How do you convert 0.135 (135 being repeated) to a fraction?

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Answer 1 · 2016-03-16T04:48:49

$5/37$

We first let 0.135 be $x$ .

Since $x$ is recurring in 3 decimal places, we multiply it by 1000.

$1000x = 135.135$

Next, we subtract them.

$1000x - x = 135.135 - 0.135$

$999x = 135$

Lastly, we divide both sides by 999 to get $x$ as a fraction.

$x = 135/999$

$= 5/37$