Roman numerals

The sytem 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.

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 in the subtractive notation (which uses, e.g. IV to denote 4 instead of IIII) 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. 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.

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 of using 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
ↂ	10000
Ↄ	Reversed 100	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 designed as Roman numerals. They range from U+2160 (Ⅰ) to U+2183 (Ↄ).

Example (requires a font, such as Arial Unicode MS, that contains the necessary characters):

ⅯⅭⅯⅬⅩⅩⅩⅧ or ⅯⅭⅯⅬⅩⅩⅩⅤⅠⅠⅠ (MCMLXXXVIII)

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)