Roman numerals are a
The use of Roman numerals continued long after the decline of the
The notations IV and IX can be read as "one less than five" (4) and "one less than ten" (9), although there is a tradition favouring representation of "4" as "IIII" on Roman numeral clocks.
Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. MCM, signifying "a thousand, and a hundred less than another thousand", means 1900, so 1912 is written MCMXII. For this century, MM indicates 2000. Thus the current year is MMXIX (2019).
There is not, and never has been, an "official", "binding", or universally accepted standard for Roman numerals.[a] Usage in ancient Rome varied greatly and remained somewhat inconsistent in medieval times and later. The "rules" of the system as it is now applied have been established only by general usage over the centuries.
Roman numerals are essentially a
The underlying form of this pattern employs the symbols I and V (representing 1 and 5) as simple tally marks, to build the numbers from 1 to 9. Each marker for 1 (I) adds a unit value up to 5 (V), and is then added to (V) to make the numbers from 6 to 9. Finally the unit symbol for the next power completes a "finger count" sequence:
At some early time the Romans started to use the abbreviated forms IV ("one less than 5") for IIII and IX ("one less than 10") for VIIII – a convention that has been widely, although not universally, used ever since.[b] This convention is called "subtractive" notation, as opposed to the purely "additive" notation of IIII and VIIII. Thus the numbers from 1 to 10 are generally written as
The multiples of 10, from 10 to 100, are written according to the same pattern, with X, L, and C taking the place of I, V, and X
Note that 40 is usually written XL ("10 less than 50") rather than XXXX, and 90 as XC ("10 less than 100") rather than LXXXX.
Similarly, the multiples of 100, 100 to 1000, are written as
where CD is to be read as "100 less than 500" (that is, 400), and CM as "100 less than 1000" (that is, 900).
Since the system has no standard symbols for 5,000 and 10,000, the full pattern cannot be extended to the multiples of 1000 – restricting the "thousands" range of "normal" Roman numerals to 1,000, 2,000 and 3,000:
A number containing several decimal places is represented, as in the Arabic system, by writing its power-of-ten parts – thousands, hundreds, tens and units – in sequence, from left to right, in descending order of value. For example:
Any missing place (represented by a zero in the Arabic equivalent) is omitted, as in Latin (and English) speech:
Roman numerals for large numbers are nowadays seen mainly in the form of year numbers, as in these examples:
The largest number that can be represented in this notation is 3,999 (3,000 + 900 + 90 + 9 = MMM + CM + XC + IX = MMMCMXCIX).[c]
Forms exist that vary in one way or another from the general "standard" described above.
While subtractive notation for multiples of 4 (IV, XL and CD) has been the usual form since Roman times, additive notation (IIII, XXXX, and CCCC) continued to be used, including in compound numbers like XXIIII, LXXIIII, and CCCCLXXXX. The additive forms for 9, 90, and 900 (VIIII,LXXXX, and DCCCC) have also been used, although less frequently.
The two conventions could be mixed in the same document or inscription, even in the same numeral. On the numbered gates to the
Several monumental inscriptions created in the early 20th century use variant forms for "1900" (usually written MCM). These vary from MDCCCCX – a classical use of additive notation for MCMX (1910), as seen on
The irregular use of subtractive notation, such as IIIXX for 17, IIXX for 18, IIIC for 97, IIC for 98, and IC for 99 were occasionally used in more modern times. A possible explanation is that the word for 18 in Latin was duodeviginti, literally "two from twenty". Similarly, the words for 98 and 99 were duodecentum (two from hundred) and undecentum (one from hundred), respectively. These ways of saying 18, 98 and 99 have been attributed to influence from the Etruscans, who would say ciem zaθrum (three from twenty) for 17, eslem zaθrum (two from twenty) for 18 and θunem zaθrum (one from twenty) for 19. However, the explanation does not seem to apply to IIIXX and IIIC, since the Latin words for 17 and 97 were septendecim (seven ten) and nonaginta septem (ninety seven), respectively.
Another example of irregular subtractive notation is the use of XIIX for 18. It was used by officers of the
On the publicly displayed official Roman calendars known as
While the subtractive and additive notations seem to have been used interchangeably through history, some other Roman numerals have been occasionally observed that do not fit either system. Some of these variants do not seem to have been used outside specific contexts, and may have been regarded as errors even by contemporaries.
As Roman numerals are composed of ordinary alphabetic characters, there may sometimes be confusion with other uses of the same letters. For example, "