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Roman numerals

The system of Roman numerals is a numeral system originating in ancient Rome. It is based on certain letters which are given values:

• I or i for one,
• V or v for five,
• X or x for ten,
• L or l for fifty,
• C or c for one hundred (the initial of centum),
• D or d for five hundred,
• M or m for one thousand (the initial of mille).

The early Romans used the above letters, but for multiples of thousands above 4 used combinations of I and a reversed C symbol. Later Romans used a horizontal line above a particular numeral to represent one thousand times that numeral, and additional vertical lines on either side of the numeral to denote one hundred times the number, as in these examples:

The same overline was also used with a different meaning, to clarify that the letters were numbers.

When describing members of a list, first A, B, C, D tended to be used, then 1, 2, 3 then i, ii, iii, iv.

Zero

In general, zero did not have its own Roman numeral, but the concept of zero as a number was well known by all medieval computists (calculators of Easter). They included zero (via the Latin word nullae meaning nothing) as one of nineteen epacts, or the age of the moon on March 22. The first three epacts were nullae, xi, and xxii (written in miniscule or lower case). The first known computist to use zero was Dionysius Exiguus in 525, but the concept of zero was no doubt well known earlier. Only one instance of a Roman numeral for zero is known. About 725, Bede or one of his colleagues used the letter N, the initial of nullae, in a table of epacts, all written in Roman numerals.

It is often stated that the lack of a character to represent zero prevented the Romans from developing a true positional notation system.

IIII or IV?

Throughout the centuries, there has been variation in some of its symbols — specifically, the subtractive notation (which uses, e.g., IV instead of IIII to denote the number represented by 4) has entered universal use only in modern times. For example, Forme of Cury, a manuscript from 1390, uses IX for 9, but IIII for 4. Another document in the same manuscript, from 1381, uses IV and IX. A third document in the same manuscript uses IIII, IV, and IX.

The Romans themselves didn't seem to bother that much about what was the correct formation of a number; constructions such as IIX for eight have been discovered. In many cases, there seems to have been a certain reluctance in the use of subtractive notation.

Some rules regarding Roman numerals state that a symbol representing 10^x may not precede any symbol larger than 10^x+1; use XCIX not IC for 99. However, these rules are not set in stone.

The use of subtractive notation with Roman numerals increased the complexity of performing Roman arithmetic without conveying the benefits of a full positional notation system.

Calendars and clocks

Clock faces typically show IIII for 4 o'clock and IX for 9 o'clock — using the subtractive principle in one case and not in the other. There are several suggested reasons for this:

• It has been said that the reason 4 o'clock is IIII (and not IV), is because IV is the first two letters of IVPITER, the supreme god of the Romans.
• The total number of symbols on the clock totals 20 I's, four V's and four X's; so clock makers only need a mould with five I's, a V and an X, in order to make the correct number of numerals for the clocks.
• IV is difficult to read up-side down and on an angle, particularly at that location on the clock.
• A particular Roman ruler had a clock manufactured incorrectly (with IIII) and others started making their clocks that way in order not to offend him.
• Louis XIV, king of France, preferred IIII over IV, ordered his clockmakers to produce clocks with IIII and not IV, and thus it has remained.

Roman numerals remained in common use until about the 14th century, when they were replaced by Arabic numerals (thought to have been introduced to Europe by Arab traders around the 11th century). The use of Roman numerals today is mostly restricted to ordinal numbers, such as volumes or chapters in a book or the numbers identifying monarchs (e.g. Elizabeth II). The BBC uses them to denote the year in which a television program was made (the Australian Broadcasting Corporation has largely stopped this practice but still occasionally lapses). Sometimes they are written using lower-case letters (thus: i, ii, iii, iv, etc.), particularly if numbering paragraphs or sections within chapters. Undergraduate degrees at British universities are generally graded using I, IIi, IIii, III for first, upper second, lower second and third class respectively.

Roman numerals are today still used on building faces for dates: 2004 can be represented as MMIV.

Due to the use of alphabetic symbols in Roman numerals, the Roman system could also be used to write chronograms, sentences or inscriptions in which the capital letters stand for a particular date.

Modern usage

The "modern" Roman numerals, post-Victorian era, are shown below:

Roman	Alternative	Arabic	Notes
none	none	0	There was no need for a zero.
I	Ⅰ	1
II	ⅠⅠ (or Ⅱ)	2
III	ⅠⅠⅠ (or Ⅲ)	3
IV	ⅠⅤ (or Ⅳ)	4	IIII (ⅠⅠⅠⅠ) is still used on clock and card faces.
V	Ⅴ	5
VI	ⅤⅠ (or Ⅵ)	6
VII	ⅤⅠⅠ (or Ⅶ)	7
VIII	ⅤⅠⅠⅠ (or Ⅷ)	8
IX	ⅠⅩ (or Ⅸ)	9
X	Ⅹ	10
XI	ⅩⅠ (or Ⅺ)	11
XII	ⅩⅠⅠ (or Ⅻ)	12
XIII	ⅩⅠⅠⅠ	13
XIV	ⅩⅠⅤ	14
XV	ⅩⅤ	15
XIX	ⅩⅠⅩ	19
XX	ⅩⅩ	20
XXX	ⅩⅩⅩ	30
XL	ⅩⅬ	40
L	Ⅼ	50
LX	ⅬⅩ	60
LXX	ⅬⅩⅩ	70	The abbreviation for the Septuagint
LXXX	ⅬⅩⅩⅩ	80
XC	ⅩⅭ	90
C	Ⅽ	100	This is the origin of using the slang term "C-bill" or "C-note" for "$100 bill".
CC	ⅭⅭ	200
CD	ⅭⅮ	400
D	Ⅾ	500
CM	ⅭⅯ	900
M	Ⅿ	1000
ⅭⅠↃ	ↀ	1000	Conjoined C, I and reversed C, alternative to M.
∞	none	1000	A glyph similar to the Infinity sign, alternative to M.
MCMXLV	ⅯⅭⅯⅩⅬⅤ	1945
MCMXCIX	ⅯⅭⅯⅩⅭⅠⅩ	1999	Note that officially there are no short cuts, and the I can only precede V or X. IMM (ⅠⅯⅯ) or MIM (ⅯⅠⅯ) is therefore invalid.
MM	ⅯⅯ	2000
MMM	ⅯⅯⅯ	3000
ↁ	ⅠↃↃ	5000	I followed by two reversed C, an adapted Chalcidic sign
ↂ	ⅭⅭⅠↃↃ	10000	CCI, then two reversed C
Ↄ	none	Reversed 100	Reversed C, used in combination with C and I to form large numbers.

An accurate way to write large numbers in Roman numerals is to handle first the thousands, then hundreds, then tens, then units.
Example: the number 1988.
One thousand is M, nine hundred is CM, eighty is LXXX, eight is VIII.
Put it together: MCMLXXXVIII (ⅯⅭⅯⅬⅩⅩⅩⅤⅠⅠⅠ).

The "shortcut method" for large numbers such as 1998 is not recommended, but still used by some:
1998
Two thousand is MM (ⅯⅯ), so subtract two (II [ⅠⅠ]) and you have 1998
MIIM (ⅯⅠⅠⅯ) or alternatively IIMM (ⅠⅠⅯⅯ).

Unicode has a number of characters specifically designated as Roman numerals, as part of the Number Forms range from U+2160 to U+2183. This range includes both upper- and lowercase numerals, as well as pre-combined glyphs for numbers up to 12 (Ⅻ or XII), mainly intended for the clock faces for compatibility with non–West-European languages. The pre-combined glyphs should only be used to represent the individual numbers where the use of indidivual glyphs is not wanted, and not to replace compounded numbers. Similarily precombined glypgs for 5000 and 10000 exist.

The Unicode characters should be used rather than the letters whenever possible, to avoid confusion. For example, MCMLXXXVIII could alternatively be written as ⅯⅭⅯⅬⅩⅩⅩⅤⅠⅠⅠ. Of course displaying these characters requires a user agent and font that can display the necessary characters.

Games

During the Renaissance, it was common to put in the first page of a book some Latin phrase, so that when adding the I, V, X, L, C, D, M present in the phrase, the reader would obtain a number, usually the year of publication.