Percentages 1
Fractions, Decimals and Percentages

A percentage is a means of expressing a number as a fraction of 100, the term 'percentage' simply means 'per hundred'. Converting percentages to fractions is a simple process. Percentages can also be converted very easily to decimals, which can be useful when using a calculator. Fractions and decimals can also be converted back to percentages.

Worked Examples

1

Convert each of the following percentages to fractions.

(a)

50%

Show me 50% = =
(b)

40%

Show me 40% = =
(c)

8%

Show me 8% = =
2

Convert each of the following percentages to decimals.

(a)

60%

Show me 60% = = 0.6
(b)

72%

Show me 72% = = 0.72
(c)

6%

Show me 6% = = 0.06
3

Convert each of the following decimals to percentages.

(a)

0.04

Show me 0.04 = = 4%
(b)

0.65

Show me 0.65 = = 65%
(c)

0.9

Show me 0.9 = = 90%
4

Convert each of the following fractions to percentages.

To convert fractions to percentages, multiply the fraction by 100%. This gives its value as a percentage.

(a)

Show me
= × 100
= × %
= %
= 30%
(b)

Show me
= × 100
= × %
= %
= 25%
(c)

Show me
= × 100
= × %
= %
= %

Information

'Per cent' probably comes from the Latin , 'per centum', which means 'for each hundred'.

Exercises

Convert each of the following percentages to fractions, giving your answers in their simplest form.

(a)
10 %
(b)
80 %
(c)
90 %
(d)
5 %
(e)
25 %
(f)
75 %
(g)
35 %
(h)
38 %
(i)
4 %
(j)
12 %
(k)
82 %
(l)
74 %

Convert each of the following percentages to decimals.

(a)
32 %
(b)
50 %
(c)
34 %
(d)
20 %
(e)
15 %
(f)
81 %
(g)
4 %
(h)
3 %
(i)
7 %
(j)
18 %
(k)
75 %
(l)
73 %

Convert the following decimals to percentages.

(a)
0.5%
(b)
0.74%
(c)
0.35%
(d)
0.08%
(e)
0.1%
(f)
0.52%
(g)
0.8%
(h)
0.07%
(i)
0.04%
(j)
0.18%
(k)
0.4%
(l)
0.3%

Convert the following fractions to percentages.

Write your answer correct to 1 decimal place where needed.

(a)
%
(b)
%
(c)
%
(d)
%
(e)
%
(f)
%
(g)
%
(h)
%
(i)
%
(j)
%
(k)
%
(l)
%
(a)

In the garden the vegetable garden has an area of 46.2 m2. The orange field has an area of 133.6 m2.

What is the total area of the vegetable garden and the orange field? Give your answer to the nearest square metre.

m2
(b)

The garden has an area of 400 m2.

(i)

The lawn is 30% of the garden. Calculate the area of the lawn.

m2
(ii)

A pool in the garden has an area of 80 m2 . What percentage of the garden is taken up by the pool?

%