I think you're describing the number 0.888... where the 8s will keep
going forever and never end.
Now, I've been around a long time, and worked a lot of math, but
I never knew how to make a fraction out of repeating decimal until
just a short time ago. That's exactly what we need here. Here's
the trick:
-- You have a decimal, with a set of digits ... 1 or 2 or 3 or however many ...
that repeat.
-- Take one complete set of the digits that repeat. Write them
on top of a fraction.
-- On the bottom of the fraction, write the same number of nines
as however many digits are on top.
-- THERE's your fraction that's equivalent to the repeating decimal !
You can go ahead and simplify it if it's possible and you feel like it.
In this problem, the repeating part is only one digit ... the 8 .
Write 8 on top of the fraction. Then write a single 9 on the bottom.
There's your equivalent fraction.
0.888...repeating is equal to 8/9 .