Decimals to fractions (terminating and repeating)

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Learn it Ending decimals: write over 10, 100 or 1,000 and simplify. Repeating decimals: let x be the decimal, multiply by powers of 10 to line up the repeating parts, then subtract.

Example: Write $0.\overline{27}$ as a fraction.

Let $x = 0.272727…$
$100x = 27.2727…$
Subtract: $99x = 27$, so $x = \frac{27}{99} = \frac{3}{11}$.

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