Question

What is the fractional equivalent of the repeating decimal `0.bar8`?

`0.bar8`

Answer 1

See a solution process below:

Explanation:

First, we can write:

`x = 0.bar8`

Next, we can multiply each side by `10` giving:

`10x = 8.bar8`

Then we can subtract each side of the first equation from each side of the second equation giving:

`10x - x = 8.bar8 - 0.bar8`

We can now solve for `x` as follows:

`10x - 1x = (8 + 0.bar8) - 0.bar8`

`(10 - 1)x = 8 + 0.bar8 - 0.bar8`

`9x = 8 + (0.bar8 - 0.bar8)`

`9x = 8 + 0`

`9x = 8`

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

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

`x = 8/9`