Yes, fudging the data is one solution.
The company for which I work as an independent consultant spent a few years back several hundred thousand euros trying to get their invoices "look right" (about 20 million invoices per month). After a lot of thinking, simulations on Excel, consultations with accountants, auditors and tax advisers, prototyping, etc., it was finally decided that all the invoice individual lines and subtotals would have 5 decimal digits, and only the invoice total (and VAT) would be rounded to the nearest cent. There may still be some rounding differences, but, at least, nobody really cares about a difference of 0.00001 euro.
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I have also seen invoices in which the last line before the invoice total is a "rounding compensation", something like -0.01.
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