Appendix:Roman numerals

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Roman numerals

The Roman numerals are certain Latin script letters that may be used to represent numbers.

Overview

The Roman numerals are a numerical system composed of seven Latin letters. They are, in this order, from lower to higher: I, V, X, L, C, D and M.

Each said symbol represents a different number, in this order: one, five, ten, fifty, one hundred, five hundred and one thousand. There is no symbol to represent a null quantity. It is possible to represent numbers different from these, through combinations of letters, such as XIII, MMMCCV and MCMXCIX. A combination is made of smaller groups of letters, each group in increasing order from right to left. The whole combination represents a number.

When a letter is worth a power of ten, and this letter is followed by a letter which is worth ten or five times the first, the value of this group is equal to the second letter subtracted by the first letter. Therefore, IV represents four, IX represents nine, XC represents ninety and CM represents nine hundred. By extension, XCIX represents ninety nine.

The numerical values of the symbols I, X, C and M are added if written up to three times together. Therefore, the number III represents three and the number MM represents two thousand.

A macron multiplies the value of a group of letters by one thousand. Therefore, IV represents four thousand.

Usage notes

The Arabic numerals are widely known and widely used in many languages, including English.

Roman numerals are essentially known as uppercase letters: I, V, X, L, C, D and M. However, it is possible to use lowercase letters: i, v, x, l, c, d and m. Lowercase Roman numerals are often seen as page numbers for materials prefatory to the beginning of the main body of a work.

There are additional characters from Unicode, specifically designated as Roman numerals. Ⅰ, Ⅱ, Ⅲ, Ⅳ, Ⅴ, Ⅵ, Ⅶ, Ⅷ, Ⅹ, Ⅺ, ⅺ, Ⅼ, Ⅽ, Ⅾ, Ⅿ, ⅰ, ⅱ, ⅲ, ⅳ, ⅴ, ⅵ, ⅶ, ⅷ, ⅸ, ⅹ, Ⅻ, ⅻ, ⅼ, ⅽ, ⅾ and ⅿ, ↀ, ↁ, ↂ, Ↄ, ↄ, ↅ, ↆ, ↇ, ↈ.

List of numbers

For information about number names in English, see Appendix:English numerals.

English meaning	Arabic numerals	Roman numerals	Roman numerals Unicode single characters
zero	0	N (nūlla / nihil, rare, used by Bede)
one	1	I, i	Ⅰ, ⅰ
two	2	II, ii	Ⅱ, ⅱ
three	3	III, iii	Ⅲ, ⅲ
four	4	IV, iv	Ⅳ, ⅳ
five	5	V, v	Ⅴ, ⅴ
six	6	VI, vi	Ⅵ, ⅵ
seven	7	VII, vii	Ⅶ, ⅶ
eight	8	VIII, viii	Ⅷ, ⅷ
nine	9	IX, ix	Ⅸ, ⅸ
ten	10	X, x	Ⅹ, ⅹ
eleven	11	XI, xi	Ⅺ, ⅺ
twelve	12	XII, xii	Ⅻ, ⅻ
fifty	50	L, l	Ⅼ, ⅼ
one hundred	100	C, c	Ⅽ, ⅽ
five hundred	500	D, d	Ⅾ, ⅾ
one thousand	1,000	M, m	ↀ, Ⅿ, ⅿ
five thousand	5,000	V	ↁ
ten thousand	10,000	X	ↂ
fifty thousand	50,000	L	ↇ
one hundred thousand	100,000	C	ↈ

Fractions

While less known, Roman numerals expressing fractions existed. For twelfths, named uncia (“ounce”), a middot (·) was used, which could have been arranged in a horizontal line or in the same ways as the pips of a modern dice. Half was written with the letter S, short for semis (“half”). Each twelfth had its own name:

${\frac {1}{12}}$ : uncia
${\frac {2}{12}}={\frac {1}{6}}$ : sextans (“sixth-part”)
${\frac {3}{12}}={\frac {1}{4}}$ : quadrans (“fourth-part”)
${\frac {4}{12}}={\frac {1}{3}}$ : triens (“third-part”)
${\frac {5}{12}}$ : quincunx (“five-ounces”)
${\frac {6}{12}}={\frac {1}{2}}$ : semis
${\frac {7}{12}}$ : septunx (“seven-ounces”)
${\frac {8}{12}}={\frac {2}{3}}$ : bes (“twice [a third]”)
${\frac {9}{12}}={\frac {3}{4}}$ : dodrans (“less a quarter”)
${\frac {10}{12}}={\frac {5}{6}}$ : dextans (“less a sixth”)
${\frac {11}{12}}$ : deunx (“less an ounce”)

Smaller fractions did exist, such as the sescuncia (“one-and-a-half ounces”) (Σ·, ${\frac {1}{8}}$ ), the semuncia (“half-ounce”) (Σ, ${\frac {1}{24}}$ ), the sicilicus (Ↄ, ${\frac {1}{48}}$ ), the sextula (“sixth [of an ounce]”) (𐆓, ${\frac {1}{72}}$ ), the dimidia sextula (𐆔, ${\frac {1}{144}}$ ), the scrupulum (“scruple”) (℈, ${\frac {1}{288}}$ ) and the siliqua (𐆕, ${\frac {1}{1728}}$ ).

The word semis (“half”), when coupled with an ordinary numeral, would be understood by the Romans to mean half-less from that number. The most commonly known example is the word sestertium (“sesterce”), whose symbol HS was derived from an earlier IIS, and whose etymology is from semis (“half”) tertium (“third”), which translates to two and a half.