How do you convert -0.16 (6 being repeated) to a fraction?

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Answer 1 · 2016-08-02T11:25:17

$-13/18$

$color(red)("Note that this is a negative number")$

Write as $(-1) xx 0.16bar6$

Let $x=0.16bar6$

Then $10 x = 1.66bar6$

So $10x-x ->x(10-1) -> 9x= 1.66bar6$
$" "ul(0.16bar6) larr" Subtract"$

$9x=1.5$

Double both sides $" "18x=3$

Divide both sides by 18

$x=3/18$

But this now needs to be $(-1)xx3/18 = -3/18$