It is often said that Romans (see below) had a terrible number system, which made a computations a mess. I do believe this, but I'm really suspicious of the claim that nobody had better ways to do computations until Fibonacci brought Eastern techniques to Europe. This is even more suspicious when you think about how big was the Roman empire, so that it featured a lot of fiscal checks (such as census), infrastructural works (hence engineering and logistics) and, above all, economic activity (can you believe greedy merchants didn't think of better ways to make calculations?). So, were arithmetic algorithms so inefficient before Arabic numerals were adopted Western Europe?
EDIT: I use Romans as a proxy for "ancient Western Europe civilization". I suppose anything known to Europeans (e.g. Greeks) in the last centuries BC and first centuries AD was known to Romans as well. Also I assume anything known before was inherited, i.e. if Egyptians/Babylonians/Etruscan had wonderful arithmetical techniques I doubt they got lost in history, since these are the kind of things that tend to be spread (see merchants, see what happened with modern numerals).
EDIT2: I'm not asking about numerals, but about techniques of computation. From the comments I see that the two things had indeed disjoint developments.