No, it does not work this way. Any good accountant will see a different in values, even smallest one, as a sign of an incorrect calculation. Does not matter which way it goes, they will feel compelled to figure out who is wrong. At least a good accountant will.
There is no accounting error; let's say customer has purchased / used a service for 1.433 USD.
You issue an invoice for 1.44 USD (aka, amount due), then the 1.44 USD is used as a basis for accounting and is all consistent.
Then, if you are a nice company and the situation applies in your case, you may issue a credit in favor of the customer for 1.44 USD - 1.433 USD that will be used as a discount on a future invoice
The best part is that the moment where you decide to issue the credit invoice or not, is the perfect moment to track the rounding errors and even keep a very detailed journal of the entries (e.g. for auditors).
You added 10 of those items as inventory with a total value of 14.33, then you sold each individually as a total value of 14.40. After that transaction, your inventory account has -0.07 on it, but there aren't any items at all there.
From experience, those differences surface during stock taking. Amd most companies are really bad at that. And if they surfacey they are corrected by inventors adjustments (in unit of measure, not value, which is a differwnt can of worms). As long as those adjustments aren't to extreme, nobody really cares.
A good accountant so will sooner or later investigate those rounding errors, as they will show up somewhere ultimately. And a general policy of rounding in one direction is the last thing you want an auditor to find.
One can use more than 2 decimal places for rates, but final invoicing has to be two decimal places (atleast in most countries). Banks/tax authorities dont carry anything beyond 2 decimal.
Eg: fuel is usually priced 3 decimal, so 4 gallons x 25.5444 usd/gallon gives = $102.1776 to 4 dp, but will be billed as $102.18
That is absolutely not how it works. Rounding is exactly specified in the underlying contract always and you need to implement the correct rounding. For example, here is the rounding table for compounding calculations in the ISDA definitions (these are very standard for a wide range of contracts, but this particular table is for various overnight swap rates used in interest rate derivatives)[1].
Interesting side note:ASME also has a standard for rounding on engineering drawings. A few years back I had to build a custom function in Excel to match the standard, because our calcs weren't matching the customer's calcs.
Where issues could come in is when these things are multiplied with a bunch of other numbers (each number with defined rounding but not after each operation) and then have some defined rounding at the end. There different computer numerics could in give slightly different results, but those can easily be resolved on settlement (for small stuff that stays well within the back offices - at least that is how I remember it).
Also, not totally unusual for one or both participants to forget about some rounding they might have agreed bilaterally if it was some one off etc.
Heh. But usually it's the other way around unless they remembered to specify it the right way. Forgiving $0.01*N customers is cheaper than dealing with an irate customer.
round in favor of the bank / financial institution you are working for