Equivalent fractions, decimals and percentages​

​​In a nutshell

Fractions, decimals and percentages are all ways of representing quantities with parts that are less than one. Learning to convert between them is an important skill used all the time in maths.

Equivalence

​​Definition

Equivalent means equal in value. If any fractions, decimals or percentages are equivalent to one another, they represent the same value.

​

Equivalent simple fractions, decimals and percentages

There are some simple fractions that it's really useful to know the decimal and percentage equivalences for.

FRACTION	DECIMAL	PERCENTAGE	VISUAL REPRESENTATION
​$$0$$​​	​$$0$$​​	$$0\%$$​​
​$$\dfrac{1}{4}$$​​	$$0.25$$​​	$$25\%$$​​
​$$\dfrac{1}{2}$$​​	​$$0.5$$​​	​$$50\%$$​​
​$$\dfrac{3}{4}$$​​	​$$0.75$$​​	​$$75\%$$​​
​$$1$$​​	​$$1$$​​	​$$100\%$$​​

​

Converting between other fractions, decimals and percentages

For the more complicated fractions, decimals and percentages, there are steps you can use to convert between the different forms.

Fractions to decimals to percentages 

​​PROCEDURE

Note: To turn trickier fractions into decimals, you might need to use a calculator or use the bus stop method!​

Percentages to fractions to decimals

​​procedure

Tip: Percent means 'out of one hundred'.

Example 1

What is $$67\%$$ as a fraction and decimal?

Write $$67\%$$ as a fraction with $$100$$ as the denominator.

$$67\%=\underline{\dfrac{67}{100}}$$

Divide $$67$$ by $$100$$ to get a decimal.

​$$67\div100=\underline{0.67}$$

Example 2

What is $$\dfrac{3}{8}$$ as a decimal and percentage?

Divide $$3$$ by $$8$$ to get a decimal.

$$8\overset{\,\,\,\,\,0\,.\,\,\,\,3\,\,\,\,\,7\,\,\,5\,\,}{\overline{\smash{)}\cancel3.^30^60^40}} \\$$

$$3\div8=\underline{0.375}$$​​

Multiply by one hundred to get a percentage.

​$$0.375\times100=\underline{37.5\%}$$​

​