Converting between fractions, decimals and percentages

In a nutshell

Fractions, decimals and percentages are all different ways of expressing parts of a whole. It is important to know how to convert between all three representations.

Common equivalences

Below are some common fraction-decimal-percentage equivalences that you should know:

fraction	decimal	percentage
$\frac{1}{2}$	$0.5$	$50\%$
$\frac{1}{4}$	$0.25$	$25\%$
$\frac{3}{4}$	$0.75$	$75\%$
$\frac{1}{3}$	$0.33333....$	$33.333....\%$
$\frac{2}{3}$	$0.66666....$	$66.666....\%$
$\frac{X}{10}$	$0.X$	$(X\times10)\%$

Note: The ellipsis in $0.33333...$ means that the $3$ is repeated forever. This is called a recurring decimal. Another way of writing this is $0.\overset{.}{3}$ .

Converting between fractions, decimals and percentages

Fraction to decimal: Divide the top number by the bottom number.
Decimal to fraction: Write the decimal as a whole number on the top. On the bottom, write $1$ followed by the same amount of zeroes as there are decimal places in the number.
Decimal to percentage: Multiply by $100$ and add the percentage symbol ( $\%$ ).
Percentage to decimal: Remove the percentage symbol and divide by $100$ .
Fraction to percentage: Convert the fraction to a decimal, then convert the decimal to a percentage.

Examples

What is $\frac{3}{8}$ as a decimal?
What is $0.38$ as a percentage?
What is $45\%$ as a fraction?

1. Using short division ${\frac{3}{8}=3\div8=\underline{0.375}}$ 

2. $0.38 = (0.38\times100)\%=\underline{38\%}$

3. First convert $45\%$ to a decimal:

$45\%=45\div100=0.45$ 

Then convert $0.45$ to a fraction:

$45\%=\underline{\frac{45}{100}}$ 