In Exercise 12.1 of Chapter 12, we shall discuss problems based on expressing percentages as a fraction, a ratio, decimal form and vice-versa. Students who are preparing for the final exams and who wish to present their answers without any mistakes can refer to RD Sharma Solutions, formulated by our subject experts. Through regular practice, students can speed up the method of solving problems by using short-cut tips to secure high marks in the examination. Students can download the PDF from the links provided below.
RD Sharma Solutions for Class 8 Maths Exercise 12.1 Chapter 12 Percentage
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1. Write each of the following as percentage.
(i) 7/25
(ii) 14/625
(iii) 5/8
(iv) 0.8
(v) 0.005
(vi) 3:25
(vii) 11: 80
(viii) 111: 125
(ix) 13: 75
(x) 15: 16
(xi) 0.18
(xii) 7/125
Solution:
(i) 7/25
To change any number to percentage we have to multiply that number by 100,
i.e., 7/25 × 100 = 28%
(ii) 14/625
To change any number to percentage we have to multiply that number by 100,
i.e., 14/625 × 100 = 56/25 = 2.24%
(iii) 5/8
To change any number to percentage we have to multiply that number by 100,
i.e., 5/8 × 100 = 125/2 = 62.5%
(iv) 0.8
To change any number to percentage we have to multiply that number by 100,
i.e., 0.8 can be written as 8/10
so, 8/10 × 100 = 80%
(v) 0.005
To change any number to percentage we have to multiply that number by 100,
i.e., 0.005 can be written as 5/1000
so, 5/1000 × 100 = 5/10 = 0.5%
(vi) 3:25
To change any number to percentage we have to multiply that number by 100,
i.e., 3/25 × 100 = 3 × 4 = 12%
(vii) 11 : 80
To change any number to percentage we have to multiply that number by 100,
i.e., 11/80 × 100 = 55/4 = 13.75%
(viii) 111 : 125
To change any number to percentage we have to multiply that number by 100,
i.e., 111/125 × 100 = 444/5 = 88.8%
(ix) 13 : 75
To change any number to percentage we have to multiply that number by 100,
i.e., 13/75 × 100 = 52/3 = 17.3%
(x) 15 : 16
To change any number to percentage we have to multiply that number by 100,
i.e., 15/16 × 100 = 375/4 = 93.75%
(xi) 0.18
To change any number to percentage we have to multiply that number by 100,
i.e., 0.18 can be written as 18/100
so, 18/100 × 100 = 18%
(xii) 7/125
To change any number to percentage we have to multiply that number by 100,
i.e., 7/125 × 100 = 28/5 = 5.6%
2. Convert the following percentages to fractions and ratios.
(i) 25%
(ii) 2.5%
(iii) 0.25%
(iv) 0.3%
(v) 125%
Solution:
(i) 25%
To convert percentage to fractions we have to divide by 100,
i.e., 25/100 = 1/4 or 1:4
(ii) 2.5%
To convert percentage to fractions we have to divide by 100,
i.e., 2.5% can be written as 25/10
so, (25/10)/100 = 25/1000 = 1/40 or 1:40
(iii) 0.25%
To convert percentage to fractions we have to divide by 100,
i.e., 0.25% can be written as 25/100
so, (25/100)/100 = 25/10000 = 1/400 or 1:400
(iv) 0.3%
To convert percentage to fractions we have to divide by 100,
i.e., 0.3% can be written as 3/10
so, (3/10)/100 = 3/1000 or 3:1000
(v) 125%
To convert percentage to fractions we have to divide by 100,
i.e., 125/100 = 5/4 or 5:4
3. Express the following as decimal fractions.
(i) 27%
(ii) 6.3%
(iii) 32%
(iv) 0.25%
(v) 7.5%
(vi) 1/8%
Solution:
(i) 27%
To convert percentage to decimal fractions we have to divide by 100,
i.e., 27% = 27/100 = 0.27
(ii) 6.3%
Here 6.3 can be written as 63/10
To convert percentage to decimal fractions we have to divide by 100,
i.e., 6.3% = 63/(10 × 100) =63/1000 = 0.063
(iii) 32%
To convert percentage to decimal fractions we have to divide by 100,
i.e., 32% = 32/100 = 0.32
(iv) 0.25%
Here 0.25 can be written as 25/100
To convert percentage to decimal fractions we have to divide by 100,
i.e., 0.25% = 25/(100 × 100) = 25/10000 = 0.0025
(v) 7.5%
Here 7.5 can be written as 75/10
To convert percentage to decimal fractions we have to divide by 100,
i.e., 7.5% = 75/(10 × 100) =75/1000 = 0.075
(vi) 1/8%
To convert percentage to decimal fractions we have to divide by 100,
i.e., 1/8% = 1/(8 × 100) =1/800 = 0.00125
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