Write percentages as fractions and decimals

Learning focus

Learn how to write a percentage as a decimal and a fraction with a denominator of 100.

This includes:

  • one quiz
  • learning summary
  • one video

Quiz

Test what you know about finding equivalent fractions, percentages and decimals with this quiz.

Learn

Watch this video from BBC Teach which explains how to convert from a fraction to a percentage, and from a decimal to a percentage.

Converting percentages into fractions

Percentages, fractions and decimals all have equivalents of each other.

Per cent means out of a hundred. When we talk about percentages, we are referring to a fraction that is out of one hundred. Instead of writing it as a fraction, we use the per cent symbol (%).

For example:

59% is the same as \( \frac{59}{100}\)

That’s how easy it is to convert a percentage into a fraction. The percentage becomes the numerator and the denominator is always 100.

Converting percentages into decimals

What about turning a percentage into a decimal? This has an easy method too - you just divide the percentage by 100.

Why divide? This actually links back to the fact that per cent means out of 100 - did you know that the fraction line also means divide?

Since you know that all percentages relate to a fraction that has a denominator of 100, to turn it into a decimal, you simply divide the numerator by the denominator which is always 100.

So since 59% is the same as \( \frac{59}{100}\) , to turn it into a decimal you have to work out 59 ÷ 100.

So:

59 ÷ 100 = 0.59

Therefore:

59% = \( \frac{59}{100}\) = 0.59

Example 1:

What would 15% be as a fraction and a decimal?

Fraction - The percentage becomes the numerator and denominator becomes 100.

\( \frac{15}{100}\)

Decimal - Divide 15 by 100

15 ÷ 100 = 0.15

Therefore:

15% = \( \frac{15}{100} \)= 0.15

Example 2:

What would 33% be as a fraction and a decimal?

Fraction - The percentage becomes the numerator and denominator becomes 100.

\( \frac{33}{100}\)

Decimal - Divide 33 by 100.

33 ÷ 100 = 0.33

Therefore:

33% = \( \frac{33}{100}\) = 0.33

Play

Play Guardians: Defenders of Mathematica to learn more and sharpen your skills on this topic.

Guardians: Defenders of Mathematica

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