Page 184 - ICSE Math 5

Relationship between Fractions, Decimals and Percentages

Since percentages are the fractions having denominators as 100, they can be easily converted
and written in a decimal form.
62
For example, 62% = = 0.62.
100
Similarly, decimals can also be converted to percentages.
2 41
For example, 0.02 = = 2% and 0.41 = = 41%.
100 100
Now let’s learn conversion of fractions to percentages, percentages to fractions, decimals to
percentages and percentages to decimals.
Conversion of a Fraction to Percentage and Vice Versa

Conversion of a fraction to percentage

To convert a fraction to percentage, we multiply the given fraction by 100 and put the per cent (%)
sign or we change the fraction to equivalent fraction with 100 as the denominator, where its
numerator gives the percentage.

Example 2: Convert the following fractions to percentage.
 (a) 2 (b) 12
5 25

2 2 20 12 12 4
Solution: (a) = × 100% = 2 × 20% = 40% (b) = × 100% = 12 × 4% = 48%
5 5 25 25
Alternatively, Alternatively,

  2 = 2 × 20 = 40 = 40% 12 = 12 × 4 = 48 = 48%
5 5 × 20 100 25 25 × 4 100

Conversion of a percentage to fraction

To convert a percentage to fraction, we remove the % sign and divide the number of the percentage
1
by 100 or multiply it by . Then we reduce the fraction to its lowest term, if needed.
100

Example 3: Convert the following percentages to fractions. Reduce to the lowest terms, if
possible.
1
(a) 27% (b) 75% (c) 6 %
2
15 3
27 75 3 1 13 13 1 13
Solution: (a) 27% = (b) 75% = = (c) 6 % = % = × =
100 100 4 2 2 2 100 200
20 4

Conversion of a Decimal to Percentage and Vice Versa

Conversion of a decimal to percentage

To convert a decimal to percentage, we change the given decimal to fractional form and then
multiply it by 100 and put the % sign.

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