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,
• D or d for five hundred,
• M or m for one thousand.

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 paricular 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:

_           _            _                 _
I for 1000  V for 5000  |I| for 100 000   |V| for 500 000

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

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 the 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 to not offend him.

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 programme was made. 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.

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

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

Unicode has a number of characters specifically designated as Roman numerals, most of them only included for compatibility with East Asian standards. They range from U+2160 to U+2183. For example, MCMLXXXVIII could alternatively be written as ⅯⅭⅯⅬⅩⅩⅩⅧ or ⅯⅭⅯⅬⅩⅩⅩⅤⅠⅠⅠ (this requires a font, such as Arial Unicode MS, that contains the necessary characters).

See also

Numeral system, Arabic numerals, Armenian numerals, Babylonian numerals, Chinese numerals, Greek numerals, Hebrew numerals, Indian numerals, Mayan numerals.

External link

• Mathworld on Roman Numerals
• Converter of Google:
  • Convert to Roman numerals (replace "123" with the number, under 5000)
  • Convert from Roman numerals (replace "IV" by the Roman number in capitals)