Question

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

Answer 1

`-13/18`

Explanation:

`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`