### Class 7 Chapter 2 – Fractions and Decimals Exercise 2.6

**Find:**

**(i) 0.2 × 6**

**Solution:-**

We have,

= (2/10) × 6

= (12/10)

On dividing a decimal by 10, the decimal point is shifted to the left by one place.

Then,

= 1.2

**(ii) 8 × 4.6**

**Solution:-**

We have,

= (8) × (46/10)

= (368/10)

On dividing a decimal by 10, the decimal point is shifted to the left by one place.

Then,

= 36.8

**(iii) 2.71 × 5**

**Solution:-**

We have,

= (271/100) × 5

= (1355/100)

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

Then,

= 13.55

**(iv) 20.1 × 4**

**Solution:-**

We have,

= (201/10) × 4

= (804/10)

On dividing a decimal by 10, the decimal point is shifted to the left by one place.

Then,

= 80.4

**(v) 0.05 × 7**

**Solution:-**

We have,

= (5/100) × 7

= (35/100)

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

Then,

= 0.35

**(vi) 211.02 × 4**

**Solution:-**

We have,

= (21102/100) × 4

= (84408/100)

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

Then,

= 844.08

**(vii) 2 × 0.86**

**Solution:-**

We have,

= (2) × (86/100)

= (172/100)

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

Then,

= 1.72

**2. Find the area of rectangle whose length is 5.7cm and breadth is 3 cm.**

**Solution:-**

From the question, it is given that,

Length of the rectangle = 5.7 cm

Breadth of the rectangle = 3 cm

Then,

Area of the rectangle = length × Breadth

= 5.7 × 3

= 17.1 cm^{2}

**3. Find:**

**(i) 1.3 × 10**

**Solution:-**

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.

We have,

= 1.3 × 10 = 13

**(ii) 36.8 × 10**

**Solution:-**

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.

We have,

= 36.8 × 10 = 368

**(iii) 153.7 × 10**

**Solution:-**

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.

We have,

= 153.7 × 10 = 1537

**(iv) 168.07 × 10**

**Solution:-**

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.

We have,

= 168.07 × 10 = 1680.7

**(v) 31.1 × 100**

**Solution:-**

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.

We have,

= 31.1 × 100 = 3110

**(vi) 156.1 × 100**

**Solution:-**

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.

We have,

= 156.1 × 100 = 15610

**(vii) 3.62 × 100**

**Solution:-**

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.

We have,

= 3.62 × 100 = 362

**(viii) 43.07 × 100**

**Solution:-**

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.

We have,

= 43.07 × 100 = 4307

**(ix) 0.5 × 10**

**Solution:-**

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.

We have,

= 0.5 × 10 = 5

**(x) 0.08 × 10**

**Solution:-**

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.

We have,

= 0.08 × 10 = 0.8

**(xi) 0.9 × 100**

**Solution:-**

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.

We have,

= 0.9 × 100 = 90

**(xii) 0.03 × 1000**

**Solution:-**

On multiplying a decimal by 1000, the decimal point is shifted to the right by three places.

We have,

= 0.03 × 1000 = 30

**4. A two-wheeler covers a distance of 55.3 km in one litre of petrol. How much distance will it cover in 10 litres of petrol?**

**Solution:-**

From the question, it is given that,

Distance covered by two-wheeler in 1L of petrol = 55.3 km

Then,

Distance covered by two wheeler in 10L of petrol = (10 × 55.3)

= 553 km

∴Two-wheeler covers a distance in 10L of petrol is 553 km.

**5. Find:**

**(i) 2.5 × 0.3**

**Solution:-**

We have,

= (25/10) × (3/10)

= (75/100)

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

Then,

= 0.75

**(ii) 0.1 × 51.7**

**Solution:-**

We have,

= (1/10) × (517/10)

= (517/100)

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

Then,

= 5.17

**(iii) 0.2 × 316.8**

**Solution:-**

We have,

= (2/10) × (3168/10)

= (6336/100)

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

Then,

= 63.36

**(iv) 1.3 × 3.1**

**Solution:-**

We have,

= (13/10) × (31/10)

= (403/100)

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

Then,

= 4.03

**(v) 0.5 × 0.05**

**Solution:-**

We have,

= (5/10) × (5/100)

= (25/1000)

On dividing a decimal by 1000, the decimal point is shifted to the left by three places.

Then,

= 0.025

**(vi) 11.2 × 0.15**

**Solution:-**

We have,

= (112/10) × (15/100)

= (1680/1000)

On dividing a decimal by 1000, the decimal point is shifted to the left by three places.

Then,

= 1.680

**(vii) 1.07 × 0.02**

**Solution:-**

We have,

= (107/100) × (2/100)

= (214/10000)

On dividing a decimal by 10000, the decimal point is shifted to the left by four places.

Then,

= 0.0214

**(viii) 10.05 × 1.05**

**Solution:-**

We have,

= (1005/100) × (105/100)

= (105525/10000)

On dividing a decimal by 10000, the decimal point is shifted to the left by four places.

Then,

= 10.5525

**(ix) 101.01 × 0.01**

**Solution:-**

We have,

= (10101/100) × (1/100)

= (10101/10000)

On dividing a decimal by 10000, the decimal point is shifted to the left by four places.

Then,

= 1.0101

**(x) 100.01 × 1.1**

**Solution:-**

We have,

= (10001/100) × (11/10)

= (110011/1000)

On dividing a decimal by 1000, the decimal point is shifted to the left by three places.

Then,

= 110.011