Learn how to convert percentages to fractions and decimals – KS3 Maths

Key points

are always out of 100. This is important to remember when converting percentages to fractions and decimals.
Being able to fractions and work out will make converting percentages to fractions easier.
Knowing how to multiply by 100 is a useful skill when converting a percentage to a decimal.

How to convert a percentage to a fraction

Write the percentage value as the of the fraction.
The of the fraction is 100
the fraction if possible by dividing the numerator and denominator by their (HCF). The HCF is found by finding all of two numbers and selecting the largest one.

If the numerator is a decimal, multiply the numerator and denominator by the lowest to get a whole number value. Then simplify the fraction.

Examples

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$Example 1. Thirty six percent equals blank fraction.$
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Convert 36% to a fraction.
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The numerator is the percentage value. The denominator is 100.
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36% is 36 out of 100. Simplify the fraction by dividing the numerator (36) and the denominator (100) by their HCF (4). 36⁄100 simplifies to 9⁄25
$Example 2. Two point five percent equals blank fraction.$
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Convert 2∙5% to a fraction.
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2∙5% is 2∙5 out of 100. The numerator is not a whole number.
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Make the numerator (2∙5) a whole number by multiplying by the lowest power of 10. This is 10. The denominator is also multiplied by 10 to give a proper fraction. 2∙5% is 25⁄1000
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25⁄1000 can be simplified by dividing the numerator (25) and the denominator (1000) by their HCF (25). 2∙5% is 1⁄40 as a fraction.

Question

What is 60% as a fraction?

Game - Comparing decimals, fractions and percentages

Test your comparing percentages, fractions and decimals skills with these puzzles from our Divided Islands maths game.

Play the full Divided Islands game.

How to convert a percentage to a decimal

To convert a percentage to a decimal, divide the percentage value by 100

Examples

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Convert 36% to a decimal.
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36% is 36 out of 100. This is the same as 36 divided by 100. 36% is 0∙36 as a decimal.
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Convert 2∙5% to a decimal.
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2∙5% is 2∙5 divided by 100. 2∙5% is 0∙025 as a decimal.

Question

What is 60% as a decimal?

Game - Equivalent percentages

Now practise your equivalent percentages skills with these puzzles from Divided Islands.

Play the full Divided Islands game.

Practise converting percentages to fractions and decimals

Quiz

Try this quiz to practise converting percentages to fractions and decimals.

Real-world maths

A woman holding a small card and using that to refer to whilst typing something into a video subscription streaming service. — Image caption,
A business may use fractions or percentages when advertising a product.

A business may choose to convert a percentage to a fraction or decimal when thinking about advertising and marketing.

A subscription service running a discount may choose to convert a percentage to a fraction when advertising this discount. For example, ‘half price’ may attract more potential customers than ‘50% off’.