How do you convert 0.345 (345 being repeated) to a fraction?

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Answer 1 · 2016-03-17T04:59:57

$115/333$

We first let 0.345 (345 being repeated) be $x$ .

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

$1000x = 345.345$

Next, we subtract them.

$1000x - x = 345.345 - 0.345$

$999x = 345$

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

$x = 345/999$

$= 115/333$