Converting Between Fractions, Decimals and Percentages

This lesson covers the methods for converting between fractions, decimals and percentages — a key skill for AQA GCSE Mathematics. You must be fluent in all six conversion directions and be able to recognise common equivalences. This topic also includes converting recurring decimals to fractions, which is a higher-tier skill.

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The Three Forms

Fractions, decimals and percentages are all different ways of representing the same value.

graph TD
    A[Fraction] -->|"Divide numerator by denominator"| B[Decimal]
    B -->|"Multiply by 100"| C[Percentage]
    C -->|"Divide by 100"| B
    B -->|"Write as a fraction and simplify"| A
    A -->|"Convert to decimal, then x100"| C
    C -->|"Write over 100 and simplify"| A

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Common Equivalences

You should memorise these common conversions: