You will NOT get 0.000 by touching the probes together though
Well in that case you need to clean your probes - what's the point of a meter which always gives you an inaccurate reading? In your case, every resistance reading would be out by 1.6 ohms!
Only 4-wire probes have any chance of an accurate zero ohms reading. Even my expensive LCR meter has an offset. Does yours not?