Roman numerals

Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each with a fixed integer value. The modern style uses only these seven:


1	5	10	50	100	500	1000

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process was gradual, and the use of Roman numerals persisted in various places, including on clock faces. For instance, on the clock of Big Ben, the hours from 1 to 12 are written as:
The notations and can be read as "one less than five" and "one less than ten", although there is a tradition favouring the representation of "4" as "" on Roman numeral clocks.
Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of films and television programmes., signifying "a thousand, and a hundred less than another thousand", means 1900, so 1912 is written. For the years of the current century, indicates 2000; this year is .

Description

Roman numerals use different symbols for each power of ten, and there is no zero symbol, in contrast with the place value notation of Arabic numerals.
This allows some flexibility in notation, and there has never been an official or universally accepted standard for Roman numerals. Usage varied greatly in ancient Rome and became thoroughly chaotic in medieval times. The more recent restoration of a largely "classical" notation has gained popularity among some, while variant forms are used by some modern writers as seeking more "flexibility". Roman numerals may be considered legally binding expressions of a number, as in U.S. copyright law before the Berne Convention Implementation Act of 1988.

Standard form

The following table displays how Roman numerals are usually written in modern times:

	Thousands	Hundreds	Tens	Units
1
2
3
4
5
6
7
8
9

The numerals for 4 and 9 are written using subtractive notation, where the smaller symbol is subtracted from the larger one, instead of and. Subtractive notation is also used for 40, 90, 400 and 900. These are the only subtractive forms in standard use.
A number containing two or more decimal digits is built by appending the Roman numeral equivalent for each, from highest to lowest, as in the following examples:

39 = + = '.
246 = + + = '.
789 = + + = '.
2,421 = + + + = '.

Any missing place is omitted, as in Latin speech:

160 = + = '
207 = + = '
1,009 = + = '
1,066 = + + = '

The largest number that can be represented in this manner is 3,999, but this is sufficient for the values for which Roman numerals are commonly used today, such as year numbers:

1776 = + + + = '.
1918 = + + + = '
1944 = + + + = '
= '

For larger numbers : Both before and after the introduction of Arabic numerals in the West, from ancient times through medieval and modern, users of Roman numerals have used various means to write larger numbers.

Other forms

Forms exist that vary in one way or another from the general standard represented above.

Other additive forms

While subtractive notation for 4, 40, and 400 has been the usual form since Roman times, additive notation to represent these numbers very frequently continued to be used, including in compound numbers like 24, 74, and 490. The additive forms for 9, 90, and 900 have also been used, although less often.
The two conventions could be mixed in the same document or inscription, even in the same numeral. For example, on the numbered gates to the Colosseum, is systematically used instead of, but subtractive notation is used for ; consequently, gate 44 is labelled.
Especially on tombstones and other funerary inscriptions, 5 and 50 have been occasionally written and instead of and, and there are instances such as and rather than or.
Modern clock faces that use Roman numerals still very often use for four o'clock but for nine o'clock, a practice that goes back to very early clocks such as the Wells Cathedral clock of the late 14th century. However, this is far from universal: for example, the clock on the Palace of Westminster tower uses a subtractive for 4 o'clock.
Several monumental inscriptions created in the early 20th century use variant forms for "1900". These vary from for 1910 as seen on Admiralty Arch, London, to the more unusual, if not unique for 1903, on the north entrance to the Saint Louis Art Museum.

Other subtractive forms

There are numerous historical examples of being used for 8; for example, was used by officers of the XVIII Roman Legion to write their number. The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius. On the publicly displayed official Roman calendars known as Fasti, is used for the 18 days to the next Kalends, and for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the Fasti Antiates Maiores.
There are historical examples of other subtractive forms: for 17, for 18, for 97, for 98, and for 99. A possible explanation is that the word for 18 in Latin is duodevigintiliterally "two from twenty"⁠while 98 is duodecentum and 99 is undecentum. However, the explanation does not seem to apply to and, since the Latin words for 17 and 97 were septendecim and nonaginta septem, respectively.
The function in Microsoft Excel supports multiple subtraction modes depending on the "" setting. For example, the number "499" can be rendered as ++), +), +) or . The relevant Microsoft help page offers no explanation for this function other than to describe its output as "more concise".

Non-standard variants

There are also historical examples of other additive and multiplicative forms, and forms which seem to reflect spoken phrases. Some of these variants may have been regarded as errors even by contemporaries.

was how people associated with the XXII Roman Legion used to write their number. The practice may have been due to a common way to say "twenty-second" in Latin, namely duo et vicesima rather than the "regular" vicesima secunda. Apparently, at least one ancient stonecutter mistakenly thought that the of "22nd Legion" stood for 18, and "corrected" it to.
Other numerals that do not fit the usual patterns – such as for 45, instead of the usual — may be due to scribal errors, or the writer's lack of familiarity with the system, rather than being genuine variant usage.
Zero

As a non-positional numeral system, Roman numerals have no "place-keeping" zeros. Furthermore, the system as used by the Romans lacked a numeral for the number zero itself. The word was used to represent 0, although the earliest attested instances are medieval. For instance Dionysius Exiguus used nulla alongside Roman numerals in a manuscript from 525 AD. About 725, Bede or one of his colleagues used the letter, the initial of nulla or of for 0, in a table of epacts, all written in Roman numerals.
The use of to indicate "none" long survived in the historic apothecaries' system of measurement: used well into the 20th century to designate quantities in pharmaceutical prescriptions.
In later times, the Arabic numeral "0" has been used as a zero to open enumerations with Roman numbers. Examples include the 24-hour Shepherd Gate Clock from 1852 and tarot packs such as the 15th-century Sola Busca and the 20th century Rider–Waite packs.

Fractions

The base "Roman fraction" is, indicating. The use of is attested in some ancient inscriptions and in the now rare apothecaries' system : but while Roman numerals for whole numbers are essentially decimal, does not correspond to, as one might expect, but.
The Romans used a duodecimal rather than a decimal system for fractions, as the divisibility of twelve makes it easier to handle the common fractions of and than does a system based on ten. Notation for fractions other than is mainly found on surviving Roman coins, many of which had values that were duodecimal fractions of the unit As. Fractions less than are indicated by a dot for each uncia "twelfth", the source of the English words inch and ounce; dots are repeated for fractions up to five twelfths. Six twelfths, is for semis "half". Uncia dots were added to for fractions from seven to eleven twelfths, just as tallies were added to for whole numbers from six to nine. The arrangement of the dots was variable and not necessarily linear. Five dots arranged like are known as a quincunx, from the name of the Roman fraction/coin. The Latin words sextans and quadrans are the source of the English words sextant and quadrant.
Each fraction from to had a name in Roman times; these corresponded to the names of the related coins:

Fraction	Roman numeral	Name	Meaning
	·	Uncia	"Ounce"
=	·· or :	Sextans	"Sixth"
=	··· or ∴	Quadrans, quadrantis	"Quarter"
=	···· or ∷	Triens, trientis	"Third"
	····· or ⁙	Quincunx	"Five-ounce"
=		Semis, semissis	"Half"
	·	Septunx, septuncis	"Seven-ounce"
=	·· or :	Bes	"Twice"
=	··· or ∴	Dodrans, dodrantis or nonuncium, nonuncii	"Less a quarter" or "ninth ounce"
=	···· or ∷	Dextans, dextantis or decunx, decuncis	"Less a sixth" or "ten ounces"
	····· or ⁙	Deunx, deuncis	"Less an ounce"
= 1		As	"Unit"

Other Roman fractional notations included the following:

Fraction	Roman numeral	Name	Meaning
=12⁻³		Siliqua, siliquae
		Scripulum, scripuli	"scruple"
=12⁻²		Dimidia sextula, dimidiae sextulae	"half a sextula"
		Sextula, sextulae	" of an uncia"
		Sicilicus, sicilici
		Binae sextulae, binarum sextularum	"two sextulas"
	or or	Semuncia, semunciae	" uncia"
	· or · or ·	Sescuncia, sescunciae	" uncias"

Fractions could also be indicated with a slash through the last letter in a numeral, which subtracted the number by an amount less than one.