Answer to Question #198638 in Functional Analysis for smi

Question

Find p-adic norm of |3/4|_2

Answer 1

The p-adic norm of $x$ :

$|x|_p=p^{-a}$

where $p$ is a prime number, $a$ is a unique integer.

Then:

$\frac{3}{4}=3\cdot2^{-2}$

$|\frac{3}{4}|_2=2^2=4$