GCSE Maths Revision Guide

Recurring Decimals to Fractions

Convert recurring decimals into fractions using algebra. This free GCSE Maths module combines short explanations, worked examples, flashcard-style recall, and timed practice so students can revise the topic without creating an account.

Foundation Skills

Common Recurring Decimals

Learn these standard conversions.

Example: 0.333... = 1/3 0.666... = 2/3 0.111... = 1/9 0.1666... = 1/6

Higher Skills

Algebraic Method

Let x = the decimal. Multiply by 10 (or 100) to shift the recurring part. Subtract to eliminate it.

Example: x = 0.272727... 100x = 27.2727... 100x − x = 27 99x = 27 x = 27/99 = 3/11

Single Recurring Digit

For 0.aaa... where one digit repeats, the fraction is a/9.

Formula: 0.ṙ = r/9

Example: 0.444... = 4/9 0.777... = 7/9