How do you convert 0.809 (09 being repeated) to a fraction?

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Answer 1 · 2016-03-16T04:40:15

$89/110$

We first let 0.809 (09 being repeated) be $x$ .

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

$100x = 80.909$

Next, we subtract them.

$100x - x = 80.909 - 0.809$

$99x = 80.1$

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

$x = 80.1/99$

$= 801/990$

$= 89/110$