Characterisation of Terminal P-adic Expansion

Theorem
Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers for some prime $p$.

Let $x \in \Q_p$.

Then:
 * the $p$-adic expansion of $x$ terminates $x$ is a non-negative rational number whose denominator is a power of $p$.