Chapter 3: Decimals Exercise – 3.2

Question: 1

Find the product:

(i) 4.74 x 10

(ii) 0.45 x 10

(iii) 0.0215 x 10

(iv) 0.0054 x 100

Solution:

(i) 4.74 x 10

Shifting the decimal point by one place to the right

4.74 x 10 = 47.4

(ii) 0.45 x 10

Shifting the decimal point by one place to the right

0.45 × 10 = 4.5

(iii) 0.0215 x 10

Shifting the decimal point by one place to the right

0.0215 × 10 = 0.215

(iv) 0.0054 x 100

Shifting the decimal point by two places to the right

0.0054 × 100 = 0.054

Question: 2

Find the product:

(i) 35.853 x 100

(ii) 42.5 x 100

(iii) 12.075 x 100

(iv) 100 x 0.005

Solution:

(i) 35.853 x 100

Shifting the decimal point by two places to the right

35.853 = 3585.3

(ii) 42.5 x 100

Shifting the decimal point by two places to the right

42.5 × 100 = 4250

(iii) 12.075 x 100

Shifting the decimal point by two places to the right

12.075 × 100 = 1207.5

(iv) 100 x 0.005

Shifting the decimal point by two places to the right

0.005 × 100 = 0.5

Question: 3

Find the product:

(i) 2.506 x 1000

(ii) 20.708 x 1000

(iii) 0.0529 x 1000

(iv) 1000 x 0.1

Solution:

(i) 2.506 x 1000

Shifting the decimal point by three places to the right

2.506 × 1000 = 2506

(ii) 20.708 x 1000

Shifting the decimal point by three places to the right

20.708 × 1000 = 20708

(iii) 0.0529 x 1000

Shifting the decimal point by three places to the right

0.0529 × 1000 = 52.9

(iv) 1000 x 0.1

Shifting the decimal point by three places to the right

0.1 × 1000 = 100

Question: 4

Find the product:

(i) 3.4 x 17

(ii) 0.745 x 12

(iii) 28.73 x 47

(iv) 0.0415 x 59

Solution:

(i) 3.4 x 17

Multiply the number without looking into the decimal points

3.4 × 17 = 578

Mark the decimal point in the product to have one place of decimal as there in the given decimal

= 57.8

(ii) 0.745 x 12

Multiply the number without looking into the decimal points

745×12 = 8940

Mark the decimal point in the product to have three places of decimal as there in the given decimal

0.745 x 12= 8.940

(iii) 28.73 x 47

Multiply the number without looking into the decimal points

2873 × 47 = 135031

Mark the decimal point in the product to have two places of decimal as there in the given decimal

28.73 × 47 = 1350.31

(iv) 0.0415 x 59

Multiply the number without looking into the decimal points

415 × 59 = 24485

Mark the decimal point in the product to have two places of decimal as there in the given decimal

0.0415 × 59 = 2.4485

Question: 5

Find:

(i) 1.07 x 0.02

(ii) 211.9 x 1.13

(iii) 10.05 x 1.05

(iv) 13.01 x 5.01

Solution:

(i) 1.07 x 0.02

Multiply the number without looking into the decimal points

107× 2 = 214

Sum of the decimal places in the given decimals is 2 + 2 = 4

Mark the decimal point in the product to have four places of decimals

1.07 × 0.02 = 0.0214

(ii) 211.9 x 1.13

Multiply the number without looking into the decimal points

2119 × 113 = 239447

Sum of the decimal places in the given decimals is 1+ 2 = 3

Mark the decimal point in the product to have three places of decimals

211.9 × 1.13 = 239.447

(iii) 10.05 x 1.05

Multiply the number without looking into the decimal points

1005 × 105 = 105525

Sum of the decimal places in the given decimals is 2 + 2 = 4

Mark the decimal point in the product to have four places of decimals

10.05 × 1.05 = 10.5525

(iv) 13.01 x 5.01

Multiply the number without looking into the decimal points

1301 × 501 = 651801

Sum of the decimal places in the given decimals is 2+ 2 = 4

Mark the decimal point in the product to have four places of decimals

13.01 × 5.01 = 65.1801

Question: 6

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

Solution:

We have

Length of rectangle = 5.5 m

Breadth of rectangle = 3.4 m

Area of rectangle = Length × Breadth

= 5.5 x 3.4

=18.7 m²

Question: 7

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

Solution:

Cost of one book = Rs.25.75

Therefore cost of 24 books = 25.75 x 24

= Rs.618.00

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?

Solution:

We have,

Distance covered in one litre of petrol = 14.75 km

Distance covered in 15.5 litres of petrol = 14.75 x 15.5

= 228.625 km

Question: 9

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

Solution:

Cost of one kg rice = 42.65

Cost of 18.25kg = 42.65 x 18.25

= Rs.778.3625

Question: 10

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

Solution:

We have,

One metre of cloth cost = Rs.152.50

Cost of 10.75 metres =10.75 x 152.50

= Rs.1639.375