Fractions that don't simplify are a topic: you need prime numbers, perhaps database of, and cannot always find one or there may not be one. If they fit in memory that's fine - but some things like 1/x can make them grow and "need shortening" (but if your not using arbitrary precision - this problem is faced at EACH calculation, thus the any error multiplies, as your physics books told you in that lesson).
In that case of even arbitrary precision, Mathematica can be forced to "choose a side" (add or take 1 to a long fraction a/b part so that it can find a prime number and simplify it to save memory) (you'd like see a numerical warning if this FAILED to happened).
So here's the interesting part! If you use an equation that's "supposed to be unitary and accurate", and if you allow 1/x fractions to get out of hand by "mis-using them" (not being careful they do not get large), now lets say your "program" turns on whether (the least decimal) is Greater[.5]: you might be steered the wrong way! Your input might be SMOOTH, and hit a few points of incorrect answers, and be correct %99.999999 of the time!
Interesting isn't it? Texas schools offered (offers) classes on it: ie, how to do correct calculations (never getting steered wrong) using limited hand-calculators.
It's interesting but too rare for most people to "worry about". Yet ... don't forget that problem exists.