How do you convert 0.571428 (571428 being repeated) to a fraction?

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Answer 1 · 2016-03-18T04:01:03

$\frac{4}{7}$ $4/7$

We first let 0.571428 (571428 being repeated) be $x$ $x$ .

Since $x$ $x$ is recurring in 6 decimal places, we multiply it by $10^{6}$ $10^6$ .

$1000000 x = 571428.571428$ $1000000x = 571428.571428$

Next, we subtract them.

$1000000 x - x = 571428.571428 - 0.571428$ $1000000x - x = 571428.571428 - 0.571428$

$999999 x = 571428$ $999999x = 571428$

Lastly, we divide both sides by 999999 to get $x$ $x$ as a fraction.

$x = \frac{571428}{999999}$ $x = 571428/999999$

$= \frac{4}{7}$ $= 4/7$