Firstly, if you treat floating-point without the proper care, that will still be the case if you use an integer for all currency amounts (as a number of cents) but reach for floating-point for percentage calculations and such.

Secondly, you can implement pencil-and-paper rounding rules using binary floating point! It's done by serializing to decimal text, working with the digits (perhaps as integers) and then converting back to floating point.

> those errors don’t match the ones you get when using a paper ledger.

If you have errors in your paper ledger, you're not much of an accountant.