So, this is more of a mathematical question than a historical question. Put simply, Roman numerals are an awful way of counting things and decimal counting is a great way of counting things. But why?

Well, there's the obvious benefit of having very clear rules defining what each symbol means. If I see an "I", what does that mean? It could mean 1, it could mean somethings else if it's part of a collection of other "I's" or something else if it's proceeding a different numeral. And "I" is the easiest symbol to understand. If you were trying to communicate with someone who didn't understand Roman numerals, they could probably figure out what a line drawn in the ground meant. But what if you drew a "V" or and "X"? They would have no idea. The symbols have no relation to what they represent, they were just arbitrarily chosen because they're easy to carve.

Then there's the issue of calculations. It is agonising to try to add things in Roman numerals, especially large numbers. Never mind trying to do multiplication, division, trigonometry or calculus in them. That's because in Roman numerals, a symbol's meaning depends on what digits surround it, which can be difficult to work with. Really, the only reason the system remained in use was because Rome used it and because the Romans didn't think up a better method, the Empire just stuck with it.

Then along comes decimal counting in around 700 C.E. It has a lot of advantages compared to numerals, like being more relatable to humans (since we have 10 fingers and 10 toes) and having clearer rules about what each symbol meant. But the biggest advantage was the inclusion of the recently discovered 0.

Having a 0 in the counting system allowed for some really funky maths to be implemented. Now, we could count in bases, which make multiplication and division so much easier. Now we could understand more complex mathematics, like advanced trigonometry and some early calculus. All around, a number system involving a 0 is a great system, and the decimal system happened to be the first.

So, the system picked up traction in India, before moving to the Arab world where they popularised the method during the Islamic Golden Age, where they used this new method to discover many of the mathematics I described above. By around the 11th centuary, the Spanish had mingled with the Islamic Moors enough that the system spread to them, and before long the system was adopted throughout the rest of Europe.