The tricky thing about solving $0.5/\overline{305}$ is knowing where the decimal goes in the answer. First you need to know that the original number $305$ can be written as $305.00$. (The number of zeros after the decimal point is not important.) So $0.5/\overline{305}$ can be written as $0.5/\overline{305.00}$.

Now follow the four steps for dividing decimal numbers:

1. Move outside decimal all the way to the right
2. Move the inside decimal to the right the same number of places as the outside decimal
3. Raise the inside decimal up
4. Divide

So instead of doing $0.5/\overline{305}$, you actually solve

$5/\overline{3050.0}$