Answer to Question #198631 in Functional Analysis for smi

Question

Find p-adic norm of |6|_3

Answer 1

The $p-$adic norm of a rational number $\frac{a}{b}=p^\alpha\frac{a'}{b'}$ where $p\nmid a', b'$ is given by $p^{-\alpha}$. As $6=3\times 2$ and $3$ does not divide $2$, we have $|6|_3=3^{-1}=1/3$ .