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Is there a generally accepted term for fractions of Currency Units?
I recently bought a stock -  which was priced exactly as your question ponders, to the 1/100 cent. I happened to buy 2000 shares, but just a round lot of 100 would be enough to create no need for rounding.  It's common for industry to price this way as well, where an electronic component purchased by the thousands, is priced to the tenth or hundredth of a cent.  There's nothing magic about this, and you'll have more to ponder when your own lowest unit of currency is no longer minted. (I see you are in UK. Here, in the US, there's talk of dropping our cent. A 5 cent piece to be the smallest value coin. Yet, any non-cash transactions, such as checks, credit card purchases, etc, will still price to the penny.) To specifically answer the question - it's called decimal currency. 1/10, 1/100 of a cent.