Every base other than binary has some fractions that expand 'nicely', and some that repeat infinitely. It depends on the factors of your base.

When you're expanding a fraction, you're trying to match up each factor of the denominator with a factor of the base. Let me show you how it works in base 10.

10 factored is 2 x 5.

2 factored is 2.
So 1/2, in base 10, will be one digit long, because the 2s match up.

4 factored is 2 x 2.
So 1/4 won't be only one digit long, because the first 10 can only 'use up' one of the 4's 2s.
But if we take a second 10, we have another 2 (and another 5) to work with, so we can 'use up' the 4's other 2.
1/4 in base 10 is two digits long (0.25)

6 factored is 2 x 3.
We can use up the 2 on our first go-round, but then we're stuck. No matter how many 10s we take, we'll never get a 3.
1/6 in base 10 repeats infinitely (0.16666....)

8 factored is 2 x 2 x 2
1/8 in base 10 is three digits long, cause we need three tens to use up those 2s. (0.125)

This isn't limited to numbers lower than your base:

50 factored is 5 x 5 x 2
Our first 10 uses up the two and one of the fives; our second 10 takes care of the other five.
1/50 in base 10 is two digits long (0.02)

Clear as mud?

So base 9 doesn't solve the problem, it just moves it to different numbers. Anything with factors other than 3 will repeat infinitely in base 9. Sorry, but that does include 1/2.