In scientific computations, it is often sufficient that the final answer is correct to a few significant figures. There are several reasons for this. One is tha

In scientific computations, it is often sufficient that the final answer is correct to a few significant figures. There are several reasons for this. One is that the model uncertainty is typically quite large (unless you are dealing with particle physics). Another is measurement uncertainty. Except for some unique scenarios measurements aren't going to have more than a few significant figures as well. So there isn't a big difference between 3.14 and 3.14159 and pi to 100 decimals. I'm sure one can think of plenty of counter examples, but I'll give an example where floating point numbers are used heavily and you don't typically don't care about minor rounding issues. Computational chemistry can be used to predict the geometry of molecules. The model used to make this prediction has to describe the interactions between the atoms, which is computationally expensive (solving Schrodinger's equation). So often times the molecule is only modeled in a vacuum and not as a liquid (where there would be many other molecules included). All of these add up that even if there was no IEEE-754 floating point error, the answer would still maybe only be right to +/- 10%. So science is quite different from finance, where the main goal is to converse a certain quantity. Money shouldn't be created or lost though rounding errors.