygon  = 2.5 cm

Perimeter of the polygon = 12.5 cm

Let the number of sides of the polygon be z.

$\therefore$ 2.5 $\times$ z = 12.5 ( Perimeter = Length of one side multiplied by the number of sides)
or, z = $$\begin{gathered} \frac{12.5}{2.5} \\ =5 \end{gathered}$$

Thus, the polygon has 5 sides.

Question 13:

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

Answer 13:

One decimal is 12.46.

Let the other decimal be x.

According to the question:

12.46 $\times$ x = 42.987
 $$\begin{gathered} x =\frac{42.987}{12.46} \\ =\frac{42987\times 100}{1246\times 1000} \\ =\frac{42987}{12460} \\ =3.45 \end{gathered}$$

Thus, the other decimal 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.

Answer 14:

Number of bags = 34

Weight of 34 bags = 3483.3 kg

$\therefore$ Weight of one bag = $\frac{\mathrm{Weight} \mathrm{of} 34 \mathrm{bags}}{\mathrm{Number} \mathrm{of} \mathrm{bags}}$
$$\begin{gathered} \frac{3483.3}{34} \\ =\frac{34833}{340} \\ =102.45 \end{gathered}$$

Thus, weight of each bag = 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?

Answer 15:

Capacity of one bucket = 8.5 litres

Total water in all buckets = 586.5 litres

Let the number of buckets with equal capacity be x.

According to the question:

8.5 $\times$ x = 586.5
$$\begin{gathered} x =\frac{586.5}{8.5} \\ =\frac{5865}{85} \\ =69 \end{gathered}$$

Thus, there are 69 buckets.

Question 1:

Mark the correct alternative in each of the following:

When 0.48 is written in the simplest form of its terms, the sum of its numerator and denominator is

(a) 148                                         (b) 74                                         (c) 37                                         (d) 147                                      

Answer 1:

$$\begin{gathered} 0.48=\frac{48}{100} \\ =\frac{48÷4}{100÷4} \left(\mathrm{HCF}\hspace{0.17em}\mathrm{of} 48 \mathrm{and} 100=4\right) \\ =\frac{12}{25} \end{gathered}$$

Here,

Numerator = 12

Denominator = 25

∴ Sum of the numerator and denominator = 12 + 25 = 37

Hence, the correct answer is option (c).

Question 2:

Mark the correct alternative in each of the following:

The improper fraction $2\frac{1}{25}$ in decimal form is

(a) 2.4                                        (b) 2.04                                        (c) 2.004                                         (d) None of these                                      

Answer 2:

The given fraction is $2\frac{1}{25}$. Now,
$$\begin{gathered} 2\frac{1}{25} \\ =2+\frac{1}{25} \\ =2+\frac{1\times 4}{25\times 4} \\ =2+\frac{4}{100} \\ =2+0.04 \\ =2.04 \end{gathered}$$

Hence, the correct answer is option (b).

Question 3:

Mark the correct alternative in each of the following:

4 + 4.4 + 44.4 + 4.04 + 444 =

(a) 500.88                                         (b) 577.2                                         (c) 495.22                                         (d) 472.88                                       

Answer 3:

Converting the decimals to like decimals, we have 4.00, 4.40, 44.40, 4.04 and 444.00.

Now,
 

			4	.	0	0
			4	.	4	0
		4	4	.	4	0
			4	.	0	4
+	4	4	4	.	0	0

5

0

0

.

8

4

∴ 4 + 4.4 + 44.4 + 4.04 + 444 = 500.84


Disclaimer: None of the options given in the question matches with the answer.