# How do you convert 0.36 (36 repeating) to a fraction?

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Oct 1, 2016

$0.363636363636 \ldots \ldots \ldots \ldots \ldots \ldots = \frac{4}{11}$

#### Explanation:

Le $x = 0.363636363636 \ldots \ldots \ldots \ldots \ldots \ldots$

Now as there are two digits repeating immediately after decimal point, we multiply above by $100$ and get

$100 x = 36.363636363636 \ldots \ldots \ldots \ldots \ldots \ldots$

Now subtracting first equation from second we get

$99 x = 36$ and hence $x = \frac{36}{99} = \frac{9 \times 4}{9 \times 11} = \frac{4}{11}$

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