Roman Notation

Roman Notation

Roman notation is an additive (and subtractive) system of numerical notation, originally used within the ancient Roman empire that extended far past the Italian peninsula, in which letters are used to denote certain "base" numbers. Arbitrary numbers are then denoted using combinations of these base symbols. Roman numerals were developed about 500 b.c. and were at least partially derived from old Greek alphabet symbols that were not used in the new Latin alphabet. Other symbols were more creatively derived. Some Roman numerals probably came about from counting on fingers. The "I" for one came from holding up one finger, as were the symbols "II" and "III" likewise created from holding up two and three fingers, respectively. The number five was derived from holding up five fingers with the "V" shape made by the thumb and the forefinger. Although not known for sure, the symbol "X" for 10 is speculated to have been created by combining a regular "V" on top of an upside down "V", thereby making it two times five, or ten. The seven letters (or symbols) of the Roman numeral system are I, V, X, L, C, D, and M, that stand, respectively, for 1, 5, 10, 50, 100, 500, and 1,000 in the Arabic numeral system. The Roman numerals representing one to nine are in order: I, II, III, IV, V, VI, VII, VIII, and IX. Roman numerals may be written in lowercase letters, though they more commonly appear in capitals. A bar over a letter multiplies it by 1,000; thus, equals 10,000 (10 x 1,000). For the Romans, multiple bars were possible but, in practice, only one bar was usually used; with two bars rarely used and more than two bars almost never used. The ancient Roman numerals at one time went no higher than 100,000. However, large debts accumulated under the rule of Vespian made the use of the number 1,000,000 (million) necessary. At that time the Romans wrote it as "10 x 100,000", or an X with a frame around it, that is |X|. So with just the aforementioned seven number symbols, and modifiers like the "bar", the Romans expressed numbers from 1 to 1,000,000. Examples of large numbers (such as calendar years) expressed with Roman numerals are MDCCCLXXXII for 1882, MCMIL for 1949, and MCMLXXIV for 1974.

Today Roman numerals are read according to five basic rules that in some cases have only recently been incorporated into use.

In rule one, a letter repeated once or twice repeats its value that many times. For example, XXX = 30 and CC = 200. In rule two, if one or more letters are placed immediately after another one of equal or lesser value, the two values are added. For example, II = 2, XV = 15, LX = 60, and DM = 1,500. In rule three, if a letter is placed immediately before another one of greater value, the first is subtracted from the second. For example, IV = 4, XL = 40, CD = 400, and CM = 900. (As a note, the practice of placing smaller digits before large ones to indicate subtraction was rarely used by Romans but came into popularity in Europe after the invention of the printing press.) In rule four, instead of using four symbols to represent, for instance, 4 (IIII) and 40 (XXXX), such numbers are instead denoted by preceding the symbol for 5, 50, 10, 100, etc., with a symbol indicating subtraction. During the ancient Roman days VIIII for 9, for instance, was commonly found. Today IX would be used to denote 9. In rule five, a bar placed on top of a letter or string of letters increases the numeral's value by 1,000 times. For example, XV = 15, while = 15,000 (15 x 1,000).

The history of Roman numerals is not well documented and many written articles are contradictory. It is known that the Roman numerals were part of the customs and culture of the Roman people. The Roman numeral system was abandoned by AD 1500 for the newer Arabic numbers. But, up until the eighteenth century, Roman numerals were still used in Europe for bookkeeping even though the Arabic numerals were known and widely used from around AD 1000. Roman numerals do not lend themselves easily to complex multiplication or subtraction. Thus, the switchover to the new Arabic "figure" numbers was a necessary development as money became more commonly used than barter, and as trade merchants desired more efficient ways to keep their books. Roman numerals are still in used today, more than 2000 years after their introduction, but only for certain limited purposes. Examples of today's uses are in the release year and copyright date of movies, television programs and videos; pagination of preliminary pages of books before the main page numbering begins and numbering of paragraphs in complex documents; numerals on the faces of many time pieces; inscription dates on public buildings, monuments, and gravestones; names of monarchs (e.g., King Edward VII of England) and Popes (e.g., John Paul II); and wars (e.g., World War I and WWII). These uses are based mostly on formality or variety.