Division by 3 does not exist

Think about it... how can you have 3 equal parts of an object? The decimate representation is impossible and one side always has to be bigger then the other. This is also why there is no such thing as 360 equal degrees in a circle as one degree has to be off by a little bit... There are no 360 numbers that will add up to 1 whole object either.

Your math professors must be dumb as hell. If I have three cm3 of water, and I divide that into three exact parts, I have three separate cm3 of water. Explain that, please?