Quite right. Either this OP spends every day writing letters to banks, shops and credit card companies complaining about the fractional cents that they have been cheated out of, probably in green ink. OR they should be able to recognize that plenty of people have good-enough solutions for this.
As someone who works in fintech, my observation is not that the caveat is "as long as the errors are small enough" but rather "as long as whoever governs the business logic is aware of the impact".
The size of the errors almost always is a large factor in their decision, but ultimately the software we write exists to serve the needs of the business, and if the business decides that larger errors are okay for some reason, then so be it.
True, but the world also runs on standards (whether explicitly defined or customary), and doing things differently from everybody else makes it painful to work together.
Sometimes there's also value in doing something objectively poorly, but in a predictable and well-understood way.
Unilaterally starting to "do numbers better" sounds like a recipe for, let's say, interesting times in the finance/accounting world.
Yeah even in university in my intro-level accounting classes they said in the real world nobody cares about discrepancies less than a dollar (and that amount scales with the size of the business). I don't know if that's actually true and I wasn't an accounting major so I don't know what they said in the more advanced classes.
But if I imagine myself as a business owner I would be annoyed with my accounting firm if they spent billable hours chasing down a discrepancy of a few pennies.
Years of practice have led me to this practical wisdom:
As long as things are consistent, no one cares if you are correct. If you lose a penny in the backend calculation, and the frontend shows the amount without the penny, and the email contains the amount without the penny, and the PDF download contains the amount without the penny, no one will care that there should be a penny there.
It becomes problematic if some places are wrong and some are right, and they are not consistent. You won't get credit for being right in only some places.
As long as the error is small enough to be inconsequential, being consistent is more important than being correct.
This observation should tell you that's it actually quite viable to be off as long as the errors are small enough.