# How do you convert 3.3 (3 repeating) as a fraction?

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14
Jun 11, 2016

$3 \frac{1}{3}$

#### Explanation:

This question is an example of repeating decimals.
And, it is rather simple.
Let's say $x$ is the number above, $3.3333 \ldots$

$x = 3.33333 \ldots$

Multiply that by 10.
$10 x = 33.33333 \ldots$

Take the second equation, and subtract the first equation from it.
$10 x - x = 33.33333 \ldots - 3.33333 \ldots$
$9 x = 30$
$x = \frac{30}{9}$
$x = \frac{10}{3}$
$x = 3 \frac{1}{3}$

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