How do you convert 5.2108 (108 being repeated) to a fraction?

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Answer 1 · 2016-03-17T04:39:28

$\frac{964}{185}$ $964/185$

We first let 5.2108 (108 being repeated) be $x$ $x$ .

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

$1000 x = 5210.8108$ $1000x = 5210.8108$

Next, we subtract them.

$1000 x - x = 5210.8108 - 5.2108$ $1000x - x = 5210.8108 - 5.2108$

$999 x = 5205.6$ $999x = 5205.6$

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

$x = \frac{5201.6}{999}$ $x = 5201.6/999$

$= \frac{52016}{9990}$ $= 52016/9990$

$= \frac{964}{185}$ $= 964/185$