How do you convert 3.123 (123 being repeated) to a fraction?

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Answer 1 · 2016-03-18T03:46:58

$\frac{41}{333}$ $41/333$

We first let 0.123 (123 being repeated) be $x$ $x$ .

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

$1000 x = 123.123$ $1000x = 123.123$

Next, we subtract them.

$1000 x - x = 123.123 - 0.123$ $1000x - x = 123.123 - 0.123$

$999 x = 123$ $999x = 123$

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

$x = \frac{123}{999}$ $x = 123/999$

$= \frac{41}{333}$ $= 41/333$