How do you learn Roman Numerals?

Answer 1

There are only 7 major symbols, I, V, X, L, C, D and M, for 1, 5, 10, 50, 100, 500 and 1000 respectively.

Symbols are normally written in descending order, from left to right. Adding up the individual values gives the number. Thus VI would be read as 5+1=6.

The value 4 was originally written as IIII, but modern conventions replaced it with IV, which literally means one short of five (or 5-1). We call this a subtractive pair, of which there are 6 available: IV, IX, XL, XC, CD and CM (4, 9, 40, 90, 400 and 900 respectively). Each is regarded as a symbol in its own right.

These 13 symbols (7 major, 6 subtractive) can be used in any combination. However, the accepted convention is that no symbol may be repeated more than 3 times in succession, and that all symbols (including subtractive pairs) must be in descending order of value, from left to right. This means that Roman numerals are limited to the range 1-3999, because 4,000 would require 4 Ms in succession.

However, there are no specific rules with regards Roman numerals. That is, there is no authority that can say whether 1999 should be written as MCMXCIX, MIM, or even MCMXCVIIII. Purists will argue that the latter is the "correct" form as used by the Ancient Romans (IX being a 20th century convention for the number 9), but today we would generally consider the former to be the "acceptable" form. However, there's really nothing intrinsically wrong with MIM either. It's just that IM is not considered to be a valid subtractive pair, and is almost certainly not one that would have been used by the Ancient Romans themselves.

Another example that is perhaps less obvious is IIXX, which is taken to mean "two short of twenty" which is 18. However, the accepted standard would use XVIII to mean 18 (10+5+1+1+1).