809
IEEE 754
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Simulations maybe? Like the ones for chaotic systems where even the slightest inaccuracy massively throws the result off, where the tiny difference between an exact fraction and a float can seriously impact the accuracy as small errors build up over time.
Are you aware of one that takes place completely within fractions of a few select types? Usually they're continuous.
I can think of some that are all integers, but I covered that in the edit.