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# Roman Numeral

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### Roman Numeral

Roman numerals, the numeric system used in ancient Rome, employs combinations of letters from the Latin alphabet to signify values. The numbers 1 to 10 can be expressed in Roman numerals as follows:

I, II, III, IV, V, VI, VII, VIII, IX, X.

The Roman numeral system is a cousin of Etruscan numerals. Use of Roman numerals continued after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by more convenient Hindu-Arabic numerals; however this process was gradual, and the use of Roman numerals in some minor applications continues to this day.

 Template:Rn "2014" as a Roman numeral

Roman Numerals, as used today, are based on seven symbols:[1]

Symbol Value
1
5
10
50
100
500
1,000

Numbers are formed by combining symbols together and adding the values. So Template:Rn is two ones, i.e. 2, and Template:Rn is a ten and three ones, i.e. 13. There is no zero in this system, so 207, for example, is Template:Rn, using the symbols for two hundreds, a five and two ones. 1066 is Template:Rn, one thousand, fifty and ten, a five and a one.

Symbols are placed from left to right in order of value, starting with the largest. However, in a few specific cases,[2] to avoid four characters being repeated in succession (such as Template:Rn or Template:Rn) these can be reduced using subtractive notation as follows:[3][4]

• the numeral Template:Rn can be placed before Template:Rn and Template:Rn to make 4 units (Template:Rn) and 9 units (Template:Rn) respectively
• Template:Rn can be placed before Template:Rn and Template:Rn to make 40 (Template:Rn) and 90 (Template:Rn) respectively
• Template:Rn can be placed before Template:Rn and Template:Rn to make 400 (Template:Rn) and 900 (Template:Rn) according to the same pattern[5]

An example using the above rules would be 1904: this is composed of 1 (one thousand), 9 (nine hundreds), 0 (zero tens), and 4 (four units). To write the Roman numeral, each of the non-zero digits should be treated separately. Thus 1,000 = Template:Rn, 900 = Template:Rn, and 4 = Template:Rn. Therefore, 1904 is Template:Rn. This reflects typical modern usage rather than a universally accepted convention: historically Roman numerals were often written less consistently.[6]

A common exception to the practice of placing a smaller value before a larger in order to reduce the number of characters, is the use of Template:Rn instead of Template:Rn for 4, especially, although by no means exclusively, on clock faces; see below. Another example of the additive rather than subtractive form of numbers is the representation of 1910 in Roman Numerals on Admiralty Arch, London - where Template:Rn is used instead of Template:Rn for 900 (see illustration). In general, the "rules" about subtractively applied symbols are the most frequently "broken".

Below are some examples of the modern use of Roman Numerals.

## History

### Pre-Roman times and Ancient Rome

Although Roman numerals are now written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used Template:Rn, Λ, Template:Rn, ⋔, 8, ⊕, for Template:Rn, Template:Rn, Template:Rn, Template:Rn, Template:Rn, and Template:Rn, of which only Template:Rn and Template:Rn happened to be letters in their alphabet.

#### Hypotheses About the Origin of Roman Numerals

##### Tally sticks

One hypothesis is that the Etrusco-Roman numerals actually derive from notches on tally sticks, which continued to be used by Italian and Dalmatian shepherds into the 19th century.[8]

Thus, 'I' descends not from the letter 'I' but from a notch scored across the stick. Every fifth notch was double cut i.e. , , , , etc.), and every tenth was cross cut (Template:Rn), IIIIΛIIIIXIIIIΛIIIIXII..., much like European tally marks today. This produced a positional system: Eight on a counting stick was eight tallies, IIIIΛIII, or the eighth of a longer series of tallies; either way, it could be abbreviated ΛIII (or Template:Rn), as the existence of a Λ implies four prior notches. By extension, eighteen was the eighth tally after the first ten, which could be abbreviated Template:Rn, and so was XΛIII. Likewise, number four on the stick was the Template:Rn-notch that could be felt just before the cut of the Λ (Template:Rn), so it could be written as either Template:Rn or IΛ (Template:Rn). Thus the system was neither additive nor subtractive in its conception, but ordinal. When the tallies were transferred to writing, the marks were easily identified with the existing Roman letters Template:Rn, Template:Rn and Template:Rn. The tenth Template:Rn or Template:Rn along the stick received an extra stroke. Thus 50 was written variously as N, И, K, Ψ, , etc., but perhaps most often as a chicken-track shape like a superimposed Template:Rn and Template:Rn: . This had flattened to (an inverted T) by the time of Augustus, and soon thereafter became identified with the graphically similar letter Template:Rn. Likewise, 100 was variously Ж, , , H, or as any of the symbols for 50 above plus an extra stroke. The form Ж (that is, a superimposed Template:Rn and Template:Rn) came to predominate. It was written variously as >Template:Rn< or ƆIC, was then abbreviated to Ɔ or Template:Rn, with Template:Rn variant finally winning out because, as a letter, it stood for centum, Latin for "hundred".

The hundredth Template:Rn or Template:Rn was marked with a box or circle. Thus 500 was like a Ɔ superimposed on a or — that is, like a Þ with a cross bar,— becoming D or Ð by the time of Augustus, under the graphic influence of the letter D. It was later identified as the letter D; an alternative symbol for "thousand" was (I) or CIƆ, and half of a thousand or "five hundred" is the right half of the symbol, I) or IƆ, and this may have been converted into D.[9] This at least was the false etymology given to it later on.

Meanwhile, 1000 was a circled or boxed X: , , ⊕, and by Augustinian times was partially identified with the Greek letter Φ phi. Over time, the symbol changed to Ψ and . The latter symbol further evolved into , then , and eventually changed to Template:Rn under the influence of the Latin word mille "thousand".

##### Hand signals

Alfred Hooper has an alternative hypothesis for the origin of the Roman numeral system, for small numbers.[10] Hooper contends that the digits are related to hand signals. For example, the numbers Template:Rn, Template:Rn, Template:Rn, Template:Rn correspond to the number of fingers held up for another to see. Template:Rn, then represents that hand upright with fingers together and thumb apart. Numbers 6–10, are represented with two hands as follows (left hand, right hand) 6=(Template:Rn,Template:Rn), 7=(Template:Rn,Template:Rn), 8=(Template:Rn,Template:Rn), 9=(Template:Rn,Template:Rn), 10=(Template:Rn,Template:Rn) and Template:Rn results from either crossing of the thumbs, or holding both hands up in a cross.

##### Intermediate symbols deriving from few original symbols

A third hypothesis about the origins states that the basic ciphers were Template:Rn, Template:Rn, Template:Rn and Φ (or ⊕) and that the halfthrough ones derived from taking half of those (half a Template:Rn is Template:Rn, half a Template:Rn is Template:Rn and half a Φ/⊕ is Template:Rn).[11]

### Middle Ages and Renaissance

Minuscule (lower case) letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and lower-case versions of Roman numbers are now also commonly used: Template:Rn, Template:Rn, Template:Rn, Template:Rn, etc. In the Middle Ages, a j was sometimes substituted for the final Template:Rn of a number, such as iij for 3 or vij for 7. This j was considered a swash variant of Template:Rn. The use of a final j is still used in medical prescriptions to prevent tampering with or misinterpretation of a number after it is written.[12][13]

Subtractive Roman numerals (for instance IV for IIII and IX for VIIII) were introduced relatively late (the Romans themselves did without them) and for many years they were applied patchily and inconsistently.

A unique, more comprehensive shorthand for writing Roman numerals was developed during the Middle Ages, which today are called "medieval Roman numerals." This system used almost every other letter of the Roman alphabet to stand as abbreviations for more longhand numbers (usually those that consisted of repetitions of the same symbol). They are still listed today in most dictionaries, although through disfavor are primarily out of use.[14]

Modern
number
Medieval
abbreviation
Notes
5 A Resembles an upside-down V. Also said to equal 500.
6 Ϛ Either a ligature of VI, or the Greek letter stigma (Ϛ), having the same numerical value.[15]
7 S, Z Presumed abbreviation of septem, Latin for 7.
11 O Presumed abbreviation of (e.g.) onze, French for 11.
40 F Presumed abbreviation of English forty.
70 S Also could stand for 7, and has same etymology.
80 R
90 N Presumed abbreviation of nonaginta, Latin for 90.
150 Y Possibly derived from the lowercase y's shape.
151 K This unusual abbreviation's origin is unknown; it has also been said to stand for 250.[16]
160 T Possibly derived from Greek tetra, as 4 x 40 = 160.
200 H
250 E
300 B
400 P, G
500 Q Redundant with D, abbreviation for quingenti, Latin for 500.
2000 Z

Chronograms, messages with a numbers encoded into them, were popular during the Renaissance era. The chronogram would be a phrase containing the letters Template:Rn, Template:Rn, Template:Rn, Template:Rn, Template:Rn, Template:Rn, and Template:Rn. By putting these letters together, the reader would obtain a number, usually indicating a particular year.

### Modern usage

By the 11th century Hindu–Arabic numerals had been introduced into Europe from al-Andalus, by way of Arab traders and arithmetic treatises. Roman numerals however proved very persistent, remaining in common use in the "west" well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been by abacus). Their eventual almost complete replacement by their more convenient "Arabic" equivalents happened quite gradually, in fact Roman numerals are still used today in several niche contexts. A few examples of their current use are:

• Names of monarchs and Popes, e.g. Elizabeth II of the United Kingdom, Pope Benedict XVI. These are referred to as monarchical ordinals; e.g. "Template:Rn" is pronounced "the second". This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England only during the reign of Henry VIII. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor.
• Generational suffixes, particularly seen in the USA, for people who share the same name across generations, for example William Howard Taft IV.
• The year of production of films, television shows and other works of art within the work itself, which according to BBC News was originally done "in an attempt to disguise the age of films or television programmes."[17] Outside reference to the work will use regular Hindu–Arabic numerals.
• Hour marks on timepieces. In this context 4 is usually written Template:Rn.
• The year of construction on building faces and cornerstones.
• Page numbering of prefaces and introductions of books.
• Book volume and chapter numbers.
• Sequels of movies, video games, and other works.
• Outlines, which use numbers to show hierarchical relationships.
• Occurrences of a recurring grand event, for instance:

In astronomy, the natural satellites or "moons" of the planets are traditionally designated by capital Roman numerals.

In chemistry, Roman numerals are often used to denote the groups of the periodic table. They are also used in the IUPAC nomenclature of inorganic chemistry, for the oxidation number of cations which can take on several different positive charges. They are also used for naming phases of polymorphic crystals, such as ice.

In earthquake seismology, Roman numerals are used to designate degrees of the Mercalli intensity scale.

In music theory, the diatonic functions are identified using Roman numerals. See: Roman numeral analysis.

In musical performance practice, individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings.

In photography, Roman numerals (with zero) are used to denote varying levels of brightness when using the Zone System.

In Tarot, Roman numerals (with zero) are also used to denote the cards of the Major Arcana.

#### Modern non-English-speaking usage

Capital Roman numerals are used to denote centuries (e.g., Template:Rn refers to the eighteenth century) in Bulgarian, Croatian, French, Hungarian, Italian, Polish, Portuguese, Romanian, Russian, Serbian, Georgian, and Spanish languages. This use has largely been replaced by Hindu-Arabic numerals (e.g. 18.) in Czech and Slovak languages.

In Central Europe, Italy, Russia, and in Bulgarian, Croatian, Portuguese, Romanian, and Serbian languages, mixed Roman and Hindu-Arabic numerals are used to record dates (usually on tombstones, but also elsewhere, such as in formal letters and official documents). The month is written in Roman numerals while the day is in Hindu-Arabic numerals: 14.  Template:Rn. 1789 is 14 June 1789. This use has largely been replaced by Hindu-Arabic numerals (e.g. 14.06.1789) in Czech, Slovene, Slovak, Polish, Portuguese and Russian languages.

In the Baltic and Eastern Europe nations, Roman numerals are used to represent the days of the week in hours-of-operation signs displayed in windows or on doors of businesses, and also sometimes in railway and bus timetables. Monday is represented by Template:Rn, which is the initial day of the week. Sunday is represented by Template:Rn, which is the final day of the week. The hours of operation signs are tables composed of two columns where the left column is the day of the week in Roman numerals and the right column is a range of hours of operation from starting time to closing time. The following example hours-of-operation table would be for a business whose hours of operation are 9:30 AM to 5:30 PM on Mondays, Wednesdays, and Thursdays; 9:30 AM to 7:00 PM on Tuesdays and Fridays; and 9:30 AM to 1:00 PM on Saturdays; and which is closed on Sundays.

 Template:Rn 9:30–17:30 Template:Rn 9:30–19:00 Template:Rn 9:30–17:30 Template:Rn 9:30–17:30 Template:Rn 9:30–19:00 Template:Rn 9:30–13:00 Template:Rn —

In Rome, Greece, Romania, and other European countries to a lesser extent, Roman numerals are used for floor numbering. Likewise, apartments in central Amsterdam are indicated as 138-Template:Rn, with both an Hindu-Arabic numeral (number of the block or house) and a Roman numeral (floor number). The apartment on the ground floor is indicated as '138-huis'.

In Italy, where roads outside built-up areas have kilometer signs, major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from I to IX for the smaller intervals. The sign IX | 17 thus marks km. 17·900.

## Special values

### Zero

The number zero does not have its own Roman numeral, but the word nulla (the Latin word meaning "none") was used by medieval computists in lieu of 0. Dionysius Exiguus was known to use nulla alongside Roman numerals in 525.[18][19] About 725, Bede or one of his colleagues used the letter N, the initial of nulla, in a table of epacts, all written in Roman numerals.[20]

### Fractions

Though the Romans used a decimal system for whole numbers, reflecting how they counted in Latin, they used a duodecimal system for fractions, because the divisibility of twelve (12 = 3 × 2 × 2) makes it easier to handle the common fractions of 1/3 and 1/4 than does a system based on ten (10 = 2 × 5). On coins, many of which had values that were duodecimal fractions of the unit as, they used a tally-like notational system based on twelfths and halves. A dot (•) indicated an uncia "twelfth", the source of the English words inch and ounce; dots were repeated for fractions up to five twelfths. Six twelfths (one half) was abbreviated as the letter S for semis "half". Uncia dots were added to S for fractions from seven to eleven twelfths, just as tallies were added to Template:Rn for whole numbers from six to nine.[21]

Each of these fractions had a name, which was also the name of the corresponding coin:

Fraction Roman Numeral Name (nominative and genitive) Meaning
1/12 uncia, unciae "ounce"
2/12 = 1/6 •• or : sextans, sextantis "sixth"
4/12 = 1/3 •••• or :: triens, trientis "third"
5/12 ••••• or :·: quincunx, quincuncis "five-ounce" (quinque unciaequincunx)
6/12 = 1/2 S semis, semissis "half"
7/12 S• septunx, septuncis "seven-ounce" (septem unciaeseptunx)
8/12 = 2/3 S•• or S: bes, bessis "twice" (as in "twice a third")
9/12 = 3/4 S••• or S dodrans, dodrantis
or nonuncium, nonuncii
or "ninth ounce" (nona uncianonuncium)
10/12 = 5/6 S•••• or S:: dextans, dextantis
or decunx, decuncis
"less a sixth" (de-sextansdextans)
or "ten ounces" (decem unciaedecunx)
11/12 S••••• or S:·: deunx, deuncis "less an ounce" (de-unciadeunx)
12/12 = 1 I as, assis "unit"

The arrangement of the dots was variable and not necessarily linear. Five dots arranged like (:·:) (as on the face of a die) 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.

Other Roman fractions include the following:

• 1/8 sescuncia, sescunciae (from sesqui- + uncia, i.e. 1½ uncias), represented by a sequence of the symbols for the semuncia and the uncia.
• 1/24 semuncia, semunciae (from semi- + uncia, i.e. ½ uncia), represented by several variant glyphs deriving from the shape of the Greek letter Sigma (Σ), one variant resembling the pound sign (£) without the horizontal line(s) and another resembling the Cyrillic letter (Є).
• 1/36 binae sextulae, binarum sextularum ("two sextulas") or duella, duellae, represented by (ƧƧ), a sequence of two reversed Ss.
• 1/48 sicilicus, sicilici, represented by (Ɔ), a reversed C.
• 1/72 sextula, sextulae (1/6 of an uncia), represented by (Ƨ), a reversed S.
• 1/144 = 12−2 dimidia sextula, dimidiae sextulae ("half a sextula"), represented by (ƻ), a reversed S crossed by a horizontal line.
• 1/288 scripulum, scripuli (a scruple), represented by the symbol ().
• 1/1728 = 12−3 siliqua, siliquae, represented by a symbol resembling closing guillemets (»).

### Large numbers

In the Middle Ages, a horizontal line was used above a particular numeral to represent one thousand times that numeral, and additional vertical lines on both sides of the numeral to denote one hundred times the number, as in these examples:

The same overline was also used with a different meaning, to clarify that the characters were numerals. Sometimes both underline and overline were used, e. g. Template:Rn, and in certain (serif) typefaces, particularly Times New Roman, the capital letters when used without spaces simulates the appearance of the under/over bar, e.g. Template:Rn.

Sometimes 500, usually D, was written as original |Ɔ, while 1,000, usually M, was written as original C|Ɔ. This is a system of encasing numbers to denote thousands (imagine the Template:Rns and Template:Rns as parentheses), which has its origins in Etruscan numeral usage. The Template:Rn and Template:Rn used to represent 500 and 1,000 were most likely derived from and CIƆ, respectively, and subsequently influenced by assumed abbreviations.

An extra Ɔ denoted 500, and multiple extra Ɔs are used to denote 5,000, 50,000, etc. For example:

Base number 1 extra Ɔ 2 extra Ɔs 3 extra Ɔs CIƆ = 1,000 CCIƆƆ = 10,000 CCCIƆƆƆ = 100,000 IƆ = 500 CIƆƆ = 1,500 CCIƆƆƆ = 10,500 CCCIƆƆƆƆ = 100,500 IƆƆ = 5,000 CCIƆƆƆƆ = 15,000 CCCIƆƆƆƆƆ = 105,000 IƆƆƆ = 50,000 CCCIƆƆƆƆƆƆ = 150,000

Sometimes CIƆ was reduced to for 1,000. John Wallis is often credited for introducing the symbol for infinity (modern ), and one conjecture is that he based it on this usage, since 1,000 was hyperbolically used to represent very large numbers. Similarly, IƆƆ for 5,000 was reduced to ; CCIƆƆ for 10,000 to ; IƆƆƆ for 50,000 to ; and CCCIƆƆƆ for 100,000 to .

## "IIII" on clocks

Clock faces that are labeled using Roman numerals conventionally show Template:Rn for four o'clock and Template:Rn for nine o'clock, using the subtractive principle in one case and not the other. There are many suggested explanations for this:

• Many clocks use Template:Rn because that was the tradition established by the earliest surviving clock, which is the Wells Cathedral clock built between 1386 and 1392. It used Template:Rn because that was the typical method used to denote 4 in contemporary manuscripts (as iiij or iiii). That clock had an asymmetrical 24-hour dial and used Hindu-Arabic numerals for a minute dial and a moon dial, so theories depending on a symmetrical 12-hour clock face do not apply.[22]
• Perhaps Template:Rn was avoided because Template:Rn represented the Roman god Jupiter, whose Latin name, IVPPITER, begins with IV. This suggestion has been attributed to Isaac Asimov.[23]
• Louis XIV, king of France, who preferred Template:Rn over Template:Rn, ordered his clockmakers to produce clocks with Template:Rn and not Template:Rn, and thus it has remained.[24]
• Using standard numerals, two sets of figures would be similar and therefore confusable by children and others unused to reading clockfaces: Template:Rn and Template:Rn are similar, as are Template:Rn and Template:Rn. As the first pair are upside down on the face, an additional level of confusion would be introduced—a confusion avoided by using Template:Rn to provide a clear distinction from Template:Rn.
• The four-character form Template:Rn creates a visual symmetry with the Template:Rn on the other side, which the two-character Template:Rn would not.
• With Template:Rn, the number of symbols on the clock totals twenty Template:Rns, four Template:Rns, and four Template:Rns,[25] so clock makers need only a single mould with a Template:Rn, five Template:Rns, and an Template:Rn in order to make the correct number of numerals for their clocks: Template:Rn. This is cast four times for each clock and the twelve required numerals are separated:
• Template:Rn
• Template:Rn
• Template:Rn
• Template:Rn
The Template:Rn and one of the Template:Rns are rotated 180° to form Template:Rn and Template:Rn. The alternative with Template:Rn uses seventeen Template:Rns, five Template:Rns, and four Template:Rns, requiring the clock maker to have several different patterns.
• Only the Template:Rn symbol would be seen in the first four hours of the clock, the Template:Rn symbol would only appear in the next four hours, and the Template:Rn symbol only in the last four hours. This would add to the clock's radial symmetry.

A well-known exception to the conventional use of Template:Rn on clock faces with Roman numerals is the clock in Elizabeth Tower (often erroneously called "Big Ben") on the Palace of Westminster in London. It uses Template:Rn for four o'clock.