Question

How do you convert 0.8 (8 repeating) to a fraction?

Answer 1

`0.bar8=8/9`

Explanation:

We have a repeating decimal, `0.bar8`

Let us put this equal to `x`.

Then,

`x=0.bar8`

Multiply both sides by `10`:

`10x=8.bar8`

We can write this `8.bar8` as a sum of a whole number and a decimal number:

`10x=color(red)(8)+color(blue)(0.bar8)`

Now, we know that `x=0.bar8`

`10x=8+x`

`10xcolor(red)(-x)=8+xcolor(red)(-x)`

`9x=8`

`(9x)/color(red)(9)=8/color(red)(9)`

`x=8/9`

Therefore,

`0.bar8=8/9`