What is "p-adic absolute value"

n. (context number theory field theory English) a norm for the rational numbers, with some prime number ''p'' as parameter, such that any rational number of the form $p^k\; Big(\{aover\; b\}Big)$ — where ''a'', ''b'', and ''p'' are coprime and ''a'', ''b'', and ''k'' are integers — is mapped to the rational number $p^\{-k\}$, and 0 is mapped to 0. (''Note:'' any rational number, except 0, can be reduced to such a form.) '''2008''', Jacqui Ramagge, (PDF file)