Roman numerals

Roman numerals are a numeral system that was used by ancient Rome. Numbers in this system use letters from the Latin alphabet. Currently, it uses seven symbols:^[1]

Numeral systems by culture
Hindu–Arabic numerals
Western Arabic Eastern Arabic Khmer	Indian family Brahmi Thai
East Asian numerals
Chinese Suzhou Counting rods	Japanese Korean
Alphabetic numerals
Abjad Armenian Cyrillic Ge'ez	Hebrew Greek (Ionian) Āryabhaṭa
Other systems
Attic Babylonian Coptic Egyptian Etruscan	Mayan Roman Urnfield
List of numeral system topics
Positional systems by base
Decimal (10)
2, 4, 8, 16, 32, 64
1, 3, 9, 12, 20, 24, 30, 36, 60, more…
v t e

The Europeans still used Roman numerals even after the fall of the Roman Empire. From the 14th century, the Europeans replaced Roman numerals with Arabic numerals. However, people still use Roman numerals to this day.

One place in which they are sometimes seen is on clock faces (the front of a clock). For example, on the clock of Big Ben, the hours from 1 to 12 are written as:

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII

The IV and IX can be read as "one less than 5" (4) and "one less than 10" (9). On many clocks that use Roman numerals, however, 4 is written as IIII.^[2]

Subtraction rule

Instead of writing the same letter four times, a rule for subtraction is used. The letter is written once, then the next largest Roman numeral is written. When a lower number (such as I) appears before a higher one (such as V), the lower number is subtracted from the higher one. For example, 4 is not written as IIII, but instead as IV, because IV is V (5) minus I (1). The same is done for 9 - it is not written as VIIII, but instead as IX, because IX is X (10) minus I (1).

Example

It is very easy to write a number as a Roman numeral. Simply subtract the largest possible Roman numeral as many times as possible from the number. This system will result in a valid Roman numeral, but will not take the subtraction rule into account.

1 × 1000

+

1 × 500

+

4 × 100

+

1 × 50

+

3 × 10

+

4 × 1

=

1984

M

+

D

+

CCCC

+

L

+

XXX

+

IIII

=

MDCCCCLXXXIIII

Getting the number from the numeral is equally simple, by adding the values of the symbols.

In general, the values for 5, 50, and 500 are not subtracted. Here is the same number using the subtraction rule:

1 × 1000	+	(1 × 1000) - (1 × 100)	+	1 × 50	+	3 × 10	+	(1 × 5) - (1 × 1)	=	1984
M	+	CM	+	L	+	XXX	+	IV	=	MCMLXXXIV

Special values

Zero

The number zero has its own Roman numeral, which is O. At about 727, Bede or one of his colleagues used the letter N, the abbreviation (short form) of nihil (the Latin word for "nothing").^[3]

Fractions

A semis (S) coin.

The Romans also used fractions. The most common base for fractions was 1/12, which in Latin is called uncia (ounce).

Fraction	Numeral	Name (nominative and genitive)	Meaning
1/12 = 0.083	·	Uncia, unciae	"Ounce"
2/12 = 0.166	·· or :	Sextans, sextantis	"Sixth"
3/12 = 0.25	··· or ∴	Quadrans, quadrantis	"Quarter"
4/12 = 0.333	···· or ∷	Triens, trientis	"Third"
5/12 = 0.416	····· or ⁙	Quincunx, quincuncis	"Five-ounce" (quinque unciae → quincunx)
6/12 = 0.5	S	Semis, semissis	"Half"
7/12 = 0.583	S·	Septunx, septuncis	"Seven-ounce" (septem unciae → septunx)
8/12 = 0.666	S·· or S:	Bes, bessis	"Twice" (as in "twice a third")
9/12 = 0.75	S··· or S∴	Dodrans, dodrantis or nonuncium, nonuncii	"Less a quarter" (de-quadrans → dodrans) or "ninth ounce" (nona uncia → nonuncium)
10/12 = 0.833	S···· or S∷	Dextans, dextantis or decunx, decuncis	"Less a sixth" (de-sextans → dextans) or "ten ounces" (decem unciae → decunx)
11/12 = 0.916	S····· or S⁙	Deunx, deuncis	"Less an ounce" (de-uncia → deunx)
12/12 = 1	I	As, assis	"Unit"

Large numbers

A number of numeral systems are developed for large numbers that cannot be shown with I, V, X, L, C, D and M.

Apostrophus

One of the systems is the apostrophus,^[4] in which D is written as IƆ (500) and M is written as CIƆ (1,000).^[5] In this system, an extra Ɔ means 500, and multiple extra Ɔs are used to mean 5,000, 50,000 etc.

Numeral	IƆ	CIƆ	CIƆƆ	IƆƆ	CCIƆƆ	CCIƆƆƆ	CCIƆƆƆƆ	IƆƆƆ	CCCIƆƆƆ	CCCIƆƆƆƆ	CCCIƆƆƆƆƆ	CCCIƆƆƆƆƆƆ
Value	500	1,000	1,500	5,000	10,000	10,500	15,000	50,000	100,000	100,500	105,000	150,000

Vinculum

Another system is the vinculum, in which V, X, L, C, D and M are multiplied by 1,000 by adding an overline.

Numeral	V	X	L	C	D	M
Value	5,000	10,000	50,000	100,000	500,000	1,000,000

Usage

• In the Baltics and Russia, the days of the week are often written as Roman numerals, with I being Monday.
• When writing dates by hand, the month is sometimes written as a Roman numeral, especially for dates written in day-month-year sequence. For example: 26.XI.2014 or XI.26.2014 = 26 November 2014.
• Some video games use Roman numerals to indicate the game position in a series. The most famous examples are Final Fantasy games (Final Fantasy VII, Final Fantasy VIII, Final Fantasy X, etc...).
• When movies or books are published, the year of publication or year of copyright may be written as a Roman numeral.
• When people write about Monarchs or Popes, Patriarchs, or other leading figures, they are sometimes counted with Roman numbers, e.g. Queen Elizabeth II (of England), Pope John Paul II, Pope Benedict XVI, Patriarch Alexius II (of the Russian-Orthodox church)
• In France, the centuries are sometimes written with Roman numerals (example : "XXe siècle" meaning "20th century", XVIIIe siècle = "18th century", etc...).
• In Poland, roman numerals are used to show the month in dates and as a short method of writing ordinals (i.e. VI instead of 6th).
• Unicode has a code block called Number Forms, which also contains representations of Roman numerals, at the positions U+2160 to U+2188.

Related pages

• Arabic numerals
• Greek numerals

References

1. Gordon, Arthur E. (1982). Illustrated Introduction to Latin Epigraphy. Berkeley: University of California Press. ISBN 0-520-05079-7. Alphabetic symbols for larger numbers, such as Q for 500,000, have also been used to various degrees of standardization.
2. "The Mathematical Tourist : IIII versus IV on Clocks". Ivars Peterson. 4 August 2010. Retrieved 31 May 2019. Expressed as Roman numerals, the first twelve numbers are usually given as I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII. However, on many clock faces, when the numbers on the dial are in Roman numerals, IIII replaces IV.
3. C. W. Jones, ed., Opera Didascalica, vol. 123C in Corpus Christianorum, Series Latina.
4. "Merriam-Webster Unabridged Dictionary".
5. Asimov, Isaac (1966). Asimov On Numbers (PDF). Pocket Books, a division of Simon & Schuster, Inc. p. 12.

Other websites

• Roman Numerals (Totally Epic Guide) - Know The Romans
• Roman Numeral Converter