# Repeating decimal. 0.01234567901234

Express the repeating base-10 decimal number $$0.0123456790123456790...$$ as a fraction $$\dfrac{1}{x}$$ in any base system up to hexadecimal such that $$x$$ has a minimal number of only 0s and 1s.

$$\frac{1}{81}$$
in base $$9$$ as $$\frac{1}{100}$$