"What is the value of 0.02 cm rounded to the nearest centimeter?"
Is it logical to approximate a real value (however small) to zero? I know that following a simple 'rounding' or approximation algorithm, the answer is zero cm. This offends my sense of logic, given that we are talking about a real value.
What do others think?
On
You could be taking the difference in two person's heights, rounded to the nearest centimeter. If the measured difference is only $0.02$ cm then it may make sense to say the two persons are the same height, that is, the height difference is zero.
If you are trying to measure the gap between two electrodes in an electronic device then it makes no sense to round $0.02$ cm to zero, but it makes no sense to round to the nearest centimeter then anyway. On the other hand it hardly makes sense to round the distance from Paris to Moscow to the nearest centimeter. You have to assume you're working at a scale where whole centimeters represent the values we care about.
Pythagoras would say no as zero is not a number, but then he would also say no to rounding to one, for the same reason. However the rest of the modern world would say yes (with the reservation that it does depend on what you are going to do with the result). But if this is homework of an exercise in rounding then very definitely it rounds to zero if you are asked to round to the nearest centimetre.
Summary: it is not a matter of logic but of what you are going to do with the approximation.