How to Convert Repeating Decimals to Fractions Definition, Types, Examples & Uses

How to Convert Repeating Decimals to Fractions

Subject: Mathematics

Book: Maths Mastery

A repeating decimal, such as 0.333... or 0.727272..., can be turned into a fraction using algebraic manipulation. For example, let x = 0.333.... Multiplying by 10 if there is 1 repeating digit, we get 10x = 3.333..., then 10x – x = 3.333... – 0.333... = 3, so 9x = 3, x = 3/9 = 1/3. For 0.727272..., let x = 0.727272..., multiply by 100 to shift two repeating digits: 100x = 72.727272..., subtract x to isolate the repeating part. This skill is crucial in pure math, simplifying exact decimal expansions, or verifying repeating patterns in financial or scientific data analysis.