For instance, let's say that . We then want to multiply by a power of 10 such that we maintain the repeating decimal. In this case, we see that , preserving the repeating decimal.
Next, we observe that
Solving for , we now observe that .
However, sometimes its not obvious at first and you need to be creative, in cases like , but the same idea applies.
To answer the second question, write it like you would if you were dealing with percentages that don't have repeating decimals: .
Does this clarify things?