What Are Roman Numerals?

Roman numerals are a numbering system which was widespread throughout Europe until approximately 900 CE, when Arabic numerals supplanted Roman numerals for most applications. Roman numerals can still be seen on formal documents to mark the date or being used to iterate simple numerals, such as those used on an outline. For mathematical purposes, however, these numerals have long since been discarded, because they are clumsy and difficult to work with in comparison to Arabic numerals.

The inspiration for Roman numerals can be found in Attic numerals, which were used in Greece from around the seventh century BCE. Attic numerals used symbols to represent the numbers one, five, 10, 100, 1,000, and 10,000. The symbol representations probably came from tally sticks which would have been used to mark down goods as they were counted. The Etruscans, located in what is now Italy, picked up the Attic numeral system and adapted it for their own use, creating symbols to represent one, five, 10, 50, and 100.

The Romans changed the symbols used for Etruscan numerals in addition to adding a few. Under the system of Roman numerals, I represents one, V stands for five, X means 10, L is used for 50, C marks 100, D indicates 500, and M is 1000. A bar placed over a symbol multiplies its value by 1,000. All numbers in Roman times would have been written out using these symbols. 17, for example, would have been written as XVII. As can be seen, this system requires the reader to add the symbols together in order to discern the number being represented. This can be quite time consuming, especially with large numbers such as MMMDCXIII, which reads as 1,000+1,000+1,000+500+100+10+1+1+1, or 3,613.

However, numbers such as four are not, by convention, written out in Roman numerals as IIII. Instead, a system called subtractive notation is used. Subtractive notation means that if a symbol of lesser value is placed in front of a symbol of higher value, the lesser symbol should be subtracted from the greater one. Hence, IV means four, just as MCMLXXXIV means 1984. When using subtractive notation, only multiples of 10 are used, so VC for 95 would be incorrect, and XCV would be proper. It is also considered improper to skip orders of magnitude when using subtractive notation, meaning that XM would not be used to represent 990, but CM could be used to indicate 900.