The document RD Sharma Solutions - Ex-3.2, Decimals, Class 7, Math Class 7 Notes | EduRev is a part of the Class 7 Course RD Sharma Solutions for Class 7 Mathematics.

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**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

=18.7m^{2}

**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

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