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