← Teacher guide Markdown for Prepare

Recurring decimals: cheat sheet

Irrational numbers and index laws · The words and methods from the lessons, with an example of each.

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.

38=0.37517=0.142857‾\tfrac{3}{8} = 0.375 \qquad \tfrac{1}{7} = 0.\overline{142857}
1 ÷ 7: the remainders come round again
1 ÷ 7: the remainders come round again

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.

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