I think the function you look for is Round, that does give the result you (I think) expect:
Round[1/3, 0.01]
Round[1./3., 0.01]
gives:
0.33
0.33
Also what Kuba says: the function N is designed to give a numerical value of an exact expression. So it does not make much sense to give something with finite precise to the function. You have Round for that purpose...