arithmetic - Converting repeating decimal in base b to a fraction the same base

The repeating decimal .36666... in base 8 can be written in a fraction in base 8.

I understand simple patterns such as 1/9 in base 10 is .1111.... so 1/7 in base 8 is .1111.
But I'm not too sure how to convert this decimal in this base to the fraction in the same base.