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

Exercise 3C

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Question 1:

Find the product:

(i) 73.92 × 10
(ii) 7.54 × 10
(iii) 84.003 × 10
(iv) 0.83 × 10
(v) 0.7 × 10
(vi) 0.032 × 10

Answer 1:

We have the following:

(i) 73.92 × 10 = 739.2                 [Shifting the decimal point to the right by 1 place]
(ii) 7.54 × 10 = 75.4                    [Shifting the decimal point to the right by 1 place]
(iii) 84.003 × 10 = 840.03           [Shifting the decimal point to the right by 1 place]
(iv) 0.83 × 10 = 8.3                     [Shifting the decimal point to the right by 1 place]
(v) 0.7 × 10 = 7                           [Shifting the decimal point to the right by 1 place]
(vi) 0.032 × 10 = 0.32                 [Shifting the decimal point to the right by 1 place]

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Question 2:

Find the product:

(i) 2.397 × 100
(ii) 6.83 × 100
(iii) 2.9 × 100
(iv) 0.08 ×100
(v) 0.6 × 100
(vi) 0.003 × 100

Answer 2:

We have the following:

(i) 2.397 × 100 = 239.7           [Shifting the decimal point to the right by 2 places]
(ii) 6.83 × 100 = 683               [Shifting the decimal point to the right by 2 places]
(iii) 2.9 × 100 = 290                [Shifting the decimal point to the right by 2 places]
(iv) 0.08 ×100 = 8                   [Shifting the decimal point to the right by 2 places]
(v) 0.6 × 100 = 60                   [Shifting the decimal point to the right by 2 places]
(vi) 0.003 × 100 = 0.3             [Shifting the decimal point to the right by 2 places]

Question 3:

Find the product:

(i) 6.7314 × 1000
(ii) 0.182 × 1000
(iii) 0.076 × 1000
(iv) 6.25 × 1000
(v) 4.8 × 1000
(vi) 0.06 × 1000

Answer 3:

We have:
(i) 6.7314 × 1000 = 6731.4            [Shifting the decimal point to the right by 3 places]
(ii) 0.182 × 1000 = 182                  [Shifting the decimal point to the right by 3 places]          
(iii) 0.076 × 1000 = 76                   [Shifting the decimal point to the right by 3 places]
(iv) 6.25 × 1000 = 6250                  [Shifting decimal point to the right by 3 places]
(v) 4.8 × 1000 = 4800                     [Shifting the decimal point to the right by 3 places]
(vi) 0.06 × 1000 = 60                      [Shifting the decimal point to the right by 3 places]

Question 4:

Find the product:

(i) 5.4 × 16
(ii) 3.65 × 19
(iii) 0.854 × 12
(iv) 36.73 × 48
(v) 4.125 × 86
(vi) 104.06 × 75
(vii) 6.032 × 124
(viii) 0.0146 × 69
(ix) 0.00125 × 327

Answer 4:

We have the following:

(i)      54 $\times$ 16 = 864
     ∴ 5.4 $\times$ 16 = 86.4                            [1 place of decimal]

(ii)    365 $\times$ 19 = 6935
       ∴ 3.65 $\times$ 19 = 69.35                      [2 places of decimal]

(iii)  854 $\times$ 12 = 10248
        ∴ 0.854 $\times$ 12 = 10.248                 [3 places of decimal]

(iv)  3673 $\times$ 48 = 176304
       ∴ 36.78 $\times$ 48 = 1763.04                [2 places of decimal]

(v) 4125 $\times$ 86 = 354750
      ∴ 4.125 $\times$ 86 = 354.750                [3 places of decimal] 
                           = 354.75

(vi) 10406 $\times$ 75 = 780450
      ∴ 104.06 $\times$ 75 = 7804.50               [2 places of decimal]       
                              = 7804.5

(vii)  6032 $\times$ 124 = 747968
        ∴ 6.032 $\times$ 124 = 747.968             [3 places of decimal] 

(viii) 146 $\times$ 69 = 10074          
         ∴ 0.0146 $\times$ 69 = 1.0074              [4 places of decimal] 

(ix) 125 $\times$ 327 = 40875
       ∴ 0.00125 $\times$ 327 = 0.40875           [5 places of decimal]   

Question 5:

Find the product

(i) 7.6 × 2.4
(ii) 3.45 × 6.3
(iii) 0.54 × 0.27
(iv) 0.568 × 4.9
(v) 6.54 × 0.09
(vi) 3.87 × 1.25
(vii) 0.06 × 0.38
(viii) 0.623 × 0.75
(ix) 0.014 × 0.46
(x) 54.5 × 1.76
(xi) 0.045 × 2.4
(xii) 1.245 × 6.4

Answer 5:

(i) First, we will multiply 76 by 24.
    
∴ 76 $\times$ 24 = 1824
Sum of decimal places in the given numbers = (1 + 1) = 2
∴ 7.6 $\times$ 2.4 = 18.24     [2 places of decimal]

(ii) First, we will multiply 345 by 63.
    
∴ 345 $\times$ 63 = 21735
Sum of decimal places in the given numbers = (2 + 1) = 3
∴ 3.45 $\times$ 6.3 = 21.735     [3 places of decimal]

(iii) First, we will multiply 54 by 27.
      
∴ 54 $\times$ 27 = 1458
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 0.54 $\times$ 0.27 = 0.1458    [4 places of decimal]

(iv) First, we will multiply 568 by 49.
      
∴ 568 $\times$ 49 = 27832
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 0.568 $\times$ 4.9 = 2.7832    [4 places of decimal]

(v) First, we multiply 654 by 9.
     
∴ 654 $\times$ 9 = 5886
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 6.54 $\times$ 0.09 = 0.5886     [4 places of decimal]

(vi) First, we will multiply 387 by 125.
      
∴ 387 $\times$ 125 = 48375
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 3.87 $\times$ 1.25 = 4.8375    [4 places of decimal]

(vii) First, we will multiply 38 by 6.
        
∴ 38 $\times$ 6 = 228
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 0.06 $\times$ 0.38 = 0.0228    [4 places of decimal]

(viii) First, we will multiply 623 by 75.
        
∴ 623 $\times$ 75 = 46725
Sum of decimal places in the given numbers = (3 + 2) = 5
∴ 0.623 $\times$ 0.75 = 0.46725    [5 places of decimal]

(ix) First, we will multiply 14 by 46.
      
∴ 14 $\times$ 46 = 644
Sum of decimal places in the given numbers = (3 + 2) = 5
∴ 0.014 $\times$ 0.46 = 0.00644    [5 places of decimal]

(x) First, we will multiply 545 by 176.
     
∴ 545 $\times$ 176 = 95920
Sum of decimal places in the given numbers = (1 + 2) = 3
∴ 54.5 $\times$ 1.76 = 95.920  [3 places of decimal]
                       = 95.92

(xi) First, we will multiply 45 by 24.
      
∴ 45 $\times$ 24 = 1080
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 0.045 $\times$ 2.4 = 0.1080    [4 places of decimal]
                       = 0.108

(xii) First, we will multiply 1245 by 64.
       
∴ 1245 $\times$ 64 = 79680
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 1.245 $\times$ 6.4 = 7.9680   [4 places of decimal]
                       = 7.968

Question 6:

Find the product:

(i) 13 × 1.3 × 0.13
(ii) 2.4 × 1.5 × 2.5
(iii) 0.8 × 3.5 × 0.05
(iv) 0.2 × 0.02 × 0.002
(v) 11.1 × 1.1 × 0.11
(vi) 2.1 × 0.21 × 0.021

Answer 6:

(i) First, we will find the product 13 ⨯ 1.3 ⨯ 0.13.
     Now, 13 ⨯ 13 ⨯ 13 = 169 x 13
                                    = 2197
    
     Sum of decimal places in the given numbers = (1 + 2) = 3
     So, the product must have three decimal places.

     ∴ 13 ⨯ 1.3 ⨯ 0.13 = 2.197

(ii) First, we will find the product 2.4 ⨯ 1.5 ⨯ 2.5.
     Now, 24 ⨯ 15 ⨯ 25 = 360 x 25
                                   = 9000
    
     Sum of decimal places in the given numbers = (1 + 1 + 1) = 3
     So, the product must have three decimal places.

     ∴ 2.4 ⨯ 1.5 ⨯ 2.5 = 9.000
                                 = 9

(iii) First, we will find the product 0.8 ⨯ 3.5 ⨯ 0.05.
       Now, 8 ⨯ 35 ⨯ 5 = 280 ⨯ 5
                                 = 1400
      
       Sum of decimal places in the given numbers = (1 + 1 + 2) = 4
       So, the product must have four decimal places.

       ∴ 0.8 ⨯ 3.5 ⨯ 0.05 = 0.1400
                                     = 0.14

(iv) First, we will find the product 0.2 ⨯ 0.02 ⨯ 0.002.
       Now, 2 ⨯ 2 ⨯ 2 = 4 ⨯ 2
                                = 8
       Sum of decimal places in the given numbers = (1 + 2 + 3) = 6
       So, the product must have six decimal places.
      
∴ 0.2 ⨯ 0.02 ⨯ 0.002 = 0.000008

(v) First, we will find the product 11.1 ⨯ 1.1 ⨯ 0.11.
       Now, 111 ⨯ 11 ⨯ 11 = 1221 ⨯ 11
                                       = 13431
      
       Sum of decimal places in the given numbers = (1 + 1 + 2) = 4
       So, the product must have four decimal places.

       ∴ 11.1 ⨯ 1.1 ⨯ 0.11 = 1.3431

(vi) First, we will find the product 2.1 ⨯ 0.21 ⨯ 0.021.
       Now, 21 ⨯ 21 ⨯ 21 = 441 ⨯ 21
                                     = 9261
      
       Sum of decimal places in the given numbers = ( 1 + 2 + 3) = 6
       So, the product must have six decimal places.

       ∴ 2.1 ⨯ 0.21 ⨯ 0.021 = 0.009261

Question 7:

Evaluate:

(i) (1.2)²
(ii) (0.7)²
(iii) (0.04)²
(iv) (0.11)²

Answer 7:

(i) (1.2)² = 1.2 $\times$ 1.2
     First, we will find the product 1.2 $\times$ 1.2.
     Now, 12 $\times$ 12 = 144
     Sum of decimal places in the given numbers = (1 + 1) = 2
     So, the product must have two decimal places.

     ∴ (1.2)² = 1.2$\times$ 1.2 = 1.44

(ii) (0.7)² = 0.7 $\times$ 0.7
      First, we will find the product 0.7 $\times$ 0.7.
      Now, 7 $\times$ 7 = 49
      Sum of decimal places in the given numbers = (1 + 1) = 2
      So, the product must have two decimal places.
      ∴ (0.7)² = 0.7 $\times$ 0.7 = 0.49

(iii) (0.04)² = 0.04 $\times$ 0.04
       First, we will find the product 0.04 $\times$ 0.04.
       Now, 4$\times$ 4 = 16
       Sum of decimal places in the given numbers = (2 + 2) = 4
       So, the product must have four decimal places.
       ∴ (0.04)² = 0.04$\times$ 0.04 = 0.0016

(iv) (0.11)² = 0.11 $\times$ 0.11
       First, we will find the product 0.11 $\times$ 0.11.
       Now, 11 $\times$ 11 = 121
       Sum of decimal places in the given numbers = ( 2 + 2) = 4
       So, the product must have four decimal places.
       ∴ (0.11)² = 0.11 $\times$ 0.11 = 0.0121

Question 8:

Evaluate:

(i) (0.3)³
(ii) (0.05)³
(iii) (1.5)³

Answer 8:

(i) (0.3)³ = 0.3 $\times$ 0.3 $\times$ 0.3
     First, we will find the product 3 $\times$ 3 $\times$ 3.
     Now, 3 $\times$ 3 $\times$ 3 = 27
     Sum of decimal places in the given numbers = (1 + 1 + 1) = 3
     So, the product must have three places of decimal.
     ∴ (0.3)³ = 0.3 $\times$ 0.3 $\times$ 0.3 = 0.027

(ii) (0.05)³ = 0.05 $\times$ 0.05 $\times$ 0.05
     First, we will find the product 5 $\times$ 5 $\times$ 5.
     Now, 5 $\times$5 $\times$ 5 = 125
     Sum of decimal places in the given numbers = (2 + 2 + 2) = 6
     So, the product must have six decimal places.
     ∴ (0.05)³ = 0.05 $\times$ 0.05 $\times$ 0.05 = 0.000125

(iii) (1.5)³ = 1.5 $\times$1.5 $\times$1.5
       First, we will find the product 15 $\times$15 $\times$ 15.
       Now, 15 $\times$15 $\times$ 15 = 225 $\times$ 15 = 3375
      
       Sum of decimal places in the given numbers = (1 + 1 + 1) = 3
       So, the product must have three decimal places.
       ∴ (1.5)³ = 1.5 $\times$ 1.5 $\times$ 1.5 = 3.375

Question 9:

A bus can cover 62.5 km in one hour. How much distance can it cover in 18 hours?

Answer 9:

Distance covered by the bus in 1 hour = 62.5 km
∴ Distance covered in 18 hours = (62.5 $\times$ 18) km
                                                            = 1125 km
Hence, the bus can cover a distance of 1125 km in 18 hours.

Question 10:

A tin of oil weighs 16.8 kg. What is the weight of 45 such tins?

Answer 10:

Weight of 1 tin of oil = 16.8 kg
∴ Weight of 45 such tins = (16.8 $\times$ 45) kg
                                              = 756 kg
Hence, the weight of 45 tins of oil is 756 kg.

Question 11:

A bag of wheat weighs 97.8 kg. How much wheat is contained in 500 such bags?

Answer 11:

Weight of 1 bag of wheat = 97.8 kg
∴ Weight of 500 such bags = (97.8 x 500) kg
                                               = 48900 kg
Hence, the weight of 500 bags of wheat is 48900 kg.

Question 12:

Find the weight of 16 bags of sugar, each weighing 48.450 kg.

Answer 12:

Weight of 1 bag of sugar = 48.450 kg
∴ Weight of 16 bags of sugar = (48.450 ⨯ 16) kg
                                                     = 775.2 kg


Hence, the weight of 16 bags of sugar is 775.2 kg.

Question 13:

A small bottle holds 0.845 kg of sauce. How much sauce will be there in 72 such bottles?

Answer 13:

Capacity of 1 sauce bottle = 0.845 kg
∴ Capacity of 72 such bottles = (0.845 $\times$ 72) kg
                                                     = 60.84 kg

Hence, the capacity of 72 bottles of sauce will be 60.84 kg.

Question 14:

A bottle holds 925 g of jam. How many kg of jam will be there in 25 such bottles?

Answer 14:

Weight of 1 bottle of jam = 925 g =0.925 kg
∴ Weight of 25 such bottles = (0.925 $\times$ 25) kg
                                                   = 23.125 kg

∴ The weight of 25 bottles of jam will be 23.125 kg.

Question 15:

If one drum can hold 16.850 litres of oil, how many litres can 48 such drums hold?

Answer 15:

Capacity of 1 drum of oil = 16.850 litres
∴ Capacity of 48 such drums = (16.850 x 48) litres
                                                     = 808.800 litres

Hence, the capacity of 48 drums of oil is 808.800 litres.

Question 16:

1 kg of rice costs Rs 56.80. What is the cost of 16.25 kg of rice?

Answer 16:

Cost of 1 kg of rice =Rs 56.80
∴ Cost of 16.25 kg of rice = Rs (56.80 $\times$ 16.25)
                                                = Rs 923

Hence, the cost of 16.25 kg of rice is Rs 923.

Question 17:

1 metre of cloth costs Rs 108.50. What is the cost of 18.5 metres of this cloth?

Answer 17:

Cost of 1 m of cloth = Rs 108.50
∴ Cost of 18.5 m of cloth = Rs (108.50 x 18.5)
                                              = Rs 2007.25

Hence, the cost of 18.5 m of cloth is Rs 2007.25.

Question 18:

A car can cover a distance of 8.6 km on one litre of petrol. How far can it go on 36.5 litres of petrol?

Answer 18:

Distance covered by the car with 1 litre of petrol = 8.6 km
∴ Distance covered with 36.5 litres of petrol = (8.6 $\times$ 36.5) km
                                                                                   = 313.900 km
Hence, the distance covered by the car with 36.5 litres of petrol is 313.900 km.

Question 19:

A taxi driver charges Rs 9.80 per km. How much will he charge for a journey of 106.5 km?

Answer 19:

Charges for 1 km = Rs 9.80
∴ Charges for 106.5 km = Rs (9.80 $\times$ 106.5)
                                             = Rs 1043.70
Hence, the taxi driver will charge Rs 1043.70 for a journey of 106.5 km.