Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.6 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.6

Question 1.

Find:

(i) 0.2 x 6

(ii) 8 x 4.6

(iii) 2.71 x 5

(iv) 20.1 x 4

(v) 0.05 x 7

(vi) 211.02 x 4

(vii) 2 x 0.86

Solution:

(i) 0.2 x 6

Since 2 x 6 = 12 and there is one digit to the right of decimal point in 0.2.

∴ 0.2 x 6 = 1.2

(ii) 8 x 4.6

∵ 8 x 46 = 368 and there is one digit to the right of decimal point in 4.6.

∴ 8 x 4.6 = 36.8

(iii) 2.71 x 5

∵ 271 x 5 = 1355 and there are two digits to the right of decimal point in 2.71.

∴ 2.71 x 5 = 13.55

(iv) 20.1 x 4

∵ 201 x 4 = 804 and there is 1 digit to the right of decimal point in 20.1.

∴ 20.1 x 4 = 80.4

(v) 0.05 x 7

∵ 5 x 7 = 35 and there are 2 digits to the right of decimal point in 0.05.

∴ 0. 05 x 7 = 0.35

(vi) 211.02 x 4

∵ 21102 x 4 = 84408 and there are two digits – to the right of the decimal point in 211.02.

∴ 211.02 x 4 = 844.08

(vii) 2 x 0.86

∵ 2 x 86 = 172 and there are two digits to the right of the decimal point in 0.86.

∴ 2 x 0.86 = 1.72

Question 2.

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

Solution:

Length of the rectangle = 5.7 cm

Breadth of the rectangle = 3 cm

Area of the rectangle = Length X Breadth = 5.7 cm x 3 cm

= \(\frac { 57 }{ 10 }\) x 3 cm²

= 17.1 cm²

Question 3.

Find:

(i) 1.3 x 10

(ii) 36.8 x 10

(iii) 153.7 x 10

(iv) 168.07 x 10

(v) 31.1 x 100

(vi) 156.1 x 100

(vii) 3.62 x 100

(viii) 43.07 x 100

(ix) 0.5 x 10

(x) 0.08 x 10

(xi) 0.9 x 100

(xii) 0.03 x 1000

Solution:

(i) 1.3 x 10

∵ There is one zero in 10.

∴ The decimal point is shifted to the right by one place.

Thus, 1.3 x 10 = 13

(ii) 36.8 x 10

∵ There is one zero in 10.

∴ The decimal point is shifted to the right by one place.

∴ 36.8 x 10 = 368

(iii) 153.7 x 10

∵ There is one zero in 10.

∴ The decimal point is shifted to the right by one place.

∴ 153.7 x 10 = 1537

(iv) 168.07 x 10

∵ There is one zero in 10.

∴ The decimal point is shifted to the right by one place.

∴ 168.7 X 10 = 1680.7

(v) 31.1 x 100

∵ There are two zeros in 100

∴ The decimal point is shifted to the right by two places.

∴ 31.1 x 100 = 3110.0

(vi) 156.1 x 100

∵ There are two zeros in 100.

∴ The decimal point is shifted to the right by two places.

∴ 156.1 x 100 = 15610

(vii) 3.62 x 100

∵ There are two zeros in 100.

∴ The decimal point is shifted to the right by two places.

∴ 3.62 x 100 = 362

(viii) 43.07 x 100

∵ There are two zeros in 100.

∴ The decimal point is shifted to the right by two places.

∴ 43.07 x 100 = 4307

(ix) 0.5 x 10

∵ There is one zero in 10.

∴The decimal point is shifted to the right by one place.

∴ 0.5 x 10 = 5

(x) 0.08 x 10

∵ There is one zero in 10.

∴ The decimal point is shifted to the right by one place.

∴ 0.08 x 10 = 0.8

(xi) 0.9 x 100

∵ There are two zeros in 100.

∴ The decimal point is shifted to the right by two places.

∴ 0.9 x 100 = 90

(xii) 0.03 x 1000

∵ There are three zeros in 1000.

∴ The decimal point is shifted to the right by three places.

∴ 0.03 x 1000 = 30

Question 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:

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

∴ Distance covered by it in 10 litres of petrol = 55.3 x 10 km = 553 km

Question 5.

Find:

(i) 2.5 x 0.3

(ii) 0.1 x 51.7

(iii) 0.2 x 316.8

(iv) 1.3 x 3.1

(v) 0.5 x 0.05

(vi) 11.2 x 0.15

(vii) 1.07 x 0.02

(viii) 10.05 x 1.05

(ix) 101.01 x 0.01

(x) 100.01 x 1.1

Solution:

(i) 2.5 x 0.3

∵ 25 x 3 = 75 and total number of digits in the decimal parts of the given decimal numbers = 1 + 1 = 2

∴ Decimal point is placed in the product after 2 places from the right most digit.

Thus, 2.5 x 0.3 = 0.75

(ii) 0.1 x 51.7

∵ 1 x 517 = 517 and total number of digits in the decimal parts of the given decimal numbers = 1 + 1 = 2

∴ Decimal point is placed in the product after 2 places from the right most digit.

Thus, 0.1 x 51.7 = 5.17

(iii) 0.2 x 316.8

∵ 2 x 3168 = 6336 and total number of digits in the decimal parts of the given decimal numbers =1 + 1 = 2

∴ Decimal point is placed in the product after 2 places from the right most digit.

∴ 0.2 x 316.8 = 63.36

(iv) 1.3 x 3.1

∵ 13 x 31 = 403 and total number of digits in the decimal parts of the given decimal numbers = 1 + 1 = 2

∴ Decimal point is placed in the product after 2 places from the right most digit.

∴ 1.3 x 3.1 = 4.03

(v) 0.5 x 0.05

∵ 5 x 5 = 25 and total number of digits in the decimal parts of the given decimal numbers =1+2=3

∴ Decimal point is placed in the product after 3 places from the right most digit.

∴ 0.5 x 0.05 = 0.025

(vi) 11.2 x 0.15

∵ 112 x 15 = 1680 and there are 1 + 2 = 3 digits in the decimal part of the given decimal numbers.

∴ The decimal point is placed in the product after 3 places from the right most digit.

∴ 11.2 x 0.15 = 1.680

(vii) 1.07 x 0.02

∵ 107 x 2 = 214 and the total number of digits in the decimal part of the given decimal number is 2 + 2 = 4.

∴ The decimal point is placed in the product after 4 places from right most digit.

∴ 1.07 x 0.02 = 0.0214

(viii) 10.05 x 1.05

∵ 1005 x 105 = 105525 and the total number of digits in the decimal parts of the given decimal numbers is 2 + 2 = 4.

∴ The decimal point is placed in the product after 4 places from right most digit.

∴ 10.05 x 1.05 = 10.5525

(ix) 101.01 x 0.01

∵ 10101 x 1 = 10101 and the total number of digits in the decimal parts of the given decimal numbers is 2 + 2 = 4.

∴ The decimal point is placed after 4 places from the right most digit in the product.

∴ 101.01 x 0.01 = 1.0101

(x) 100.01 x 1.1

∵ 10001 x 11 = 110011 and the total number of digits in the decimal parts of the given decimal number is 2 + 1 = 3.

∴ The decimal point is placed after 3 places from the right most digit in the product.

∴ 100.01 x 1.1 = 110.011