Actually, floating point addition isn't necessarily commutative[1][2], which is one of the problems of thinking of floating point as just a number. Although in this case, it's at least still addition, but the type of things being added have special conditions.

It's more like doing calculations on scientific notation, where there are special rules for how to keep the right number of significant figures/precision after operations. Like scientific notation, you would probably convert to one form or another (even if in your head) before doing the operation, and keep note of the possible loss of precision.

This is exactly the reason why adding floats to ints is something that people think should require an explicit conversion, so it's more obvious that's a point that may introduce loss of accuracy.

1: https://stackoverflow.com/questions/24442725/is-floating-poi...

2: https://www.cs.umd.edu/class/sum2003/cmsc311/Notes/BinMath/a...