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?