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Think about things in a coordinate system. Lets say you have a sin wave, and your origin is in the middle of the wave. How far below or above that line is it?
Negative numbers help preserve dirrections in many other ways. the best way to find out is to enter physics and learn about vectors, or take chem 1 and 2 to learn the difference between positive and negative energy in regard to Heat, activation, and form changes. All of these studies would be much more complicated without negative numbers