The Roman system. The Arabic system was first published by Fibonacci, in Pisa, in 1202, and it was not widely adopted until the 1500s.
Fibonacci Introduces Arabic Numerals to the European Public and Describes the Fibonacci Sequence
The switch was due to the ease of doing mathematics, which had a full set of numerals for 0-9, compared to doing it in Roman, which only had three (I, V, X). It is a little berserk that a system could be base-10 and yet only allocate three numerals in that space, though one can not judge without reviewing the evolution of it. It was first adopted in academics and then made its way to accounting and commerce.
Why does the west use Arabic numbers and not Roman numerals?
The Latin language experienced a similar fate, whereby the “high” form of Latin was written and spoken by the Roman aristocracy but the common form of Latin (“Vulgar Latin”) was spoken by everyone else. As the languages evolved, the high version died and the common version evolved to modern-day Italian. The closest thing to the original, Vulgar Latin is the Sard dialect spoken in Sardinia (region of Italy). The rest of the romantic languages branched from there:
Why did Latin die out? How and why have other languages died out? What are the processes?
If something is not adopted by the common man, it is not likely to survive.
Incidentally, the Leaning Tower (of Pisa, Fibonacci’s home) was not completed until 170 years later (1372). Of course, it was started 29 years prior to Liber Abaci (the book that Fibonacci had published about the Arabic system). It took 199 years to build.
What? How? Wonder. 