Just save billing stuff in cents and do internal billing math using arbitrary precision integer math and round to %0.2f at the end. Nobody cares about mistakes that involve fractions of a cent, or whether their subscription lasts 1 year or 365 days or 52 weeks of 7 days. Just pro-rate in the easiest way possible and round in favor of the customer. You just don't need any of this fraction-of-a-cent BS.
If your billing math is easy you can even explain how it works in the FAQ so customers won't feel cheated. If your billing is complex and uses millicents in an misguided attempt to "do the right thing" then you can't explain to your customers how it works and why it's fair. That's no good from the customer's point of view.
Billing systems are easy to over-engineer and in my experience you just want a system that's straightforward and correct. That way you can focus your energy on more important stuff.