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Roman numerals were inefficient. Our modern system for numbers (the decimal system) is better because:

(1) it allows for the representation of large numbers greater than ones on the scale of M = 1000. Every step to the right in a decimal place multiplies the number by 10, so a number that takes 5 places, say 10,000, takes many more in roman numerals (10,000 = MMMMMMMMMM). Romans did not deal with large numbers on this scale.

(2) simple operations such as addition have no algorithm to calculate them by hand. If I wanted to add 45 + 659, I would put one above the other and do it the way schools teach. when the numbers 5 + 9 exceed 10 in the ones column, I can carry the ones digit, and add it on the tens. Within 5-10 seconds, I can see this is 704. There is no easy way to add in Roman numerals: how would one go about adding XVL + XXXXLIXM? In fact, this is the same problem as the one we just did. And this is just addition! Even simple operations like IX * XIV are not obvious when a Roman banker has only Roman numerals to work with.

Hope this answer wasn't too long.

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