Taken from Wikipedia (http://en.wikipedia.org/wiki/Weak_acid): "Acids with a Ka of greater than 55.5 are strong acids and almost totally dissociate when dissolved in water."
Note, the acid does not have to fully dissociate to be classified as strong.
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