Seriously, if you have a multi currency application, consult with the people who actually know how to handle multiple currencies. They will tell you what the market convention is for calculating amounts. The ones I deal with usually calculate conversion rates to 6 fractional digits. Even if you came up with a more (mathematically) correct calculation, you'd still create differences because everyone else uses the market convention. So, talk to the people who know about the market conventions in your market about how to convert between currencies.

If you're not dealing with cross-currency trading, converting back and forth between currencies will obviously introduce rounding errors. You can try to migitate these by using Math::BigRat as long as you only add/subtract/multiply/divide, but I really recommend doing all calculations in one currency and avoiding currency conversions up until the last step. Also see the part about "calculation of error" above - to minimize the introduction of errors through imprecision in the calculations, you'll need to reduce the number of such steps or arrange them in a way that they tend to cancel out each other.

That's why Corion said: or thousandths of cents or whatever precision is needed

You should analyze the calculations you are doing to determine the worst case accumulation of error. Based on this analysis you can choose a unit that is small enough that the accumulated error remains below your threshold of concern.