To answer the first part, let

be the repeating decimal.

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?