Roman numerals
Numeral systems 

Hindu–Arabic numeral system 
East Asian 
Alphabetic 
Former 
Positional systems by base 
Nonstandard positional numeral systems 
List of numeral systems 
Roman numerals are a numeric system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Modern usage employs seven symbols, each with a fixed integer value:^{[1]}
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 in most contexts by the more convenient Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day.
One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as:
 I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII
The notations IV and IX can be read as "one before five" (4) and "one before ten" (9). On most Roman numeral clock faces, however, 4 is traditionally written IIII.
Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. MCM, signifying "a thousand, and a hundred less than another thousand", means 1900, so 1912 is written MCMXII. For this century, MM indicates 2000. Thus the current year is MMXIX.
Contents
Description
There is not, and never has been an "official", "binding", or universally accepted standard for Roman numerals. Usage in ancient Rome varied greatly and remained somewhat inconsistent in medieval times and later.^{[2]} The "rules" of the system as it is now applied have been established only by general usage over the centuries.
Roman numerals are essentially a decimal or "base 10" number system. Powers of ten – thousands, hundreds, tens and units – are written separately, from left to right, in that order. Different symbols are used for each power of ten, but a common pattern is used for each of them.
The underlying form of this pattern employs the symbols I and V (representing 1 and 5) as simple tally marks, to build the numbers from 1 to 9. Each marker for 1 (I) adds a unit value up to 5 (V), and is then added to (V) to make the numbers from 6 to 9. Finally the unit symbol for the next power completes a "finger count" sequence:
 I, II, III, IIII, V, VI, VII, VIII, VIIII, X.
At some early time the Romans started to use the abbreviated forms IV ("one less than 5") and IX ("one less than 10") for IIII and VIIII, a convention that has been widely, although not universally, used ever since.^{[a]} This convention is called "subtractive" notation,^{[3]}as opposed to the purely "additive" notation of IIII and VIIII.^{[4]} Thus the numbers from 1 to 10 are generally written as
 I, II, III, IV, V, VI, VII, VIII, IX, X.^{[5]}
The multiples of 10, from 10 to 100, are written according to the same pattern, with X, L, and C taking the place of I, V, and X
 X, XX, XXX, XL, L, LX, LXX, LXXX, XC, C.
Note that 40 is usually written XL ("10 less than 50") rather than XXXX, and 90 as XC ("10 less than 100") rather than LXXXX.
Similarly, the multiples of 100, 100 to 1000, are written as
 C, CC, CCC, CD, D, DC, DCC, DCCC, CM, M.
where CD is to be read as "100 less than 500" (that is, 400), and CM as "100 less than 1000" (that is, 900).
Since the system has no standard symbols for 5,000 and 10,000, the only multiples of 1000 that can be represented in subtractive notation are 1,000, 2,000 and 3,000:
 M, MM, MMM.
A number containing several decimal places is represented, as in the Arabic system, by writing its poweroften parts — thousands, hundreds, tens and units — in sequence, from left to right, in descending order of value. For example:
 39 = 30 + 9 = XXX + IX = XXXIX.
 246 = 200 + 40 + 6 = CC + XL + VI = CCXLVI.
 789 = 700 + 80 + 9 = DCC + LXXX + IX = DCCLXXXIX.
 2421 = 2000 + 400 + 20 + 1 = MM + CD + XX +I = MMCDXXI.
Any missing place (represented by a zero in the Arabic equivalent) is omitted, as in Latin (and English) speech:
 160 = 100 + 60 = C + LX = CLX ("one hundred and sixty").
 207 = 200 + 7 = CC + VII = CCVII ("two hundred and seven").
 1009 = 1,000 + 9 = M + IX = MIX ("A thousand and nine")
 1066 = 1,000 + 60 + 6 = M + LX + VI = MLXVI ("a thousand and sixty six").^{[6]}^{[7]}
Roman numerals for large numbers are nowadays seen mainly in the form of year numbers, as in these examples:
 1776 (M+DCC+LXX+VI) = MDCCLXXVI (the date written on the book held by the Statue of Liberty).^{[8]}
 1954 (M+CM+L+IV) = MCMLIV (as in the trailer for the movie The Last Time I Saw Paris)^{[9]}
 2014 (MM+X+IV) = MMXIV (the year of the games of the XXII (22nd) Olympic Winter Games (in Sochi)
 The current year (2019) is MMXIX.
The largest number that can be represented in this notation is 3,999 (MMMCMXCIX).^{[b]}
Use of additive notation
While subtractive notation for multiples of 4 (IV, XL, CD) have been prevalent since Roman times, additive notation (IIII, XXXX,^{[10]} CCCC^{[10]}, and MMMM^{[11]}) continued to be used, including in compound numbers like XXIIII,^{[12]} LXXIIII,^{[13]} and CCCCLXXXX.^{[11]} The additive forms for 9, 90, and 900 (VIIII,^{[10]}LXXXX,^{[14]} and DCCCC,^{[15]}) have also been used, although less frequently.
The two conventions could be mixed in the same document or inscription, even in the same numeral. On the numbered gates to the colosseum, for instance, IIII is systematically used instead of IV, but subtractive notation is used for other digits; so that gate 44 is labelled XLIIII.^{[16]} Isaac Asimov speculates that the use of "IV", as the initial letters of "IVPITER" (the classical Latin spelling of the name of the Roman god Jupiter) may have been felt to have been impious in this context.^{[17]}
Modern clock faces that use Roman numerals still usually employ IIII for four o'clock but IX for nine o'clock, a practice that goes back to very early clocks such as the Wells Cathedral clock of the late 14th century.^{[18]}^{[19]}^{[20]} However, this is far from universal: for example, the clock on the Palace of Westminster tower, "Big Ben", uses a subtractive IV for 4 o'clock.^{[19]}
Several monumental inscriptions created in the early 20th century use variant forms for "1900" (usually written MCM). These vary from MDCCCCX  a classical use of additive notation for MCMX (1910), as seen on Admiralty Arch, London, to the more unusual, if not unique MDCDIII for MCMIII (1903),^{[c]} on the north entrance to the Saint Louis Art Museum .^{[21]}
Rare variants
While the subtractive and additive notations seem to have been used interchangibly through history, some other Roman numerals have been occasionally observed that do not fit either system. Some of these variants do not seem to have been used outside specific contexts, and may have been regarded as errors even by contemporaries.
 IIXX 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 "twentysecond" in Latin, namely duo et vice(n)sima (literally "two and twentieth") rather than the "regular" vice(n)sima secunda ("twentieth second").^{[22]}.
 Likewise, XIIX was used by officers of the XVIII Roman Legion to write their number.^{[23]}^{[24]} The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius (~45 BC – 9 AD). There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than XVIII.
 On the other hand, "irregular" subtractives like IIIXX for 17^{[25]} and IIXX for 18^{[26]} were occasionally used in more modern times. A possible explanation is that the word for 18 in Latin was duodeviginti, literally "two from twenty". Similarly, the word for 19 was undeviginti ("one from twenty"). These ways of saying 18 and 19 have been attributed to influence from the Etruscans, who would say "three from twenty" for 17, "two from twenty" for 18, and "one from twenty" for 19.^{[27]} Apparently, at least one ancient stonecutter mistakenly thought that the IIXX of "22nd Legion" stood for 18, and "corrected" it to XVIII.^{[22]} However, the explanation does not seem to apply to IIIXX, since the Latin word for 17 was septendecim ("seven ten"), and for "17th" was septimus decimus ("seventh tenth").
 Likewise, 98 and 99 are occasionally rendered as IIC and IC instead of XCVIII and XCIX,^{[28]} perhaps reflecting the Latin words duodecentum and undecentum ("two/one from a hundred") for those numbers.
 Sometimes 5 and 50 have been written IIIII and XXXXX instead of V and L; and there are instances such as IIIIII and XXXXXX rather than VI or LX.^{[29]}^{[30]}
 There is at least one example (see illustration) of a year number written as two Roman numerals corresponding to the spoken English "sixteen thirteen", or XVIXIII for 1613. This, and other nonstandard numerals other than those described above — such as VXL for 45, instead of the standard XLV — may be due to error rather than being genuine variant usage.
 Not all combinations of symbols used in Roman numerals are intended to be taken numerically. For example "XXX" and "XL" have other connotations besides their values as Roman numerals, while "IXL" more often than not means "I excel", and is in any case not an unambiguous Roman numeral.
Origin of the system
Due to the scarcity of surviving examples, the origins of the system are obscure and there are several competing theories, largely conjectural.
The system seems to have developed gradually in the area around Rome, possibly before the foundation of the city (sometime between 850 and 750 BC). At the time, the region was inhabited by diverse populations speaking distinct languages. These included several Italic branches of the IndoEuropean family, as well as the Etruscans, a people of unknown origin who spoke an isolated language.
By the time, the Mediterranean east of Italy had already known several advanced literate civilizations, such as the Ancient Egypt, Phoenicia, Minos, Mycenae and several others in Asia Minor and the Levant. These civilizations influenced the Romans directly or indirectly, such as in the alphabet (via the Etruscans).
The most obvious similarity to those number systems is the use of 10 as the base, instead of 60 (as had been in use in Mesopotamia for a millennium) or 20 (as was used by the Olmec and Mayans in PreColumbian America. That choice however seems to have been made through most of Eurasia, including in India and China.
The old Egyptian system had a different nonphonetic symbol for each power of ten (so that, like the Romans, they did not need a symbol for zero). However, it repeated that symbol up to nine times to get the digits 1 to 9. They had no separate symbols for 5, 50, etc. The symbol for 1 was a vertical stroke, and that for 10 was an inverted "U"; but higher powers were denoted by figurative hieroglyphs.
The use of separate symbols for 5, 50, 500 etc. is a feature of the old Greek numbers system, the Attic numerals. However, the symbols of the latter were letters of the Greek alphabet taken from the names of those numbers ("Π" from ΠΕΝΤΕ for 5), "Δ" from ΔΕΚΑ for 10, "Η" from ΗΕΚΑΤΟΝ for 100, etc.; or modified "Π" like "𐅄" for 50 an "𐅅" for 500.
The Attic numerals were latter replaced in Greece by classical Greek system, that also used letters to denote numbers, like the Romans, and a different set of letters for each power of 10. However, the similarities ended there. The Greek system (apparently borrowed from the late Egyptian Hieratic system) uses the first 9 letters of the alphabet to encode the units 1 to 9, then the next 9 letters for the tens 10 to 90, and similarly for the hundreds.
Etruscan numerals
The Etruscans were the most advanced civilization in the region, and the ancient Romans themselves admitted that they inherited much of their knowledge and customs from them. Besides the Etruscans, the original population of Rome was allegedly drawn mainly from the Latins and the Sabinians, who were only two among the several Italic groups.
The Roman numerals, in particular, are directly derived from the Etruscan number symbols: "𐌠", "𐌡", "𐌢", "𐌣", and "𐌟" for 1, 5, 10, 50, and 100 (They had more symbols for larger numbers, but it is unknown which symbol represents which number). As in the basic Roman system, the Etruscans wrote the symbols that added to the desired number, from higher to lower value. Thus the number '87', for example, would be written 50 + 10 + 10 + 10 + 5 + 1 + 1 = 𐌣𐌢𐌢𐌢𐌡𐌠𐌠 (this would appear as 𐌠𐌠𐌡𐌢𐌢𐌢𐌣 since Etruscan was written from right to left.)^{[31]}
The symbols "𐌠" and "𐌡" resembled letters of the Etruscan alphabet, but "𐌢", "𐌣", and "𐌟" did not. The Etruscans used the subtractive notation, too, but not like the Romans. They wrote 17, 18, and 19 as "𐌠𐌠𐌠𐌢𐌢", "𐌠𐌠𐌢𐌢", and 𐌠𐌢𐌢, mirroring the way they spoke those numbers ("three from twenty", etc.); and similarly for 27, 28, 29, 37, 38, etc. However they did not write "𐌠𐌡" for 4 (or "𐌢𐌣" for 40), and wrote "𐌡𐌠𐌠", "𐌡𐌠𐌠𐌠" and "𐌡𐌠𐌠𐌠𐌠" for 7, 8, and 9, respectively.^{[31]}
Early Roman symbols
In the early period of Rome, numerals were written with nonphonetic symbols, too. The replacement of those symbols by letters seems to have been relatively late development.^{[citation needed]}
The early Roman signs for 1, 10, and 100 were the Etruscan ones: "I", "X", and "𐌟". The symbols for 5 and 50 changed from "𐌡" and "𐌣" to V and ᗐ at some point.^{[citation needed]} The latter had flattened to ⊥ (an inverted T) by the time of Augustus, and soon thereafter became identified with the graphically similar letter L.^{[citation needed]}
The symbol for 100 was written variously as >I< or ƆIC, was then abbreviated to Ɔ or C, with C variant finally winning out because, as a letter, it stood for centum, Latin for "hundred".^{[citation needed]}
The sign for 50 was also written variously as N, И, K, Ψ, ⋔, etc.. Likewise, the number 100 was also written ⋉, ⋈, H, or as any of the symbols for 50 above plus an extra stroke.^{[citation needed]}
The numbers 500 and 1000 were denoted by V or X overlaid 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 a bracketed (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⟩.^{[32]} This at least was the etymology given to it later on.^{[citation needed]}
The notation for 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 ↀ. The latter symbol further evolved into ∞, then ⋈, and eventually changed to M under the influence of the Latin word mille "thousand".^{[citation needed]}
According to Paul Kayser, the basic ciphers were I, X, C and Φ (or ⊕) and that the intermediary ones were derived from taking half of those (half an X is V, half a C is L and half a Φ/⊕ is D).^{[33]}
Use in the Middle Ages and Renaissance
Lower case, minuscule, letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and since that time lowercase versions of Roman numbers have also been commonly used: i, ii, iii, iv, and so on.
Since the Middle Ages, a "j" has sometimes been substituted for the final "i" of a "lowercase" Roman numeral, such as "iij" for 3 or "vij" for 7. This "j" can be considered a swash variant of "i". 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.^{[34]}^{[35]}
Numerals in documents and inscriptions from the Middle Ages sometimes include additional symbols, which today are called "medieval Roman numerals". Some simply substitute another letter for the standard one (such as "A" for "V", or "Q" for "D"), while others serve as abbreviations for compound numerals ("O" for "XI", or "F" for "XL"). Although they are still listed today in some dictionaries, they are long out of use.^{[36]}
Number  Medieval abbreviation 
Notes and etymology 

5  A  Resembles an upsidedown V. Also said to equal 500. 
6  ↅ  Either from a ligature of VI, or from digamma (ϛ), the Greek numeral 6 (sometimes conflated with the stigma ligature).^{[37]} 
7  S, Z  Presumed abbreviation of septem, Latin for 7. 
9.5  X ̷  Scribal abbreviation, an x with a slash through it. Likewise, IX ̷ represented 8.5 
11  O  Presumed abbreviation of onze, French for 11. 
40  F  Presumed abbreviation of English forty. 
70  S  Also could stand for 7, with the same derivation. 
80  R  
90  N  Presumed abbreviation of nonaginta, Latin for 90. (N.B. N is also used for "nothing" (nullus)). 
150  Y  Possibly derived from the lowercase y's shape. 
151  K  Unusual, origin unknown; also said to stand for 250.^{[38]} 
160  T  Possibly derived from Greek tetra, as 4 × 40 = 160. 
200  H  Could also stand for 2 (see also 𐆙, the symbol for the dupondius). From a barring of two I's. 
250  E  
300  B  
400  P, G  
500  Q  Redundant with D; abbreviates quingenti, Latin for 500. 
800  Ω  Borrowed from Gothic. 
2000  Z 
Chronograms, messages with dates encoded into them, were popular during the Renaissance era. The chronogram would be a phrase containing the letters I, V, X, L, C, D, and M. By putting these letters together, the reader would obtain a number, usually indicating a particular year.
Modern use
By the 11th century, Arabic numerals had been introduced into Europe from alAndalus, 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 made using an abacus). Replacement by their more convenient "Arabic" equivalents was quite gradual, and Roman numerals are still used today in certain 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 regnal numbers and are usually read as ordinals; e.g. II is pronounced "the second". This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England during the reign of Henry VIII. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor. Some monarchs (e.g. Charles IV of Spain and Louis XIV of France) seem to have preferred the use of IIII instead of IV on their coinage (see illustration).
 Generational suffixes, particularly in the US, for people sharing the same name across generations, for example William Howard Taft IV.
 In the French Republican Calendar, initiated during the French Revolution, years were numbered by Roman numerals – from the year I (1792) when this calendar was introduced to the year XIV (1805) when it was abandoned.
 The year of production of films, television shows and other works of art within the work itself. It has been suggested – by BBC News, perhaps facetiously – that this was originally done "in an attempt to disguise the age of films or television programmes."^{[39]} Outside reference to the work will use regular Arabic numerals.
 Hour marks on timepieces. In this context, 4 is often written IIII.
 The year of construction on building faces and cornerstones.
 Page numbering of prefaces and introductions of books, and sometimes of appendices and annexes, too.
 Book volume and chapter numbers, as well as the several acts within a play (e.g. Act iii, Scene 2).
 Sequels to some films, video games, and other works (as in Rocky II).
 Outlines that use numbers to show hierarchical relationships.
 Occurrences of a recurring grand event, for instance:
 The Summer and Winter Olympic Games (e.g. the XXI Olympic Winter Games; the Games of the XXX Olympiad)
 The Super Bowl, the annual championship game of the National Football League (e.g. Super Bowl XXXVII; Super Bowl 50 is a onetime exception^{[40]})
 WrestleMania, the annual professional wrestling event for the WWE (e.g. WrestleMania XXX). This usage has also been inconsistent.
Specific disciplines
In astronomy, the natural satellites or "moons" of the planets are traditionally designated by capital Roman numerals appended to the planet's name. For example, Titan's designation is Saturn VI.
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 education, school grades (in the sense of yeargroups rather than test scores) are sometimes referred to by a Roman numeral; for example, "grade IX" is sometimes seen for "grade 9".
In entomology, the broods of the thirteen and seventeen year periodical cicadas are identified by Roman numerals.
In advanced mathematics (including trigonometry, statistics, and calculus), when a graph includes negative numbers, its quadrants are named using I, II, III, and IV. These quadrant names signify positive numbers on both axes, negative numbers on the X axis, negative numbers on both axes, and negative numbers on the Y axis, respectively. The use of Roman numerals to designate quadrants avoids confusion, since Arabic numerals are used for the actual data represented in the graph.
In military unit designation, Roman numerals are often used to distinguish between units at different levels. This reduces possible confusion, especially when viewing operational or strategic level maps. In particular, army corps are often numbered using Roman numerals (for example the American XVIII Airborne Corps or the WW2era German III Panzerkorps) with Arabic numerals being used for divisions and armies.
In music, Roman numerals are used in several contexts:
 Movements are often numbered using Roman numerals.
 In music theory, the diatonic functions are identified using Roman numerals. (See: Roman numeral analysis)
 Individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings.
In pharmacy, Roman numerals are used in some contexts, including S to denote "one half" and N to denote "zero" (See the sections below on "zero" and "fractions").^{[41]}
In photography, Roman numerals (with zero) are used to denote varying levels of brightness when using the Zone System.
In seismology, Roman numerals are used to designate degrees of the Mercalli intensity scale of earthquakes.
In sport the team containing the "top" players and representing a nation or province, a club or a school at the highest level in (say) rugby union is often called the "1st XV", while a cricket or American football team for younger or less experienced players might be the "3rd XI".
In tarot, Roman numerals (with zero) are used to denote the cards of the Major Arcana.
In theology and biblical scholarship, the Septuagint is often referred to as LXX, as this translation of the Old Testament into Greek is named for the legendary number of its translators (septuaginta being Latin for "seventy").
Modern use in continental Europe
Some uses that are rare or never seen in English speaking countries may be relatively common in parts of continental Europe. For instance:
Capital or small capital Roman numerals are widely used in Romance languages to denote centuries, e.g. the French xviii^{e} siècle^{[42]} and the Spanish siglo XVIII mean "18th century". Slavic languages in and adjacent to Russia similarly favour Roman numerals (XVIII век). On the other hand, in Slavic languages in Central Europe, like most Germanic languages, one writes "18." (with a period) before the local word for "century".
Mixed Roman and Arabic numerals are sometimes used in numeric representations of dates (especially in formal letters and official documents, but also on tombstones). The month is written in Roman numerals, while the day is in Arabic numerals: "14.VI.1789" and "VI.14.1789" both refer unambiguously to 14 June 1789.
Roman numerals are sometimes used to represent the days of the week in hoursofoperation signs displayed in windows or on doors of businesses,^{[43]} and also sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by I. Sunday is represented by VII. 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. In the example case (left), the business opens from 10 am to 7 pm on weekdays, 10 AM to 5 pm on Saturdays and is closed on Sundays. Note that the listing uses 24hour time.
Roman numerals may also be used for floor numbering.^{[44]}^{[45]} For instance, apartments in central Amsterdam are indicated as 138III, with both an Arabic numeral (number of the block or house) and a Roman numeral (floor number). The apartment on the ground floor is indicated as 138huis.
In Italy, where roads outside builtup areas have kilometre signs, major roads and motorways also mark 100metre subdivisionals, using Roman numerals from I to IX for the smaller intervals. The sign "IX  17" thus marks kilometre 17.9.
A notable exception to the use of Roman numerals in Europe is in Greece, where Greek numerals (based on the Greek alphabet) are generally used in contexts where Roman numerals would be used elsewhere.
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 scholars in lieu of 0. Dionysius Exiguus was known to use nulla alongside Roman numerals in 525.^{[46]}^{[47]} About 725, Bede or one of his colleagues used the letter N, the initial of nulla or of nihil (the Latin word for "nothing"), in a table of epacts, all written in Roman numerals.^{[48]}
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 = 2^{2} × 3) 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 tallylike 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 V for whole numbers from six to nine.^{[49]}
Each fraction from 1/12 to 12/12 had a name in Roman times; these corresponded to the names of the related coins:
Fraction  Roman numeral  Name (nominative and genitive)  Meaning 

1/12  ·  Uncia, unciae  "Ounce" 
2/12 = 1/6  ·· or :  Sextans, sextantis  "Sixth" 
3/12 = 1/4  ··· or ∴  Quadrans, quadrantis  "Quarter" 
4/12 = 1/3  ···· or ∷  Triens, trientis  "Third" 
5/12  ····· or ⁙  Quincunx, quincuncis  "Fiveounce" (quinque unciae → quincunx) 
6/12 = 1/2  S  Semis, semissis  "Half" 
7/12  S·  Septunx, septuncis  "Sevenounce" (septem unciae → septunx) 
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 
"Less a quarter" (dequadrans → dodrans) or "ninth ounce" (nona uncia → nonuncium) 
10/12 = 5/6  S···· or S∷ 
Dextans, dextantis or decunx, decuncis 
"Less a sixth" (desextans → dextans) or "ten ounces" (decem unciae → decunx) 
11/12  S····· or S⁙  Deunx, deuncis  "Less an ounce" (deuncia → deunx) 
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 fractional notations included 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 (𐆒) and another resembling the Cyrillic letter Є.
 1/36 binae sextulae, binarum sextularum ("two sextulas") or duella, duellae, represented by a sequence of two reversed Ss (𐆓𐆓).
 1/48 sicilicus, sicilici, represented by a reversed C (Ɔ).
 1/72 sextula, sextulae (1/6 of an uncia), represented by a reversed S (𐆓).
 1/144 = 12^{−2} dimidia sextula, dimidiae sextulae ("half a sextula"), represented by 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
A number of systems were developed for the expression of larger numbers that cannot be conveniently expressed using the normal seven letter symbols of conventional Roman numerals.
Apostrophus
One of these was the apostrophus,^{[50]} in which 500 (usually written as "D") was written as IƆ, while 1,000, was written as CIƆ instead of "M".^{[32]} This is a system of encasing numbers to denote thousands (imagine the Cs and Ɔs as parentheses), which has its origins in Etruscan numeral usage. The IƆ and CIƆ used to represent 500 and 1,000 most likely preceded, and subsequently influenced, the adoption of "D" and "M" in conventional Roman numerals.
In this system, an extra Ɔ denoted 500, and multiple extra Ɔs are used to denote 5,000, 50,000, etc. For example:
Base number  CIƆ = 1,000  CCIƆƆ = 10,000  CCCIƆƆƆ = 100,000  

1 extra Ɔ  IƆ = 500  CIƆƆ = 1,500  CCIƆƆƆ = 10,500  CCCIƆƆƆƆ = 100,500 
2 extra Ɔs  IƆƆ = 5,000  CCƆƆƆƆ = 15,000  CCCƆƆƆƆƆ = 105,000  
3 extra Ɔs  IƆƆƆ = 50,000  CCCIƆƆƆƆƆƆ = 150,000 
Sometimes CIƆ was reduced to ↀ 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 ↁ; CCIƆƆ for 10,000 to ↂ; IƆƆƆ for 50,000 to ↇ; and CCCIƆƆƆ for 100,000 to ↈ.^{[51]}
Vinculum
Another system is the vinculum, in which conventional Roman numerals are multiplied by 1,000 by adding an "bar" or "overline".^{[51]} Although mathematical historian David Eugene Smith disputes that this was part of ancient Roman usage,^{[52]} the notation was certainly in use in the Middle Ages, and is sometimes suggested as a workable method for modern use, although it is not standardised as such.
Any hundreds, tens or units in the number are written in ordinary Roman numerals  but instead of M, MM or MMM, "barred" notation is used to express the thousands  which greatly expands the range of numbers expressible.
For instance:
 IV = 4,000
 IVDCXXVII = 4,627
 XXV = 25,000
 XXVCDLIX = 25,459
If this were ever to be applied consistently in our own times  then the main difficulty would be what to do with "M"  one way would be to do away with "M" altogether, except perhaps for CM (=900)  thus rendering MMXVIII as IIXVIII  or alternatively to retain "M" in its current usage, with the barred numerals starting at IV (=4,000). Retaining "M" would permit our numerals to run up to MMMCMXCIXCMXCIX (= 3,999,999).
Another inconsistent medieval usage was the addition of vertical lines (or brackets) before and after the numeral to multiply it by 10 (or 100): thus M for 10,000 as an alternative form for X. In combination with the overline the bracketed forms might be used to raise the multiplier to (say) ten (or one hundred) thousand, thus:
 VIII for 80,000 (or 800,000)
 XX for 200,000 (or 2,000,000)
Through all this, and whether any kind of vinculum notation or "barring" needs to be revived or not, this needs to be distinguished from the custom, once very common, of adding both underline and overline to a Roman numeral, simply to make it clear that it is a number, e.g. MCMLXVII (1967).
Unicode
The "Number Forms" block of the Unicode computer character set standard has a number of Roman numeral symbols in the range of code points from U+2160 to U+2188.^{[53]} This range includes both upper and lowercase numerals, as well as precombined characters for numbers up to 12 (Ⅻ or XII). One justification for the existence of precombined numbers is to facilitate the setting of multipleletter numbers (such as VIII) on a single horizontal line in Asian vertical text. The Unicode standard, however, includes special Roman numeral code points for compatibility only, stating that "[f]or most purposes, it is preferable to compose the Roman numerals from sequences of the appropriate Latin letters".^{[54]} The block also includes some apostrophus symbols for large numbers, an old variant of "L" (50) similar to the Etruscan character, the Claudian letter "reversed C", etc.
See also
 Egyptian numerals
 Etruscan numerals
 Greek numerals
 Kharosthi numerals
 Roman abacus
 Protowriting
 Roman numerals in Unicode
 Pentimal system
References
Notes
 ^ Without theorising about causation, it may be noted that "IV" uses 25% fewer strokes than "IIII", and takes up 25% less space. For the other forms (IX, XL, XC, CD, and CM), the savings on either or both counts are 50% or more. "IX" is also more distinctive than "VIIII" and less likely to be confused with "VIII". This equally applies to XC, CD, and CM).
 ^ Since the largest Roman numerals likely to be used today are year numbers up to the present there is normally no need to use Roman numerals for numbers beyond this limit. In the unlikely case a larger number might be needed there is really no reason why more "M"s, as required, could not be added, cumbersome as this might prove. Through the centuries during which Roman numerals remained the standard way of writing numbers throughout Europe there were extensions to the system designed to indicate larger numbers, see the final sections of this article.
 ^ Equivalent to writing "IX" as "VIV"!
Citations

^ Gordon, Arthur E. (1982). Illustrated Introduction to Latin Epigraphy. Berkeley: University of California Press. ISBN 0520050797.
Alphabetic symbols for larger numbers, such as Q for 500,000, have also been used to various degrees of standardization.
 ^ Adams, Cecil (23 February 1990). "What is the proper way to style Roman numerals for the 1990s?". The Straight Dope.
 ^ Stanislas Dehaene (1997): The Number Sense : How the Mind Creates Mathematics. Oxford University Press; 288 pages. ISBN 9780199723096
 ^ Ûrij Vasilʹevič Prokhorov and Michiel Hazewinkel, editors (1990): Encyclopaedia of Mathematics, Volume 10, page 502. Springer; 546 pages. ISBN 9781556080050
 ^ Reddy, Indra K.; Khan, Mansoor A. (2003). Essential Math and Calculations for Pharmacy Technicians. CRC Press. ISBN 9780203495346.
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 ^ Martelli, Alex; Ascher, David (2002). Python Cookbook. O'Reilly Media Inc. ISBN 9780596001674.
 ^ "What book is the Statue of Liberty holding? What is its significance?". Quora.
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 ^ ^{a} ^{b} ^{c} Julius Caesar (5249 BC): Commentarii de Bello Gallico. Book II, Section 4: "... XV milia Atrebates, Ambianos X milia, Morinos XXV milia, Menapios VII milia, Caletos X milia, Veliocasses et Viromanduos totidem, Atuatucos XVIIII milia; ..." Section 8: "... ab utroque latere eius collis transversam fossam obduxit circiter passuum CCCC et ad extremas fossas castella constituit..." Book IV, Section 15: "Nostri ad unum omnes incolumes, perpaucis vulneratis, ex tanti belli timore, cum hostium numerus capitum CCCCXXX milium fuisset, se in castra receperunt." Book VII, Section 4: "...in hiberna remissis ipse se recipit die XXXX Bibracte."
 ^ ^{a} ^{b} Pliny the Elder (7779 AD): Naturalis Historia, Book III: "Saturni vocatur, Caesaream Mauretaniae urbem CCLXXXXVII p[assum]. traiectus. reliqua in ora flumen Tader ... ortus in Cantabris haut procul oppido Iuliobrica, per CCCCL p. fluens ..." Book IV: "Epiri, Achaiae, Atticae, Thessalia in porrectum longitudo CCCCLXXXX traditur, latitudo CCLXXXXVII." Book VI: "tam vicinum Arsaniae fluere eum in regione Arrhene Claudius Caesar auctor est, ut, cum intumuere, confluant nec tamen misceantur leviorque Arsanias innatet MMMM ferme spatio, mox divisus in Euphraten mergatur."
 ^ Angelo Rocca (1612) De campanis commentarius. Published by Guillelmo Faciotti, Rome. Title of a Plate: "Campana a XXIIII hominibus pulsata" ("Bell to be sounded by 24 men")
 ^ Gerard Ter Borch (1673): Portrait of Cornelis de Graef. Date on painting: "Out. XXIIII Jaer. // M. DC. LXXIIII".
 ^ Thomas Bennet (1731): Grammatica Hebræa, cum uberrima praxi in usum tironum ... Editio tertia. Published by T. Astley, copy in the British Library; 149 pages. Page 24: "PRÆFIXA duo sunt viz. He emphaticum vel relativum (de quo Cap VI Reg. LXXXX.) & Shin cum Segal sequente Dagesh, quod denotat pronomen relativum..."
 ^ Pico Della Mirandola (1486)`Conclusiones sive Theses DCCCC ("Conclusions, or 900 Theses").
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^ "Gallery: Museum's North Entrance (1910)". Saint Louis Art Museum. Archived from the original on 4 December 2010. Retrieved 10 January 2014.
The inscription over the North Entrance to the Museum reads: "Dedicated to Art and Free to All MDCDIII." These roman numerals translate to 1903, indicating that the engraving was part of the original building designed for the 1904 World's Fair.
 ^ ^{a} ^{b} Stephen James Malone, (2005) Legio XX Valeria Victrix.... PhD thesis. On page 396 it discusses many coins with "Leg. IIXX" and notes that it must be Legion 22. The footnote on that page says: "The form IIXX clearly reflecting the Latin duo et vicensima 'twentysecond': cf. X5398, legatus I[eg II] I et vicensim(ae) Pri[mi]g; VI 1551, legatus leg] IIXX Prj; III 14207.7, miles leg IIXX; and III 104713, a vexillation drawn from four German legions including 'XVIII PR'  surely here the stonecutter's hypercorrection for IIXX PR.
 ^ Adkins, Lesley; Adkins, Roy A (2004). Handbook to life in ancient Rome (2 ed.). p. 270. ISBN 0816050260.
 ^ Boyne, William (1968). A manual of Roman coins. p. 13.
 ^ Michaele Gasp. Lvndorphio (1621): Acta publica inter invictissimos gloriosissimosque&c. ... et Ferdinandum II. Romanorum Imperatores.... Printed by IanFriderici Weissii. Page 123: "Sub Dato Pragæ IIIXX Decemb. A. C. M. DC. IIXX". Page 126, end of the same document: "Dabantur Pragæ 17 Decemb. M. DC. IIXX"
 ^ Raphael Sulpicius à Munscrod (1621): (1692) Vera Ac Germana Detecto Clandestinarvm Deliberationvm. Page 16, line 1: "repertum Originale Subdatum IIIXXX Aug. A. C. MDC.IIXX". Page 41, upper right corner: "Decemb. A. C. MDC.IIXX". Page 42, upper left corner: "Febr. A. C. MDC.XIX". Page 70: "IIXX. die Maij sequentia in consilio noua ex Bohemia allata....". Page 71: "XIX. Maij".
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 ^ Kennedy, Benjamin H. (1879). Latin grammar. London: Longmans, Green, and Co. p. 150.
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 ^ Kennedy, Benjamin Hall (1923). The Revised Latin Primer. London: Longmans, Green & Co.
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 ^ Bachenheimer, Bonnie S. (2010). Manual for Pharmacy Technicians. ISBN 158528307X.
 ^ Lexique des règles typographiques en usage à l'imprimerie nationale (in French) (6th ed.). Paris: Imprimerie nationale. March 2011. p. 126. ISBN 9782743304829. On composera en chiffres romains petites capitales les nombres concernant : ↲ 1. Les siècles.
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 ^ Faith Wallis, trans. Bede: The Reckoning of Time (725), Liverpool, Liverpool Univ. Pr., 2004. ISBN 0853236933.
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 ^ Unicode Number Forms
 ^ The Unicode Standard, Version 6.0 – Electronic edition (PDF), Unicode, Inc., 2011, p. 486
Sources
 Menninger, Karl (1992). Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications. ISBN 9780486270968.
Further reading
Look up Appendix:Roman numerals or roman numeral in Wiktionary, the free dictionary. 
Wikimedia Commons has media related to Roman numerals. 
Library resources about Roman numerals 
 Aczel, Amir D. 2015. Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers. 1st edition. New York: Palgrave Macmillan.
 Goines, David Lance. A Constructed Roman Alphabet: A Geometric Analysis of the Greek and Roman Capitals and of the Arabic Numerals. Boston: D.R. Godine, 1982.
 Houston, Stephen D. 2012. The Shape of Script: How and Why Writing Systems Change. Santa Fe, NM: School for Advanced Research Press.
 Taisbak, Christian M. 1965. "Roman numerals and the abacus." Classica et medievalia 26: 147–60.