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I've proven the converse statement but don't know where to start for this statement. Would you suggest doing a proof by contradiction?

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If $x=0.a_1a_2\ldots a_k$, then \begin{align*} x& =0.a_1a_2\ldots a_k\\ & =\frac{a_1a_2\ldots a_k}{10^k} \end{align*}

The denominator has only possible prime factors as $2$ and $5$.

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