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
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).