Fractions to decimals (terminating and repeating)

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Learn it Divide the numerator by the denominator. If the remainders start to repeat, the digits repeat forever; put a bar over the repeating block. Denominators with only 2s and 5s give decimals that end.

Example: Write $\frac{5}{12}$ as a decimal.

$5 \div 12$: 50 ÷ 12 = 4 R2, 20 ÷ 12 = 1 R8, 80 ÷ 12 = 6 R8, 80 ÷ 12 = 6 R8, …
The remainder 8 keeps coming back, so the 6 repeats.
$\frac{5}{12} = 0.41\overline{6}$.

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