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We prove that Schneider's continued fraction map is topologically conjugateto a shift map defined on $\mathbb{Q}_p$, and the topological conjugation$f\colon\mathbb{Q}_p \rightarrow \mathbb{Q}_p$ is an isometry such that$f(\mathbb{Q})=\mathbb{Z}[\frac{1}{p}]$. Furthermore, for $x \in \mathbb{Q}_p$we proved that $x \in \mathbb{Q}$ if and only if $f(x) \in\mathbb{Z}[\frac{1}{p}]$.

Topological conjugacy between Schneider's continued fraction map and a shift map on $\mathbb{Q}_p$