How do you get to 0?

I was thinking about this a while back in my physics class, but how exactly are we able to get to 0? I mean if we were trying to touch an object that wasn't moving, and gradually moved closer to it, how would we touch it? Where's the limit between 0 and 0.0000000000000000000000000001? Do we ever actually touch the object, or do we have some weird rounding feature in our head that lets us skip over the infintely smaller values and feel the object? Is there ever 0 distance between two objects? Do we even need to be at 0 distance to touch an object?