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:

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

1. What is $$\frac{3}{8}$$​ as a decimal?
2. What is $$0.38$$​ as a percentage?
3. 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:

$$45\%=\underline{\frac{45}{100}}$$​