> You store the sums on either end, the currencies, the exchange rate and the final sum?

There is a remarkable amount of disagreement as to whether one should do one’s back office work based on the price or based on the quantity of the counter currency.

> No one has .0000145 cents in their account. Rounding occurs in the real world.

Indeed. But you either need to convince all parties to agree to round the same way or you need to accept small errors