Show that if $x$ has a terminating decimal expansion then $x=p/q$ for integers $p,q$ where the only prime factors of q are 2's and 5's.

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

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 $$5$$.