---
title: "Recurring decimals: cheat sheet"
subtitle: "Irrational numbers and index laws"
---

# Recurring decimals

> The words and methods from this unit, with an example of each.

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**terminating and recurring**: In long division a remainder of 0 means the decimal stops; a remainder that comes back means the digits repeat. A bar (or dots) marks the repeating block.

$$\tfrac{3}{8} = 0.375 \qquad \tfrac{1}{7} = 0.\overline{142857}$$

_1 ÷ 7: the remainders come round again_

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**which decimals stop**: Simplify first, then break the denominator into primes. Any prime other than 2 or 5 makes it recur, because 10 = 2 × 5.

$$\text{simplest form, denominator only 2s and 5s} \Rightarrow \text{terminates}$$

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