Roman numeral

The Roman numeral system is the system for depiction of numbers first used in ancient Rome with continued use to the present.

The Roman numeral system is decimal and positional, but does not have zero. Unlike many other ancient numeral systems which used letters of the alphabet, the Roman system only uses a subset of the alphabet; it uses repetition and subtraction to reduce the number of distinct symbols. The letters used are I for 1, V for 5, X for 10, L for 50, C for 100, D for 500, and M for 1000. Numbers between 1000 and 1,000,000 can be represented by placing a bar over the number of thousands and leaving the bar off the part of the number less than 1000.

Numbers are indicated by building up and by subtraction. The numbers 1, 2, and 3 are represented by I, II, and III, respectively, while 6, 7, and 8 are represented by VI, VII, and VIII, respectively.

For numbers one unit less than a larger unit, the smaller unit is subtracted by placing it to the left of the larger unit: the number 4 can be represented as IV, 9 as IX, 40 as XL, 90 as XC, 400 as CD and 900 as CM.

The system is positional, with the multiples of the larger exponents of 10 occurring to the left of multiples of smaller exponents of 10. Hence 1,628 is represented as MDCXXVIII, while 1,492 is represented as MCDXCII. (Initial M = 1000, CD = 900, XC = 40, II = 2.) Because of the subtractive element, the letter order matters; LX is not the same as XL.

The symbols for the numbers appear to have initally not been letters, but to have evolved into letters over time. Older inscriptions show a CIɔ as the symbol for 1000, which evolved to M; the D for 500 is believed to be the right half of the symbol. The original symbol for 100 was originally Θ or ⊕, which evolved to C, while a fragment of the symbol evolved to L for 50. V for 5 is visually one half of X (10); the X was not an original Roman letter.