OP said this is for personal finance...very rarely would you need more precision than that. Also, 1 cent is the minimum that anything can cost. Do you happen to have any 1/10 cent pieces lying around? That's a financial fiction.
Telephony providers quite often deal with fractions of the smallest amounts. A Skype call to UK will cost you 1.4p/min for example. It's quite normal for the actual company to have per-second rate and keep it as a 1000th of a penny number.
You might not have a 1/2p coin, but you can have 1/2p on your account.
