09 August 2010

The Other Roman Numerals


There are seven letters used in constructing Roman numerals &mdash I is 1, V is 5, X is 10, L is 50, C is 100, D is 500, and M is 1000. Currently, the correct method of representing numbers follows a formula which divides the numeral into groups of units (ones), tens, hundreds, etc., much like Arabic numerals. Sequences of the same letter being repeated are allowed up to three (I, II, and III are 1, 2, and 3, respectively), but for numbers which would use the Arabic digits 4 and 9, a special method is employed. For the number 9, the Roman numeral is IX, in which the letter of lesser value is placed in front to indicate subtracting one from ten, rather than adding. This doesn't necessarily mean that this method extends to, say, writing 1999 as IM. 1999 would be constructed as MCMXCIX, using M for 1000, CM for 900, XC for 90, and IX for 9. This chart can be used for easy reference.


Note how more symbols are required when amounts in excess of 3999 are written. The horizontal line above a letter is a macron (or titulus), and multiplies a letter's standard value by 1000. Thus a V with a macron becomes the letter for 5000, and so forth. Presently, macrons are not readily available on computer keyboards, and are substituted by framing a letter or string of letters in brackets or parentheses.

But, while they weren't incorporated into this standard system of enumeration, and generally only appeared by themselves, every other letter of the Roman alphabet had its own numerical value as well. Usually, these were used for marking specific quantities. A would be 500, B 300, E 250, F 40, G 400, H 200, K 250, N 900, O 11, P 100, Q 500, R 80, S 7, T 160, Y 150, and Z 2000. Rule of applying a macron to multiply a letter by 1000 holds true for each of these amounts. As the Romans did not have a J, U, or W (at least, not in the same sense as we have them today: as separate, individual letters), these letters do not have values. W eventually took on the guise of representing 55 through puzzle books and almanacs of the Victorian era, as it was seen as two intersecting Vs.

Though none of these other letters were incorporated into longer Roman numerals, the letter S could be added at the end for the fraction one-half (1/2), as it was an abbreviation for "semis", meaning "half". Other fractions used by the Romans can be seen at this site.

Source: Skinner, Hubert M. The Story of Letters and Figures. Chicago: Orville Brewing, 1905.

Source: Pflughaupt, Laurent. Letter By Letter: An Alphabetical Miscellany. New York: Princeton, 2007.