RS Aggarwal Solutions: Decimals (Exercise 3C) | Mathematics (Maths) Class 7 PDF Download

Q.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
Ans. 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]

Q.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
Ans. 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]

Q.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
Ans. 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]

Q.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
Ans. We have the following:
(i) 54 × 16 = 864
∴ 5.4 × 16 = 86.4 [1 place of decimal]
(ii) 365 × 19 = 6935
∴ 3.65 × 19 = 69.35 [2 places of decimal]
(iii)  854 × 12 = 10248
∴ 0.854 × 12 = 10.248 [3 places of decimal]
(iv)  3673 × 48 = 176304
∴ 36.78 × 48 = 1763.04 [2 places of decimal]
(v) 4125 × 86 = 354750
∴ 4.125 × 86 = 354.750 [3 places of decimal]
= 354.75
(vi) 10406 × 75 = 780450
∴ 104.06 × 75 = 7804.50 [2 places of decimal]
= 7804.5
(vii)  6032 × 124 = 747968
∴ 6.032 × 124 = 747.968 [3 places of decimal]
(viii) 146 × 69 = 10074
∴ 0.0146 × 69 = 1.0074 [4 places of decimal]
(ix) 125 × 327 = 40875
∴ 0.00125 × 327 = 0.40875 [5 places of decimal]

Q.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
Ans. (i) First, we will multiply 76 by 24.

∴ 76 × 24 = 1824
Sum of decimal places in the given numbers = (1 + 1) = 2
∴ 7.6 × 2.4 = 18.24 [2 places of decimal]
(ii) First, we will multiply 345 by 63.

∴ 345 × 63 = 21735
Sum of decimal places in the given numbers = (2 + 1) = 3
∴ 3.45 × 6.3 = 21.735 [3 places of decimal]
(iii) First, we will multiply 54 by 27.

∴ 54 × 27 = 1458
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 0.54 × 0.27 = 0.1458 [4 places of decimal]
(iv) First, we will multiply 568 by 49.

∴ 568 × 49 = 27832
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 0.568 × 4.9 = 2.7832 [4 places of decimal]
(v) First, we multiply 654 by 9.

∴ 654 × 49 = 5886
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 6.54 × 0.09 = 0.5886 [4 places of decimal]
(vi) First, we will multiply 387 by 125.

∴ 387 × 125 = 48375
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 3.87 × 1.25 = 4.8375 [4 places of decimal]
(vii) First, we will multiply 38 by 6.

∴ 38 × 6 = 228
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 0.06 × 0.38 = 0.0228 [4 places of decimal]
(viii) First, we will multiply 623 by 75.

∴ 623 × 75 = 46725
Sum of decimal places in the given numbers = (3 + 2) = 5
∴ 0.623 × 0.75 = 0.46725 [5 places of decimal]
(ix) First, we will multiply 14 by 46.
∴ 14 × 46 = 644
Sum of decimal places in the given numbers = (3 + 2) = 5
∴ 0.014 × 0.46 = 0.00644 [5 places of decimal]
(x) First, we will multiply 545 by 176.

∴ 545 × 176 = 95920
Sum of decimal places in the given numbers = (1 + 2) = 3
∴ 54.5 × 1.76 = 95.920  [3 places of decimal]
= 95.92
(xi) First, we will multiply 45 by 24.

∴ 45 × 24 = 1080
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 0.045 × 2.4 = 0.1080 [4 places of decimal]
= 0.108
(xii) First, we will multiply 1245 by 64.

∴ 1245 × 64 = 79680
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 1.245 ×× 6.4 = 7.9680   [4 places of decimal]
= 7.968

Q.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
Ans. (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

Q.7. Evaluate:
(i) (1.2)²
(ii) (0.7)²
(iii) (0.04)²
(iv) (0.11)²
Ans. (i) (1.2)² = 1.2 × 1.2
First, we will find the product 1.2 × 1.2.
Now, 12 × 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  × 1.2 = 1.44
(ii) (0.7)² = 0.7 × 0.7
First, we will find the product 0.7 × 0.7.
Now, 7 × 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 × 0.7 = 0.49
(iii) (0.04)² = 0.04 × 0.04
First, we will find the product 0.04 ×× 0.04.
Now, 4 × 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 × 0.04 = 0.0016
(iv) (0.11)² = 0.11 × 0.11
First, we will find the product 0.11 ×× 0.11.
Now, 11 × 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 × 0.11 = 0.0121

Q.8. Evaluate:
(i) (0.3)³
(ii) (0.05)³
(iii) (1.5)³
Ans. (i) (0.3)³ = 0.3 × 0.3 × 0.3
First, we will find the product 3 × 3 × 3.
Now, 3 × 3 × 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 × 0.3 × 0.3 = 0.027
(ii) (0.05)³ = 0.05 × 0.05 × 0.05
First, we will find the product 5 × 5 × 5.
Now, 5 × 5 × 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 × 0.05 × 0.05 = 0.000125
(iii) (1.5)³ = 1.5 × 1.5 ×1.5
First, we will find the product 15 ×15 × 15.
Now, 15 ×15 × 15 = 225 × 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 × 1.5 × 1.5 = 3.375

Q.9. A bus can cover 62.5 km in one hour. How much distance can it cover in 18 hours?
Ans. Distance covered by the bus in 1 hour = 62.5 km
∴ Distance covered in 18 hours = (62.5 × 18) km
= 1125 km
Hence, the bus can cover a distance of 1125 km in 18 hours.

Q.10. A tin of oil weighs 16.8 kg. What is the weight of 45 such tins?
Ans. Weight of 1 tin of oil = 16.8 kg
∴ Weight of 45 such tins = (16.8 × 45) kg
= 756 kg
Hence, the weight of 45 tins of oil is 756 kg.

Q.11. A bag of wheat weighs 97.8 kg. How much wheat is contained in 500 such bags?
Ans. 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.

Q.12. Find the weight of 16 bags of sugar, each weighing 48.450 kg.
Ans. 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.

Q.13. A small bottle holds 0.845 kg of sauce. How much sauce will be there in 72 such bottles?
Ans. Capacity of 1 sauce bottle = 0.845 kg
∴ Capacity of 72 such bottles = (0.845 ×× 72) kg
= 60.84 kg

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

Q.14. A bottle holds 925 g of jam. How many kg of jam will be there in 25 such bottles?
Ans. Weight of 1 bottle of jam = 925 g =0.925 kg
∴ Weight of 25 such bottles = (0.925 × 25) kg
= 23.125 kg

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

Q.15. If one drum can hold 16.850 litres of oil, how many litres can 48 such drums hold?
Ans. 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.

Q.16. 1 kg of rice costs Rs 56.80. What is the cost of 16.25 kg of rice?
Ans. Cost of 1 kg of rice =Rs 56.80
∴ Cost of 16.25 kg of rice = Rs (56.80 ×× 16.25)
= Rs 923

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

Q.17. 1 metre of cloth costs Rs 108.50. What is the cost of 18.5 metres of this cloth?
Ans. 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.

Q.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?
Ans. Distance covered by the car with 1 litre of petrol = 8.6 km
∴ Distance covered with 36.5 litres of petrol = (8.6 ×× 36.5) km
= 313.900 km
Hence, the distance covered by the car with 36.5 litres of petrol is 313.900 km.

Q.19. A taxi driver charges Rs 9.80 per km. How much will he charge for a journey of 106.5 km?
Ans. Charges for 1 km = Rs 9.80
∴ Charges for 106.5 km = Rs (9.80 ×× 106.5)
= Rs 1043.70
Hence, the taxi driver will charge Rs 1043.70 for a journey of 106.5 km.