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Fractions, decimals and percentages

Converting between fractions, decimals and percentages

Converting between fractions, decimals and percentages

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Converting between fractions, decimals and percentages

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Explainer Video

Tutor: Bilal

Summary

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

12\frac{1}{2}21​​​

0.50.50.5​​

​50%50\%50%​​

​14\frac{1}{4}41​​

0.250.250.25​​

​25%25\%25%​​

​34\frac{3}{4}43​​​

​0.750.750.75​​

​75%75\%75%​​

​13\frac{1}{3}31​​​

0.33333....0.33333....0.33333....​​

33.333....%33.333....\%33.333....%​​

​23\frac{2}{3}32​​​

0.66666....0.66666....0.66666....​​

66.666....%66.666....\%66.666....%​​

​X10\frac{X}{10}10X​

0.X0.X0.X​​

(X×10)%(X\times10)\%(X×10)%​​


Note: The ellipsis in 0.33333...0.33333...0.33333... means that the 333 is repeated forever. This is called a recurring decimal. Another way of writing this is 0.3.0.\overset{.}{3}0.3..



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 111​ followed by the same amount of zeroes as there are decimal places in the number.
  • Decimal to percentage: Multiply by 100100100 and add the percentage symbol (%\%%).​
  • Percentage to decimal: Remove the percentage symbol and divide by 100100100.
  • Fraction to percentage: Convert the fraction to a decimal, then convert the decimal to a percentage.


Examples
  1. What is 38\frac{3}{8}83​​ as a decimal?
  2. What is 0.380.380.38​ as a percentage?
  3. What is 45%45\%45% as a fraction?
​

1. Using short division 38=3÷8=0.375‾{\frac{3}{8}=3\div8=\underline{0.375}}83​=3÷8=0.375​​


2. 0.38=(0.38×100)%=38%‾0.38 = (0.38\times100)\%=\underline{38\%}0.38=(0.38×100)%=38%​​​


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

45%=45÷100=0.4545\%=45\div100=0.4545%=45÷100=0.45​​


   Then convert 0.450.450.45 to a fraction:

45%=45100‾45\%=\underline{\frac{45}{100}}45%=10045​​​


Read more

Learn with Basics

Learn the basics with theory units and practise what you learned with exercise sets!
Length:
Equivalent fractions

Unit 1

Equivalent fractions

Equivalent fractions, decimals and percentages

Unit 2

Equivalent fractions, decimals and percentages

Jump Ahead

Score 80% to jump directly to the final unit.

Optional

Converting between fractions, decimals and percentages

Unit 3

Converting between fractions, decimals and percentages

Final Test

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FAQs - Frequently Asked Questions

How do you convert a percentage to a decimal?

Divide by 100 and remove the percentage symbol.

How do you convert a decimal to a percentage?

Multiply by 100 and add the percentage symbol (%).

How do you convert a decimal to a fraction?

Write the decimal as a whole number on the top of the fraction. On the bottom of the fraction, write 1 followed by the same number of zeroes as there are decimal places.

How do you convert a fraction to a decimal?

To convert a fraction to a decimal, use short division to find the top number divided by the bottom number.

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