Answer
$$\frac{217}{999} $$
Work Step by Step
Let $$x= 0.217217217\cdots $$
Then
\begin{align*}
1000x-x&= 217.217217217\cdots-0.217217217\cdots \\
999x&=217\\
x&=\frac{217}{999}
\end{align*}
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