What is "p-adic ordinal"

n. (context number theory English) A function of rational numbers, with prime number ''p'' as parameter, which is defined for some non-zero integer ''x'' as the largest integer ''r'' such that ''p''^''r'' divides ''x''; is defined for some non-zero rational number ''a/b'' as the ''p''-adic ordinal of ''a'' minus the ''p''-adic ordinal of ''b''; and is defined for 0 as infinity. '''2011''', Andrew Baker, , Definition 2.3