RS Aggarwal 2019,2020 solution class 7 chapter 3 Decimals Exercise 3D

Exercise 3D

page-49

Question 1:

Divide:

(i) 131.6 by 10
(ii) 32.56 by 10
(iii) 4.38 by 10
(iv) 0.34 by 10
(v) 0.08 by 10
(vi) 0.062 by 10

Answer 1:

We have the following:

(i) 131.6 ÷ 10 = $\frac{131.6}{10}=13.16$                      [Shift the decimal point to the left by 1 place]

(ii) 32.56 ÷ 10 = $\frac{32.56}{10}=3.256$                    [Shift the decimal point to the left by 1 place]

(iii) 4.38 ÷ 10 = $\frac{4.38}{10}=0.438$                       [Shift the decimal point to the left by 1 place]

(iv) 0.34 ÷ 10 = $\frac{0.34}{10}=0.034$                       [Shift the decimal point to the left by 1 place]

(v) 0.08 ÷ 10 = $\frac{0.08}{10}=0.008$                        [Shift the decimal point to the left by 1 place]

(vi) 0.062 ÷ 10 = $\frac{0.062}{10}=0.0062$                 [Shift the decimal point to the left by 1 place]

Question 2:

Divide:

(i) 137.2 by 100
(ii) 23.4 by 100
(iii) 4.7 by 100
(iv) 0.3 by 100
(v) 0.58 by 100
(vi) 0.02 by 100

Answer 2:

We have the following:

(i) 137.2 ÷ 100 = $\frac{137.2}{100}=1.372$                          [Shifting the decimal point to the left by 2 places]

(ii) 23.4 ÷ 100 =$\frac{23.4}{100}=0.234$                              [Shifting the decimal point to the left by 2 places]

(iii) 4.7 ÷ 100 = $\frac{4.7}{100}=0.047$                               [Shifting the decimal point to the left by 2 places]

(iv) 0.3 ÷ 100 = $\frac{0.3}{100}=0.003$                               [Shifting the decimal point to the left by 2 places]

(v) 0.58 ÷ 100 = $\frac{0.58}{100}=0.0058$                           [Shifting the decimal point to the left by 2 places]

(vi) 0.02 ÷ 100 = $\frac{0.02}{100}=0.0002$                          [Shifting the decimal point to the left by 2 places]

Question 3:

Divide:

(i) 1286.5 by 1000
(ii) 354.16 by 1000
(iii) 38.9 by 1000
(iv) 4.6 by 1000
(v) 0.8 by 1000
(vi) 2 by 1000

Answer 3:

We have the following:

(i) 1286.5 ÷ 1000 = $\frac{1286.5}{1000}=1.2865$                 [Shift the decimal point to the left by 3 places]

(ii) 354.16 ÷ 1000 = $\frac{354.16}{1000}=0.35416$              [Shift the decimal point to the left by 3 places]

(iii) 38.9 ÷ 1000 = $\frac{38.9}{1000}=0.0389$                      [Shift the decimal point to the left by 3 places]

(iv) 4.6 ÷ 1000 = $\frac{4.6}{1000}=0.0046$                        [Shift the decimal point to the left by 3 places]

(v) 0.8 ÷ 1000 = $\frac{0.8}{1000}=0.0008$                         [Shift the decimal point to the left by 3 places]

(vi) 2 ÷ 1000 = $\frac{2}{1000}=0.002$                           [Shift the decimal point to the left by 3 places]

Question 4:

Divide:

(i) 12 by 8
(ii) 63 by 15
(iii) 47 by 20
(iv) 101 by 25
(v) 31 by 40
(vi) 11 by 16

Answer 4:

(i) 12 ÷ 8 = $\frac{12}{8}=\frac{3}{2}$
     

  ∴ 12 ÷ 8 = 1.5

(ii) 63 ÷ 15 = $\frac{63}{15}=\frac{21}{5}$
     
   ∴ 63 ÷ 15 = 4.2

(iii) 47 ÷ 20 = $\frac{47}{20}$
      
        ∴ 47 ÷ 20 = 2.35

(iv) 101 ÷ 25 = $\frac{101}{25}$
      
       ∴ 101 ÷ 25 = 4.04

(v ) 31 ÷ 40
    
    
    ∴ 31 ÷ 40 = 0.775

(vi) 11 ÷ 16 = $\frac{11}{16}$
      
      
       ∴ 11 ÷ 16 = 0.6875    

Question 5:

Divide:

(i) 43.2 by 6
(ii) 60.48 by 12
(iii) 117.6 by 21
(iv) 217.44 by 18
(v) 2.575 by 25
(vi) 6.08 by 8
(vii) 0.765 by 9
(viii) 0.768 by 16
(ix) 0.175 by 25
(x) 0.3322 by 11
(xi) 2.13 by 15
(xii) 6.54 by 12
(xiii) 5.52 by 16
(xiv) 1.001 by 14
(xv) 0.477 by 18

Answer 5:

(i) We have:
      43.2 ÷ 6
      
       ∴ 43.2 ÷ 6 = 7.2
(ii) We have:
       60.48 ÷ 12
       
        ∴ 60.48 ÷ 12 = 5.04

(iii) We have:
        117.6 ÷ 21
       
      ∴ 117.6 ÷ 21 = 5.6

(iv) We have:
        217.44 ÷ 18
       
     ∴ 217.44 ÷ 18 = 12.08

(v) We have:
      2.575 ÷ 25
     
       ∴ 2.575 ÷ 25 = 0.103

(vi) We have:
       6.08 ÷ 8
      
      ∴ 6.08 ÷ 8 = 0.76

(vii) We have:
        0.765 ÷ 9
       
       ∴ 0.765 ÷ 9 = 0.085

(viii) We have:
          0.768 ÷ 16
         
      ∴ 0.768 ÷ 16 = 0.048
(ix) We have:
        0.175 ÷ 25

$$\begin{gathered} =\frac{0.175}{25} \\ =\frac{0.175\times 1000}{25\times 1000} \\ =\frac{175}{25\times 1000} \\ =\frac{7}{1000} \\ =0.007 \end{gathered}$$

(x) We have:
      0.3322 ÷ 11
     
     ∴ 0.3322 ÷ 11 = 0.0302

(xi) We have:
       2.13 ÷ 15
      
     ∴ 2.13 ÷ 15 = 0.142

(xii) We have:
         6.54 ÷ 12
        
      ∴ 6.54 ÷ 12 = 0.545

(xiii) We have:
         5.52 ÷ 16
        
     ∴ 5.52 ÷ 16 = 0.345

(xiv) We have:
         1.001 ÷ 14
         
    ∴ 1.001 ÷ 14 = 0.0715

(xv) We have:
       0.477 ÷ 18
       
        ∴ 0.477 ÷ 18 =  0.0265

Question 6:

Divide:

(i) 16.46 ÷ 20
(ii) 403.8 ÷ 30
(iii) 19.2 ÷ 80
(iv) 156.8 ÷ 200
(v) 12.8 ÷ 500
(vi) 18.08 ÷ 400

Answer 6:

(i) 16.46 ÷ 20 = $\frac{16.46}{20}=\frac{16.46\times 100}{20\times 100}=\frac{1646}{2\times 1000}=\frac{823}{1000}=0.823$

(ii) 403.8 ÷ 30 = $\frac{403.8}{30}=\frac{403.8\times 10}{30\times 10}=\frac{4038}{3\times 100}=\frac{1346}{100}=13.46$

(iii) 19.2 ÷ 80 = $\frac{19.2}{80}=\frac{19.2\times 10}{80\times 10}=\frac{192}{800}=\frac{192}{8\times 100}=\frac{24}{100}=0.24$

(iv) 156.8 ÷ 200 = $\frac{156.8}{200}=\frac{156.8\times 10}{200\times 10}=\frac{1568}{2000}=\frac{784}{1000}=0.784$

(v) 12.8 ÷ 500 = $\frac{12.8}{500}=\frac{12.8\times 10}{500\times 10}=\frac{128}{5000}=\frac{25.6}{1000}=0.0256$

(vi) 18.08 ÷ 400 = $\frac{18.08}{400}=\frac{18.08\times 100}{400\times 100}=\frac{1808}{40000}=\frac{452}{10000}=0.0452$

Question 7:

Divide:

(i) 3.28 by 0.8
(ii) 0.288 by 0.9
(iii) 25.395 by 1.5
(iv) 2.0484 by 0.18
(v) 0.228 by 0.38
(vi) 0.8085 by 0.35
(vii) 21.976 by 1.64
(viii) 11.04 by 1.6
(ix) 6.612 by 11.6
(x) 0.076 by 0.19
(xi) 148 by 0.074
(xii) 16.578 by 5.4
(xiii) 28 by 0.56
(xiv) 204 by 0.17
(xv) 3 by 80

Answer 7:

(i) 3.28 ÷ 0.8 = $\frac{3.28}{0.8}=\frac{3.28\times 10}{0.8\times 10}=\frac{32.8}{8}$
Now, we have:

     
       ∴ $\frac{3.28}{0.8}=\frac{32.8}{8}=4.1$

(ii)  0.288 ÷ 0.9 = $\frac{0.288}{0.9}=\frac{0.288\times 10}{0.9\times 10}=\frac{2.88}{9}$
Now, we have:

      
      ∴ $\frac{0.288}{0.9}=\frac{2.88}{9}=0.32$

(iii)  25.395 ÷ 1.5 = $\frac{25.395}{1.5}=\frac{25.395\times 10}{1.5\times 10}=\frac{253.95}{15}$
Now, we have:

        
       ∴ $\frac{25.395}{1.5}=\frac{253.95}{15}=16.93$

(iv) 2.0484 ÷ 0.18 = $\frac{2.0484}{0.18}=\frac{2.0484\times 100}{0.18\times 100}=\frac{204.84}{18}$
Now, we have:

       
     ∴ $\frac{2.0484}{0.18}=\frac{204.84}{18}=11.38$

(v)  0.228 ÷ 0.38 = $\frac{0.228}{0.38}=\frac{0.228\times 100}{0.38\times 100}=\frac{22.8}{38}$
Now, we have:
      

     ∴ $\frac{0.228}{0.38}=\frac{22.8}{38}=0.6$

(vi) 0.8085 ÷ 0.35 = $\frac{0.8085}{0.35}=\frac{0.8085\times 100}{0.35\times 100}=\frac{80.85}{35}$
Now, we have:

      
      ∴$\frac{0.8085}{0.35}=\frac{80.85}{35}=2.31$

(vii) 21.976 ÷ 1.64 = $\frac{21.976}{1.64}=\frac{21.976\times 100}{1.64\times 100}=\frac{2197.6}{164}$
Now, we have:

       
        ∴ $\frac{21.976}{1.64}=\frac{2197.6}{164}=13.4$

(viii) 11.04 ÷ 1.6 = $\frac{11.04}{1.6}=\frac{11.04\times 10}{1.6\times 10}=\frac{110.4}{16}$
Now, we have:
          

       ∴$\frac{11.04}{1.6}=\frac{110.4}{16}=6.9$
     
(ix)  6.612 ÷ 11.6 = $\frac{6.612}{11.6}=\frac{6.612\times 10}{11.6\times 10}=\frac{66.12}{116}$
Now, we have:
      
       ∴ $\frac{6.612}{11.6}=\frac{66.12}{116}=0.57$

(x) 0.076 ÷  0.19 = $\frac{0.076}{0.19}=\frac{0.076\times 100}{0.19\times 100}=\frac{7.6}{19}$
Now, we have:
    
    ∴ $\frac{0.076}{0.19}=\frac{7.6}{19}=0.4$

(xi) 48 ÷ 0.074
 
$$\begin{gathered} =\frac{148}{0.074} \\ =\frac{148\times 1000}{0.074\times 1000} \\ =\frac{148000}{74} \\ =2\times 1000 \\ =2000 \end{gathered}$$

(xii)  16.578 ÷ 5.4 = $\frac{16.578}{5.4}=\frac{16.578\times 10}{5.4\times 10}=\frac{165.78}{54}$
Now, we have:

        
        ∴ $\frac{16.578}{5.4}=\frac{165.78}{54}=3.07$

(xiii)  28 ÷ 0.56

$$\begin{gathered} =\frac{28}{0.56} \\ =\frac{28\times 100}{0.56\times 100} \\ =\frac{2800}{56} \\ =\frac{1\times 100}{2} \\ =50 \end{gathered}$$


(xiv) 204 ÷ 0.17

$$\begin{gathered} =\frac{204}{0.17} \\ =\frac{204\times 100}{0.17\times 100} \\ =\frac{20400}{17} \\ =12\times 100 \\ =1200 \end{gathered}$$

(xv) 3 ÷ 80 = $\frac{3}{80}$

Now, we have:

      
       ∴ $\frac{3}{80}$ = 0.0375

Page-50

Question 8:

The total cost of 24 chairs is Rs 9255.60. Find the cost of each chair.

Answer 8:

Cost of 24 chairs = Rs 9255.60
∴ Cost of one chair = Rs $\left(\frac{9255.60}{24}\right)$
                                     = Rs $\left(\frac{9255.60\times 10}{24\times 10}\right)$
                                       = Rs $\left(\frac{92556}{240}\right)$
                                       = Rs 385.65


Hence, the cost of one chair is Rs 385.65.

Question 9:

1.8 m of cloth is required for a shirt. How many such shirts can be made from a piece of cloth 45 m long?

Answer 9:

Cloth required for 1 shirt = 1.8 m
∴ Number of shirts that can be made from 45 m of cloth =  $\frac{45}{1.8}$ = $\frac{15}{0.6}$ =$\frac{5}{0.2}$ = $\frac{50}{2}$= 25

Hence, 25 shirts can be made from a piece of cloth of length 45 m.

Question 10:

A car covers a distance of 22.8 km in 2.4 litres of petrol. How much distance will it cover in 1 litre of petrol?

Answer 10:

Distance covered by the car with 2.4 litres of petrol = 22.8 km
∴ Distance covered with 1 litre of petrol = $\left(\frac{22.8}{2.4}\right)$ km
                                                                         = $\left(\frac{228}{24}\right)$ km = $\left(\frac{228÷12}{24÷12}\right)$ km = $\left(\frac{19}{2}\right)$ km = $9\frac{1}{2}$ km

Hence, the distance covered by the car with 1 litre of petrol is $9\frac{1}{2}$ km.
                                                          

Question 11:

A tin holds 16.5 litres of oil. How many such tins will be required to hold 478.5 litres of oil?

Answer 11:

Capacity of 1 tin of oil = 16.5 litres
∴ Number of tins required to hold 478.5 litres of oil = $\left(\frac{478.5}{16.5}\right)=\left(\frac{4785}{165}\right)=\left(\frac{4785÷15}{165÷15}\right)=\frac{319}{11}=29$
Hence, 29 oil tins will be required to hold 478.5 litres of oil.

Question 12:

The weight of 37 bags of sugar is 3644.5 kg. If all the bags weigh equally, what is the weight of each bag?

Answer 12:

Weight of 37 bags of sugar = 3644.5 kg
∴ Weight of 1 bag of sugar = $\left(\frac{3644.5}{37}\right)$ = 98.5 kg

Hence, each bag of sugar weighs 98.5 kg.

Question 13:

If 69 buckets of equal capacity can be filled with 586.5 litres of water, what is the capacity of eacch bucket?

Answer 13:

Capacity of 69 buckets of water = 586.5 litres
∴ Capacity of one such bucket = $\left(\frac{586.5}{69}\right)$ litres = 8.5 litres.
    
Hence, the capacity of each water bucket is 8.5 litres.

Question 14:

Monica cuts 46 m of cloth into peices of 1.15 m each. How many pieces does she get?

Answer 14:

Length of one piece of cloth = 1.15 m
∴ Number of pieces she gets from 46 m of cloth = $\left(\frac{46}{1.15}\right)$
                                                                                        = $\left(\frac{46\times 100}{1.15\times 100}\right)$ = $\left(\frac{4600}{115}\right)$ = 40

Hence, Monica has 40 pieces of cloth each of length 1.15 m.

Question 15:

Mr Soni bought some bags of cement, each weighing 49.8 kg. If the total weight of all the bags is 1792.8 kg, how many bags did he buy?

Answer 15:

Total weight of all the bags of cement = 1792.8 kg
Weight of each bag = 49.8 kg
Number of bags = $\left(\frac{\mathrm{Total} \mathrm{weight}}{\mathrm{Weight} \mathrm{of} \mathrm{each} \mathrm{bag}}\right)$
                           = $\left(\frac{1792.8}{49.8}\right)=\left(\frac{17928}{498}\right)=36$
                       
Hence, Mr. Soni bought 36 bags of cement.

Question 16:

How many pieces of plywood, each 0.35 cm thick, are required to make a pile 1.89 m high?

Answer 16:

Thickness of the pile of plywood pieces = 1.89 m = 189 cm
Thickness of one piece of plywood = 0.35 cm
∴ Required number of plywood pieces = $\left(\frac{189}{0.35}\right)=\left(\frac{189\times 100}{0.35\times 100}\right)=\left(\frac{18900}{35}\right)=540$
   
Hence, 540 pieces of plywood are required to make a pile of height 1.89 m.

Question 17:

The product of two decimals is 261.36. If one of them is 17.6, find the other.

Answer 17:

Product of the given decimals = 261.36
 One decimal = 17.6
The other decimal = 261.36 ÷ 17.6
                              = $\left(\frac{261.36}{17.6}\right)=\left(\frac{261.36\times 10}{17.6\times 10}\right)=\left(\frac{2613.6}{176}\right)$
                                 = 14.85

Hence, the other decimal is 14.85.

Question 1:

Mark (✓) against the correct answer
.06 = ?

(a) $\frac{3}{5}$
(b) $\frac{3}{50}$
(c) $\frac{3}{500}$
(d) none of these

Answer 1:

(b) $\frac{3}{50}$

0.06 = $\frac{6}{100}=\frac{3}{50}$

Question 2:

Mark (✓) against the correct answer
1.04 = ?

(a) $1\frac{1}{5}$
(b) $1\frac{2}{5}$
(c) $1\frac{1}{25}$
(d) none of these

Answer 2:

(c) $1\frac{1}{25}$

1.04 = $\frac{104}{100}=\frac{26}{25}=1\frac{1}{25}$

Question 3:

Mark (✓) against the correct answer
$2\frac{2}{25}=?$

(a) 2.8
(b) 2.08
(c) 2.008
(d) none of these

Answer 3:

(b) 2.08

$2\frac{2}{25}=\frac{52}{25}$
 
On dividing, we get:

        
∴ $2\frac{2}{25}=\frac{52}{25}$ = 2.08

Question 4:

Mark (✓) against the correct answer
6 cm = ?

(a) 0.006 km
(b) 0.0006 km
(c) 0.00006 km
(d) none of these

Answer 4:

(c) 0.00006 km

6 cm = $\frac{6}{100}$m = 0.06 m

0.06 m = $\frac{0.06}{1000}$ km = 0.00006 km

∴ 6 cm = 0.00006 km

Question 5:

Mark (✓) against the correct answer
70 g = ?

(a) 0.7 kg
(b) 0.07 kg
(c) 0.007 kg
(d) none of these

Answer 5:

(b) 0.07 kg

70 g =$\frac{70}{1000}$ kg = $\frac{7}{100}$ kg

         = 0.07 kg

∴ 70 g = 0.07 kg

Question 6:

Mark (✓) against the correct answer
5 kg 6 g = ?

(a) 5.0006 kg
(b) 5.06 kg
(c) 5.006 kg
(d) 5.6 kg

Answer 6:

(c) 5.006 kg

5 kg 6 g = (5 $\times$ 1000) g + 6 g = 5006 g

= $\frac{5006}{1000}$ kg = 5.006 kg

∴ 5 kg 6 g = 5.006 kg

Question 7:

Mark (✓) against the correct answer
2 km 5 m = ?

(a) 2.5 km
(b) 2.05 km
(c) 2.005 km
(d) 2.0005 km

Answer 7:

(c) 2.005 km

2 km 5 m = (2 $\times$ 1000) m + 5 m = 2005 m

= $\frac{2005}{1000}$ km = 2.005 km

∴ 2 km 5 m = 2.005 km

Question 8:

Mark (✓) against the correct answer
(1.007 − 0.7) = ?

(a) 1
(b) 0.37
(c) 0.307
(d) none of these

Answer 8:

(c) 0.307

Converting the given decimals into like decimals, we get:
1.007 and 0.700
Writing them in column form with the larger one at the top and subtracting, we get:

Hence, the required number is 0.307.

Question 9:

Mark (✓) against the correct answer
What should be subtracted from .1 to get .03?

(a) .7
(b) .07
(c) .007
(d) none of these

Answer 9:

(b) .07

We have:
0.1 − x = 0.03
⇒ x = 0.1 − 0.03

Converting the given decimals into like decimals, we get:
0.10 and 0.03

Writing them in column form with the larger one at the top and subtracting, we get:

∴ x = 0.07
Hence, the required number is 0.07.