Definition:Canonical P-adic Expansion

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

Let $a$ be a $p$-adic number, that is left coset, in $\Q_p$.

The unique $p$-adic expansion that is a representative of $a$ is called the canonical $p$-adic expansion of $a$.

Also known as
The canonical $p$-adic expansion of $a$ is simply called the canonical expansion of $a$ when $a$ is understood to be a $p$-adic number.

Also see

 * P-adic Number has Unique P-adic Expansion Representative


 * Leigh.Samphier/Sandbox/Canonical P-adic Expansion Converges to P-adic Number