Percentages as fractions and decimals

In a nutshell

Percentages, decimals and fractions are all different ways of expressing quantities or proportions. Being able to convert between the different forms is a very important skill to have. There are also some "common" conversions which you should aim to learn off by heart.

Equivalence

Definition

Equivalent means equal in value. If a percentage, decimal or fraction is equivalent to one another, this means they represent the same value.

Halves, quarters and fifths

These fractions feature often in maths problems, so it is helpful to try to learn their equivalent values off by heart.

Percentage	Fraction	Decimal
$50\%$	$\frac{1}{2}$	$0.5$
$25\%$	$\frac{1}{4}$	$0.25$
$75\%$	$\frac{3}{4}$	$0.75$
$20\%$	$\frac{1}{5}$	$0.2$
$40\%$	$\frac{2}{5}$	$0.4$
$60\%$	$\frac{3}{5}$	$0.6$
$80 \%$	$\dfrac{4}{5}$	$0.8$

Example 1

What is $\dfrac{3}{5}$ as a percentage?

Find $\dfrac{3}{5}$ in the table above. Read along to the percentage column and give the equivalent value.

$\dfrac{3}{5} = \underline{60\%}$ 

Example 2

What is $75\%$ as a fraction?

Find $75\%$ in the table above. Read along to the fraction column and give the equivalent value.

$75\%=\underline {\dfrac{3}{4}}$ 

Tip: The more you practise with your equivalent values, the easier they become to remember!

Tenths and twenty-fifths

The table below shows the equivalent values of one tenth and one twenty-fifth.

PERCENTAGE	FRACTION	DECIMAL
$10\%$	$\dfrac{1}{10}$	$0.1$
$4\%$	$\frac{1}{25}$	$0.04$

You can use these values, along with multiplication to figure out more complicated conversions.

Example 3

What is $30\%$ as a fraction?

Recall that $10\% = \dfrac{1}{10}$ .

Calculate the multiplier to reach $30\%$ .

$10 \% \times 3 = 30\%$ 

Multiply the equivalent fraction by the multiplier.

$\dfrac{1}{10} \times 3=\underline{\dfrac{3}{10}}$ 

Example 4

What is $16 \%$ as a decimal?

Recall that $4\%= 0.04$ .

Calculate the multiplier to reach $16\%$ .

$4\%\times 4 = 16\%$ 

Multiply the equivalent decimal by the multiplier.

$0.04 \times 4 = \underline{0.16}$ 