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7.1 Finding equivalent fractions, decimals and percentages

7.1 Finding equivalent fractions, decimals and percentages

Some common equivalent fractions, decimals and percentages are shown below.

decimals 0 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 1
0.25 0.5 0.75 The numerator is the
number on top of a
fraction; the denominator is
1 1 1 3 2 1 3 7 3 4 9
fractions 0 1
10 5 4 10 5 2 5 10 4 5 10 the number at the bottom.

percentages 0 10% 20% 30% 40% 60% 70% 80% 90% 100%
25% 50% 75%

Worked example 7.1a

Write a 40% as a fraction b 0.75 as a percentage.

40
2
a 40% = 40% is a commonly used percentage. 40% as a fraction is 100 = 2 .
5
5
b 0.75 = 75% 0.75 is a commonly used decimal. 0.75 as a percentage is 75%.
You can convert between fractions, decimals and percentages. Just follow these steps.

Fraction to decimal
c Write the fraction as an equivalent fraction with a denominator Example: 3 = 6
5 10
of 10 or 100 or 1000 or … 6
.
10 = 06
d Write this equivalent fraction as a decimal. Use a decimal place-value table.
Decimal to percentage
Multiply the decimal by 100 to turn it into a percentage. Example: 0.6 × 100 = 60%
Fraction to percentage
Follow the ‘Fraction to decimal’ steps, then the ‘Decimal to
4
4
2
,
percentage’ step. Example: 50 = 100 100 = 4%
Or if you can, write the fraction with a denominator of 100,
then the numerator is the same as the percentage.
.
Decimal to fraction Example: 022 = 22
100
c Write the decimal as a fraction. Use a decimal place-value table. 22 = 11
100 50
d Cancel this fraction to its lowest terms.
Percentage to decimal
Example: 5% ÷ 100 = 0.05
Divide the percentage by 100 to turn it into a decimal.
Percentage to fraction
Example: 64% = 64
c Write the percentage as a fraction with a denominator of 100. 100
d Cancel this fraction to its lowest terms. 64 = 16
100 25

7 Fractions 71