Roma numerals were generally used to represent a single number such as an ordinal linguistic (the first, the second, etc), or to record a total. Although it was possible to perform complex computations using Roman numerals, it was laborious due to its non-positional nature. The advent of the base-10 Hindu-Arabic numerals revolutionised numeric computation, thus Roman numerals fell from favour. However, we still use them today, mostly for ordinal numbers or to denote a year or month.

The numerals are thought to have been derived from an Etruscan tally stick method of counting. That is, the letter I really represented a vertical notch in a tally stick, rather then the number one. Every fifth notch alternated between V and X. Thus a tally stick might have the following series of notches: IIIIVIIIIXIIIIVIIIIX. If a shepherd counting sheep reached the 16th notch, the tally would be IIIIVIIIIXIIIIVI. However, the presence of X (the tenth notch) implicates IIIIVIIII precedes it, so they can be dropped, leaving XIIIIVI. Similarly, the V implies the IIII, so the final tally can be reduced to XVI. This can be read as meaning 10+5+1, thus X came to represent the number ten, V the number 5 and I the number 1.

The tally sequence was extended, such that L represented the 50th notch, C the 100th, D the 500th and M the 1000th. Thus a Roman numeral such as MDCLXVI would mean 1000+500+100+50+10+5+1 which would be 1666. Note that all numerals are written in descending order ov value.

Over time, a subtractive notation was conceived such that IIII could be reduced to IV, which meant "one short of five", or 5-1. Similarly, IX represented 10-1, thus 9. These are known as subtractive pairs and are treated as a single value. Other subtractive pairs are: XL (40), XC (90), CD (400) and CM (900). Under this notation, no single symbol need be repeated more than three times in succession, thus a long sequence such as MDCCCCLXXXXVIIII (representing the value 1999) could be reduced to just MCMXCIX. However, the Romans themselves didn't use IV and IX consistently, so they were more likely to record the value as MCMXCVIIII.

On modern clock faces using Roman numerals, you will find the number four written IIII while nine is written IX. This is more for radial aesthetics: the first 4 hours contain only I's, the next 4 contain only I's and V's and the last 4 contain only I's and X's.

Today, the accepted convention is that no symbol may be repeated more than three times in succession, the only acceptable symbols are I, IV, V, IX, X, XL, L, XC, C, CD, D, CM and M, and all symbols must be written in descending order. This system allows any value in the range 1-3999 to be represented as a Roman numeral. This makes it ideal for representing 4-digit years, or any ordinal value in the range, including the lineage of monarchs and popes, numbering prefaces pages in a book, amongst other uses, such as ordered lists, counting planetary satellites (moons), element charges and the like.

Although it is possible to denote larger numbers than 3999, and duodecimal fractions (1/12ths), the Middle Age notation that allows it is not well known today. If the purpose is to denote a number, then it isn't much use if no-one can actually understand it. Even "standard" Roman numbers aren't universally understood, but are retained for traditional purposes.