Ka=[H+][A-]/[HA]
if Ka is 55.5 and [H+] = [A-] and for an (originally) 1 molar solution of HA then
[HA] = (1 - x) where x = [H+] = [A-]
55.5(1-x) = x^2
x^2 + 55.5x - 55.5 = 0
x= 0.986 or -56 (the negative being not possible)
so the factor x = 0.982 = [H+]
in other words it is nearly 99% dissociated
so, according to Wiki's definitions it WOULD be possible for a weak acid to be only 95% dissociated