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How do you convert 0.183 (183 repeating) to a fraction?

1 Answer

George C. · mason m

Feb 25, 2016

$0 . ¯ ¯¯¯¯ ¯ 183 = \frac{183}{999} = \frac{61}{333}$ $0.bar(183) = 183/999 = 61/333$

Explanation:

$(1000 - 1) 0 . ¯ ¯¯¯¯ ¯ 183 = 183 . ¯ ¯¯¯¯ ¯ 183 - 0 . ¯ ¯¯¯¯ ¯ 183 = 183$ $(1000-1)0.bar(183)=183.bar(183) - 0.bar(183)=183$

So:

$0 . ¯ ¯¯¯¯ ¯ 183 = \frac{183}{1000 - 1} = \frac{183}{999} = \frac{3 \cdot 61}{3 \cdot 333} = \frac{61}{333}$ $0.bar(183) = 183/(1000-1) = 183/999 = (3*61)/(3*333) = 61/333$

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