Ex-3.2, Decimals, Class 7, Math RD Sharma Solutions | RD Sharma Solutions for Class 7 Mathematics PDF Download

Q1. 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

Q2. 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

Q3. 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

Q4. 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

Q5. 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

Q6. Find the area of a rectangle whose length is 5.5 m and breadth is 3.4 m.

Solution. 

We have

Length of rectangle = 5.5m

Breadth of rectangle = 3.4m

Area of rectangle = length X Breadth

= 5.5 x 3.4

=18.7m²

Q7. 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 = 25.75x 24

= Rs.618.00

Q8. 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 = 14.75km

Distance covered in 15.5 litres of petrol = 14.75 x 15.5

= 228.625km

Q9. 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

Q10. 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