How do you convert 0.63 (63 being repeated) to a fraction?

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Answer 1 · 2016-03-16T04:14:31

$7/11$

We let 0.63 (63 being repeated) be $x$ .

$x = 0.6363...$

Since $x$ is recurring in 2 decimal places, we multiply it by 100.

$100x = 63.6363...$

Next, we subtract them.

$100x - x = 63.6363... - 0.6363...$

$99x = 63$

The recurring digits '63' cancel off and the result is that $99x$ is non-recurring.

Lastly, we divide both sides by 99 to get $x$ as a fraction.

$x = 63/99$

$= 7/11$

Therefore,

$0.6363... = 7/11$