[kbolino]

You can certainly encounter 2.675 as a multiplier, even if you wouldn't have it as a balance.

It doesn't matter that some error starts off way less than 0.005 if rounding then amplifies it. We can find two 2-digit numbers that multiply to get exactly 2.675 in reals, but whose product differs from the float number closest to 2.675 enough to affect rounding:

    abs(      2.14 * 1.25     -       2.675    ) < 0.005
    abs(round(2.14 * 1.25, 2) - round(2.675, 2)) > 0.01

And regarding integer vs fractional rounding, we can see different results for what is nominally the same computation, depending on where the decimal point is:

    abs(round(1.0  * 1.5, 0) - 2.0 ) < 0.1
    abs(round(0.01 * 1.5, 2) - 0.02) > 0.001

Now, I never said that floats were bad. I am only saying that rounding them doesn't work the way one might expect, and shouldn't be done any more than necessary; in many cases, it's not necessary at all.