Page 89 - Maths Skills - 7

Comparing Quantities 87

Absorbing Facts
But this method can be applied only to those fractions whose denominators are multiples or factors of 100.
5
Can you change into per cent using the above method? If not, why?
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(ii) Conversion of Decimals into Percentage
When we convert a decimal into per cent, we change the decimals into fraction with denominator as 100.

Example: Convert the following decimals into per cent.

(i) 0.94 (ii) 5.37 (iii) 0.007

Solution: (i) 0.94 = 0.94 × 100 = 94 = 94% (ii) 5.37 = 5.37 × 100 = 537 = 537%
100 100 100 100

(iii) 0.007 = 0.007 × 100 = 0.7 = 0.7%
100 100

(iii) Conversion of Percentage into Decimals
First convert the given per cent into fraction with denominator hundred and then divide the numerator of the
62
fraction by hundred. Thus, 62% can be changed into decimal form as 62% = 100 = 0.62
Example: Convert the following percentages into decimals.
1
(i) 90.2% (ii) 70% (iii) 0.02% (iv) 12 %
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Solution: (i) 90.2% = 90.2 = 0.902 (ii) 70% = 70 = 0.70
100 100
1
(iii) 0.02% = 0.02 = 0.0002 (iv) 12 % = 12.2% = 12.2 = 0.122
100 5 100
(iv) Conversion of Percentage into Fraction
Percentage can be changed into fraction by writing 100 in the denominator and then, reducing to its lowest form.

Example: Express the following percentages as fractions in its lowest form.
1
(i) 65% (ii) 40% (iii) 3 % (iv) 8%
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Solution: (i) 65% = 65 = 13 (ii) 40% = 40 = 2
100 20 100 5
1 16 16 4 8 2
(iii) 3 % = 5 % = 5 × 100 = 125 (iv) 8% = 100 = 25
5

(v) Conversion of Ratio into Percentage
We convert the ratio into ratio as follows:

(i) Write the ratio as fraction. (ii) Multiply the fraction with 100 and put the sign (%) along with it.
Example: Express the following percentage as per cent:

(i) 9 : 20 (ii) 3 : 4
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Solution: (i) Write 9 : 20 as 9 (ii) 3 : 4 = × 100 = 3 × 25 = 3 × 25% = 75%
20 4 100 100
9 9 100 45
or, = × = = 45%
20 20 100 100