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Percentages as fractions and decimals

Tutor: Labib

# 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.

#### 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.

$0.04 \times 4 = \underline{0.16}$​​

## FAQs - Frequently Asked Questions

### How are percentages, fractions and decimals related?

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