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**Chris L T521** To answer the first part, let $\displaystyle x$ be the repeating decimal.

For instance, let's say that $\displaystyle x=0.\overline{124}$. We then want to multiply by a power of 10 such that we maintain the repeating decimal. In this case, we see that $\displaystyle 1000x=124.\overline{124}$, preserving the repeating decimal.

Next, we observe that $\displaystyle 1000x-x=124.\overline{124}-0.\overline{124}\implies 999x=124$

Solving for $\displaystyle x$, we now observe that $\displaystyle x=\frac{124}{999}$.

However, sometimes its not obvious at first and you need to be creative, in cases like $\displaystyle .024\overline{562}$, 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: $\displaystyle 10.\overline{34}\%=.01\overline{34}$.

Does this clarify things?