Exercise 2.2 (Converting Decimals to Percentage, Percentages to Decimals)

Exercise 2.2

1. Write each of the following percentage as decimal.

(i) 21% (ii) 93.1% (iii) 151% (iv) 65% (v) 0.64%.

Solution: 

(i) 21% = 21 / 100 = 0.21

 (ii) 93.1% = 93.1 / 100 = 0.931

 (iii) 151% = 151 / 100 = 1.51

 (iv) 65% = 65 / 100 = 0.65

 (v) 0.64% = 0.64 / 100 = 0.0064

2. Convert each of the following decimal as percentage

(i) 0.282 (ii) 1.51 (iii) 1.09 (iv) 0.71 (v) 0.858

Solution:

(i) 0.282 = 0.282 × 100% = [282 / 1000] × 100% = 28.2%

(ii) 1.51 = [151 / 100] × 100% = 151%

(iii) 1.09 = [ 109 / 100 ] × 100% = 109%

(iv) 0.71 = [ 71 / 100 ] × 100% = 71%

(v) 0.858 = [ 858 / 1000 ] × 100% = 85.8%

3. In an examination a student scored 75% of marks. Represent the given percentage in decimal form?

Solution:  Student's Score = 75% = 75/100 = 0.75

4. In a village 70.5% people are literate. Express it as a decimal.

 Solution:  Percentage of literate people = 70.5% = 70.5/100 = 0.705

5. Scoring rate of a batsman is 86%. Write his strike rate as decimal.

Solution:  Scoring rate of the batsman = 86% = 86/100 = 0.86

6. The height of a flag pole in a school is 6.75m. Express it as percentage.

Solution:  Height of flag pole = 6.75m = 675/100 = 6.75%

7. The weights of two chemical substances are 20.34 g and 18.78 g. Write the difference in percentage.

Solution:  Weight of substance 1 = 20.34g

 Percentage of substance 1 = 2034/100 = 2034%

 Weight of substance 2 = 18.78g

 Percentage of substance 2 = 1878/100 = 1878%

 Their difference = 2034 – 1878 = 156%

8. Find the percentage of shaded region in the following figure.

Solution:

 Total region = 4 parts

 Shaded region = 1 part

 Fraction of shaded region = 1/4

 Percentage of shaded region = 1/4 × 100/100 = 1/4 × 100% = 25%

Objective type Questions

9. Decimal value of 142.5% is

(i) 1.425

(ii) 0.1425

(iii) 142.5

(iv) 14.25

Solution: 142.5% = 1425/10 % = 1425/10 × 1/100 = 1.425

[Answer: (i) 1.425]

10. The percentage of 0.005 is

(i) 0.005%

(ii) 5%

(iii) 0.5%

(iv) 0.05%

Solution: 0.005 = 5/1000 = (5/1000) × (100/100) = 0.5%

[Answer: (ii) 0.5%]

11. The percentage of 4.7 is

(i) 0.47%

(ii) 4.7%

(iii) 47%

(iv) 470%

Solution : 4.7 = 47 / 10 = 47/10 × 100/100 = 470%

[Answer: (iv) 470%]

ANSWERS:

Exercise 2.2

1. (i) 0.21 (ii) 0.931 (iii) 1.51 (iv) 0.65 (v) 0.0064

2. (i) 28.2% (ii) 151 % (iii) 109 % (iv) 71 % (v) 85.8 %

3. 0.75

4. 0.705

5. 0.86

6. 675%

7. 156%

8. 25%

Objective type questions

9. 1.425

10. 0.5 %

11. 470 %