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Roman numerals are a numeral system of ancient Rome based on letters of the alphabet, which are combined to signify the sum (or in some cases, the difference) of their values. The first ten Roman numerals are

$\mathrm{I,\;II,\;III,\;IV,\;V,\;VI,\;VII,\;VIII,\;IX, and \;X.}$

The Roman numeral system is decimal[1] but not directly positional and does not include a zero. It is a cousin of the Etruscan numerals, and the letters derive from earlier non-alphabetical symbols; over time the Romans came to identify the symbols with letters of the Latin alphabet. The system was modified slightly during the Middle Ages to produce the system used today.

Roman numerals are commonly used in numbered lists (such as the outline format of an article), clock faces, pages preceding the main body of a book, chord triads in music analysis, dated notices of copyright, months of the year, successive political leaders or children with identical names, and the numbering of annual events. See modern usage below.

For arithmetic involving Roman numerals, see Roman arithmetic and Roman abacus.

Numeral systems by culture
Hindu-Arabic numerals
Eastern Arabic
Indian family
Khmer
Mongolian
Thai
Western Arabic
East Asian numerals
Chinese
Counting rods
Japanese
Korean
Suzhou
Vietnamese
Alphabetic numerals
Armenian
Āryabhaṭa
Cyrillic
Ge'ez
Greek (Ionian)
Hebrew
Other systems
Attic
Babylonian
Brahmi
Egyptian
Etruscan
Inuit
Mayan
Quipu
Roman
Urnfield
List of numeral system topics
Positional systems by base
Decimal (10)
1, 2, 3, 4, 5, 8, 12, 16, 20, 60 more…
Entrance to section LII of the Colosseum, with numerals still visible

Symbols

Roman numerals are based on seven symbols: a stroke (identified with the letter I) for a unit, a chevron (identified with the letter V) for a five, a cross-stroke (identified with the letter X) for a ten, a C (identified as an abbreviation of Centum) for a hundred, etc.:

Symbol Value
I 1 (one) (unus)
V 5 (five) (quinque)
X 10 (ten) (decem)
L 50 (fifty) (quinquaginta)
C 100 (one hundred) (centum)
D 500 (five hundred) (quingenti)
M 1000 (one thousand) (mille)

Symbols are iterated to produce multiples of the decimal (1, 10, 100, 1000) values, with V, L, D substituted for a multiple of five, and the iteration continuing: I "1", II "2", III "3", V "5", VI "6", VII "7", etc., and the same for other bases: X "10", XX "20", XXX "30", L "50", LXXX "80"; CC "200", DCC "700", etc. At the fourth iteration, a subtractive principle may be employed, with the base placed before the higher base: IIII or IV "4", VIIII or IX "9", XXXX or XL "40", LXXXX or XC "90", CCCC or CD "400", DCCCC or CM "900".

The Romans only used what is called capital (upper case) letters in modern usage. In the Middle Ages, minuscule (lower case) letters were developed, and these are commonly used for Roman numerals: i, ii, iii, iv, etc. Also in medieval use was the substitution of j for a final i to end numbers, such as iij for 3 or vij for 7. This was not a separate letter, but merely a swash variant of i. It is used today, especially in medical prescriptions, to prevent tampering with or misinterpretation of the numbers after they are written.[2] [3]

For large numbers (4000 and above), a bar can be placed above a base numeral, or parentheses placed around it, to indicate multiplication by 1000, although the Romans themselves often just wrote out the "M"s:[4]

Symbol Value
V or (V) five thousand
X or (X) ten thousand
L or (L) fifty thousand
C or (C) one hundred thousand
D or (D) five hundred thousand
M or (M) one million

The parentheses are more versatile; (II) is synonymous with MM, but II is not found.

The basic multiples of Roman numerals thus follow a pattern:

×1 ×2 ×3 ×4 ×5 ×6 ×7 ×8 ×9
Ones I II III IV V VI VII VIII IX
Tens X XX XXX XL L LX LXX LXXX XC
Hundreds C CC CCC CD D DC DCC DCCC CM
Thousands M MM MMM IV V VI VII VIII IX
Ten thousands X XX XXX XL L LX LXX LXXX XC
Hundred thousands C CC CCC CD D DC DCC DCCC CM

A practical way to write a Roman number is to consider the modern Arabic numeral system, and separately convert the thousands, hundreds, tens, and ones as given in the chart above. So, for instance, 1234 may be thought of as "one thousand and two hundreds and three tens and four", obtaining M (one thousand) + CC (two hundreds) + XXX (thirty) + IV (four), for MCCXXXIV. Thus eleven is XI (ten and one), 32 is XXXII (thirty and two) and 2009 is MMIX (two thousand and nine). Note that the subtractive principle is not extended beyond the chart: for example, IL is not used for 49, rather this should be written as forty (XL) and nine (IX), or XLIX.

Origins

Although the Roman numerals are now written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used I Λ X 8 ⊕ for I V X L C M, of which only I and X happened to be letters in their alphabet. One folk etymology has it that the V represented a hand, and that the X was made by placing two Vs on top of each other, one inverted. However, the Etrusco-Roman numerals actually appear to derive from notches on tally sticks, which continued to be used by Italian and Dalmatian shepherds into the 19th century.[5]

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 (X), 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 VIII), 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 X, and so was XΛIII. Likewise, number four on the stick was the I-notch that could be felt just before the cut of the Λ (V), so it could be written as either IIII or IΛ (IV). 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 I, V, X

The tenth V or X 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 V and I - . This had flattened to (an inverted T) by the time of Augustus, and soon thereafter became identified with the graphically similar letter L. 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 X and I) came to predominate. It 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".

The hundredth V or X 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, perhaps as an abbreviation of demi-mille "half-thousand"; this at least was the folk 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. In different traditions it then evolved along several different routes. Some variants, such as Ψ and ↀ, were historical dead ends, although folk etymology later identified D for 500 as graphically half of Φ for 1000 because of the CD variant. A third line, , survives to this day in two variants:

• One, CIƆ, led to the convention of using parentheses to indicate multiplication by a thousand: the original CIƆ = (I) 1000, then (III) for 3000, (V) 5000, (IX) 9000, (X) 10 000, (L) 50 000, (C) 100 000, (D) 500 000, (M) 1000 000, etc. This was later extended to double parentheses, as in , , etc. See alternate forms below.
• In the other, became and , eventually changing to M under the influence of the Latin word mille "thousand".

Zero

In general, the number zero did not have its own Roman numeral, but a primitive form (nulla) was known by medieval computists (responsible for calculating the date of Easter). They included zero (via the Latin word nulla meaning "none") as one of nineteen epacts, or the age of the moon on March 22. The first three epacts were nulla, xi, and xxii (written in minuscule or lower case). The first known computist to use zero was Dionysius Exiguus in 525. Only one instance of a Roman numeral for zero is known. 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.

Fractions

A triens coin (1/3 or 4/12 of an as). Note the four dots •••• indicating its value.
A semis coin (1/2 or 6/12 of an as). Note the S indicating its value.

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 V for whole numbers from six to nine.

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:

• 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 Greek letter sigma Σ, one variant resembling the pound sign £ without the horizontal line(s) and another resembling Cyrillic letter Є.
• 1/36 binae sextulae, binarum sextularum ("two sextulas") or duella, duellae, represented by ƧƧ, a sequence of two reversed S.
• 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 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 siliqua, siliquae, represented by a symbol resembling closing guillemets ».

IIII and IV

The notation of Roman numerals has varied through the centuries. Originally, it was common to use IIII to represent four, because IV represented the Roman god Jupiter, whose Latin name, IVPPITER, begins with IV. The subtractive notation (which uses IV instead of IIII) has become the standard notation only in modern times. For example, Forme of Cury, a manuscript from 1390, uses IX for nine, but IIII for four. Another document in the same manuscript, from 1381, uses IV and IX. A third document in the same manuscript uses IIII, IV, and IX. Constructions such as IIIII for five, IIX for eight or VV for 10 have also been discovered. Subtractive notation arose from regular Latin usage: the number 18 was duodeviginti or “two from twenty”; the number 19 was undeviginti or "one from twenty". The use of subtractive notation increased the complexity of performing Roman arithmetic, without conveying the benefits of a full positional notation system.

An inscription on Admiralty Arch, London. The numeral translates to 1910.

Likewise, on some buildings it is possible to see MDCCCCX, for example, representing 1910 instead of MCMX – notably Admiralty Arch in London. The Leader Building in Cleveland, Ohio, at the corner of Superior Avenue and E.6th Street, is marked MDCCCCXII, representing 1912 instead of MCMXII. Another notable example is on Harvard Medical School's Gordon Hall, which reads MDCCCCIIII for 1904 instead of MCMIV. In Dubrovnik, Croatia, a commemorative inscription marking the 1000th anniversary of King Tomislav’s coronation (Croatia’s first King), appears as DCCCCXXV - MDCCCCXXV instead of CMXXV - MCMXXV (925 -1925).

Calendars and clocks

A typical clock face with Roman numerals
The Shepherd gate clock with Roman numbers up to XXIII (and 0), in Greenwich

Clock faces that are labeled using Roman numerals conventionally show IIII for four o'clock and IX for nine o'clock, using the subtractive principle in one case and not the other. There are many suggested explanations for this, several of which may be true:

• Louis XIV, king of France, who preferred IIII over IV, ordered his clockmakers to produce clocks with IIII and not IV, and thus it has remained.[6]
• Using the standard numerals, two sets of figures would be similar and therefore confusable by children and others unused to reading clockfaces: IV and the VI; and IX and XI. Since the first pair are additionally upside down on the face, an added level of confusion would be introduced. It is used to make greater character distinction between them by using IIII and VI
• The four-character form IIII creates a visual symmetry with the VIII on the other side, which the two-character IV would not.
• With IIII, the number of symbols on the clock totals twenty Is, four Vs, and four Xs, so clock makers need only a single mold with a V, five Is, and an X in order to make the correct number of numerals for their clocks: VIIIIIX. This is cast four times for each clock and the twelve required numerals are separated:
• V IIII IX
• VI II IIX
• VII III X
• VIII I IX
The IIX and one of the IXs are rotated 180° to form XI and XII. The alternative with IV uses seventeen Is, five Vs, and four Xs, requiring the clock maker to have several different molds.
• Only the I symbol would be seen in the first four hours of the clock, the V symbol would only appear in the next four hours, and the X symbol only in the last four hours. This would add to the clock's radial symmetry.
• Many clocks use IIII because that was the tradition established by the earliest surviving clock, the Wells Cathedral clock built between 1386 and 1392. It used IIII 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 Arabic numerals for a minute dial and a moon dial, so theories depending on a symmetrical 12-hour clock face do not apply.[7]

Subtractive principle

Generally, Roman numerals are written in descending order from left to right, and are added sequentially, for example MMVI (2006) is interpreted as 1000 + 1000 + 5 + 1.

Certain combinations employ a subtractive principle, which specifies that where a symbol of smaller value precedes a symbol of larger value, the smaller value is subtracted from the larger value, and the result is added to the total. For example, in MCMXLIV (1944), the symbols C, X and I each precede a symbol of higher value, and the result is interpreted as 1000 plus (1000 minus 100) plus (50 minus 10) plus (5 minus 1).

A numeral for 10n (I, X, or C) may not precede a numeral larger than 10n+1, where n is an integer.[citation needed] That is, I may precede V and X, but not L or C; X may precede L or C, but not D or M. The numerals 5×10n (V, L, or D) may not be followed by a numeral of greater or equal value.[citation needed] Any symbol that appears more than once consecutively may not be followed by a symbol of larger value.

Modern usage

Roman numbers on stern of Cutty Sark, Greenwich

Roman numerals remained in common use until about the 14th century, when they were replaced by Hindu-Arabic numerals (thought to have been introduced to Europe from al-Andalus, by way of Arab traders and arithmetic treatises, around the 11th century). The Roman number system is generally regarded as obsolete in modern usage, but is still seen occasionally. Classical numbering is often used to suggest importance or timelessness, or in other cases where an alternate numbering system is useful for clarity. Examples of their current use include:

Sometimes the numerals are written using lower-case letters (thus: i, ii, iii, iv, etc.), particularly if numbering paragraphs or sections within chapters, or for the pagination of the front matter of a book.

Undergraduate degrees at British universities are generally graded using I, IIi, IIii, III for first, upper second (often pronounced "two one"), lower second (often pronounced "two two") and third class respectively.

In chemistry, Roman numerals were formerly used to denote the group in the periodic table of the elements. But there was not international agreement as to whether the group of metals which dissolve in water should be called Group IA or IB, for example, so although references may use them, the international norm has recently switched to Arabic numerals. However, Roman numerals are still used in the IUPAC nomenclature of inorganic chemistry, for the oxidation number of cations which can take on several different positive charges. For example, FeO is iron(II) oxide and Fe2O3 is iron(III) oxide. In contrast, Arabic numerals are used to denote the formal oxidation state (which is not always the same as the oxidation number) of positively or negatively charged atoms. They are also used for naming phases of polymorphic crystals, such as ice.

In astronomy, the natural satellites or "moons" of the planets are traditionally designated by capital Roman numerals, at first by order from the center of the planet, as the four Galilean satellites of Jupiter are numbered, and later by order of discovery; e.g., Callisto was "Jupiter IV" or "J IV". Notably, the notation IV was mostly disused by the Romans for its similarity to the first two letters of Jupiter. With recent discoveries—Jupiter currently has 63 known satellites—as well as computerization, this is somewhat disparaged for the minor worlds, at least in computerized listings.

Science fiction, and not astronomy per se, has adopted the use for numbering the planets around a star; e.g., Planet Earth is called "Sol III".

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

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

Music theory

In music theory, while scale degrees are typically represented with Arabic numerals, often modified with a caret or circumflex, the triads that have these degrees as their roots are often identified by Roman numerals (as in chord symbols). See also diatonic functions. Upper-case Roman numerals indicate major triads while lower-case Roman numerals indicate minor triads, as the following chart illustrates. Some writers, however, use upper case Roman numerals for both major and minor triads. Lower-case Roman numerals with a degree symbol indicate diminished triads. For example, in the major mode the triad on the seventh scale degree, the leading tone triad is diminished.

Also in music theory, individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings. For example I signifies the E string on the violin and the A string on the viola and cello, these being the highest strings, respectively, on each instrument. They are also sometimes used to signify position. In this case, the number in Roman numerals corresponds with the position number. For example, III means third position and V means fifth.

 Roman numeral I ii iii IV V vi vii° Scale degree (major mode) tonic supertonic mediant subdominant dominant submediant leading tone
 Roman numeral i ii° (♭)III iv v (♭)VI (♭)VII vii° Scale degree (minor mode) tonic supertonic mediant subdominant dominant submediant subtonic leading tone

Modern non-English-speaking usage

The above uses are customary for English-speaking countries. Although many of them are also maintained in other countries, those countries have additional uses for Roman numerals that are not normally employed in English-speaking regions.

The French, Hungarian, Italian, Portuguese, Polish, Romanian, Russian, Spanish, Croatian and Catalan languages use capital Roman numerals to denote centuries. For example, XVIII refers to the eighteenth century, so as to avoid confusion between the 18th century and the 1800s. (The Italians also take the opposite approach, basing names of centuries on the digits of the years; quattrocento for example is a common Italian name for secolo XV, the fifteenth century.) Some scholars in English-speaking countries have adopted the former method.

In Italy, Poland, Russia, Central Europe, and in Portuguese, Romanian, Croatian and Serbian languages, mixed Roman and Arabic numerals are used to record dates (usually on tombstones, but also elsewhere, such as in formal letters and official documents). Just as an old clock recorded the hour by Roman numerals while the minutes were measured in Arabic numerals, the month is written in Roman numerals while the day is in Arabic numerals: 14.VI 1789 is 14 June 1789. This is how dates are inscribed on the walls of the Kremlin, for example. This method has the advantage that days and months are not confused in rapid note-taking, and that any range of days or months can be expressed without confusion. For instance, V-VIII is May to August, while 1.V - 31.VIII is 1 May to 31 August.

In Hungary the Roman numbers are used to record the number of the adoped Acts, for example: the XX. Act of 1949 on the Constitution of the Hungarian Republic.

In Eastern Europe, especially the Baltic 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. Monday is represented by I, which is the initial day of the week. Sunday is represented by VII, 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.

 I 9:30–17:30 II 9:30–19:00 III 9:30–17:30 IV 9:30–17:30 V 9:30–19:00 VI 9:30–13:00 VII —
A five–watt resistor as per GOST 2.728–74.

In CIS countries, capital Roman numerals I, II and V still are sometimes used according to the regional standard GOST 2.728–74 (2002), to specify rated resistor power (in watts) in schematic symbols by inscribing the numeral along inside the symbol rectangle.

Since the French use capital Roman numerals to refer to the quarters of the year (III is the third quarter), and this has become the norm in some European standards organisation, the mixed Roman–Arabic method of recording the date has switched to lowercase Roman numerals in many circles, as 4-viii-1961. (ISO has since specified that dates should be given in all Arabic numerals, in ISO 8601 formats.)

In geometry, Roman numerals are often used to show lines of equal length.

In Hungary, Poland, Romania, Serbia and other European countries to lesser extent, Roman numerals are used for floor numbering. Likewise apartments in central Amsterdam are indicated as 138-III, 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 '138-huis'.

In Poland, Roman numerals are used for ordinals in names of some institutions. In particular high schools ("V Liceum Ogólnokształcące w Krakowie" - 5th High School in Kraków), tax offices ("II Urząd Skarbowy w Gdańsku" - 2nd Office of Treasury in Gdańsk) and courts ("I Wydział Cywilny Sądu Okręgowego" - District Court, 1st Civil Division) - use Roman numerals. Institutions that use "Institution nr N" notation always use Arabic numerals. These include elementary ("Szkoła Podstawowa nr 5") and middle schools ("Gimnazjum nr 5").

Roman numerals are rarely used in Asia. The motion picture rating system in Hong Kong uses categories I, IIA, IIB, and III based on Roman numerals.

Alternate forms

In the Middle Ages, Latin writers used a horizontal line 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. MCMLXVII, 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. MCMLXVII.

Sometimes 500, usually D, was written as I followed by an apostrophus or apostrophic C (which resembles a backwards C, i.e. Ɔ), while 1,000, usually M, was written as CIƆ. This is believed to be a system of encasing numbers to denote thousands (imagine the Cs as parentheses). This system has its origins from Etruscan numeral usage. The D and M symbols to represent 500 and 1,000 were most likely derived from and CIƆ, respectively.

Roman numerals, 16th century

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 a lemniscate symbol () for denoting 1,000. John Wallis is often credited for introducing this symbol to represent infinity (), and one conjecture is that he based it on this usage, since 1,000 was hyperbolically used to represent very large numbers. Similarly, 5,000 (IƆƆ) was reduced to ; and 10,000 (CCIƆƆ) was reduced to .

In medieval times, before the letter j emerged as a distinct letter, a series of letters i in Roman numerals was commonly ended with a flourish; hence they actually looked like ij, iij, iiij, etc. This proved useful in preventing fraud, as it was impossible, for example, to add another i to vij to get viij.

Medieval Roman numerals

Most uniquely, during the Middle Ages there came about a unique, more comprehensive shorthand for writing Roman numerals, called today the "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.[8]

Modern
number
Medieval
abbreviation
Notes
5 A Resembles an upside-down V. Also said to equal 500.
6 Either a ligature of VI, or the Greek letter stigma (Ϛ), having the same numerical value.[9]
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.
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.
800 W More properly, the Greek ω, as W was a fairly new creation. Carried over from Gothic.
900 ĵ, ↑ Resembled a crooked up arrow. Carried over from Gothic.
2000 Z

Modern Roman numerals

Some "modern" Roman numerals, post-Victorian era, are shown below:

Standard Arabic Notes
none 0 N for nulla was used at least once (by Bede about 725).
I 1
II 2
III 3
IV 4 IIII is still used on clock and Tarot card faces. See Calendars and clocks above.
V 5 IIIII was used rarely in the Middle Ages.
VI 6
VII 7
VIII 8 IIX was used rarely in the Middle Ages.
IX 9
X 10 VV was used rarely in the Middle Ages.
XI 11
XII 12
XIII 13
XIV 14
XV 15
XVI 16
XVII 17
XVIII 18
XIX 19
XX 20
XXI 21
XXV 25
XXX 30
XXXV 35
XL 40
XLV 45
XLIX 49 Per rule above, IL would not be generally accepted.
L 50
LX 60
LXIX 69
LXX 70 The abbreviation for the Septuagint
LXXVI 76
LXXX 80
XC 90
XCIX 99 As opposed to the "shortcut" way IC seen above.
C 100 This is the origin of using the slang term "C-bill" or "C-note" for "\$100 bill" although there is some dispute over this because this is possibly in reference to the French word for 100 which is Cent.
CL 150
CC 200
CCC 300
CD 400
CDXCIX 499 Per rule above, ID would not be generally accepted.
D 500
DC 600
DCLXVI 666 Using every symbol except M in descending order gives the beast number.
DCC 700
DCCC 800
CM 900
CMXCIX 999 Per rule above, IM would not be generally accepted.
M 1,000
MCDXLIV 1,444 Smallest pandigital number (each symbol is used)
MDCLXVI 1,666 Largest efficient pandigital number (each symbol occurs exactly once)
MCMXC 1,990 Shortcuts like XMM and MXM disagree with the rule stated above
MCMXCVII 1,997
MCMXCIX 1,999 Shortcuts like IMM and MIM disagree with the rule stated above
MM 2,000
MMI 2,001
MMX 2,010
MMD 2,500
MMM 3,000
MMMDCCCLXXXVIII 3,888 Longest number (most symbols, without overlines or without extra symbols containing overlines).
MMMCMXCIX 3,999 Largest number without an overline at any symbol.
IV 4,000 sometimes MMMM[citation needed] or MV
V 5,000
VMDCLXVI 6,666 This number uses every symbol up to V once.
X 10,000
L 50,000
C 100,000
D 500,000
M 1,000,000
MCDXLIV 1,444,000 Smallest pandigital number (each symbol is used with one line above every symbol)
MDCLXVI 1,666,000 Largest efficient pandigital number (each symbol is used with one line above every symbol)
MM 2,000,000
MMMDCCCLXXXVIII 3,888,000 Longest number (most symbols, each symbol is used with one line above every symbol)

An accurate way to write large numbers in Roman numerals is to handle first the thousands, then hundreds, then tens, then units.

Example: the number 1988.
One thousand is M, nine hundred is CM, eighty is LXXX, eight is VIII.
Put it together: MCMLXXXVIII.

Unicode

Unicode has a number of characters specifically designated as Roman numerals, as part of the Number Forms[10] range from U+2160 to U+2188. This range includes both upper- and lowercase numerals, as well as pre-combined glyphs for numbers up to 12 ( or XII), mainly intended for the clock faces for compatibility with large East-Asian character sets such as JIS X 0213 that provide these characters. The pre-combined glyphs should only be used to represent the individual numbers where the use of individual glyphs is not wanted, and not to replace compounded numbers. Additionally, glyphs exist for archaic[10] forms of 1000, 5000, 10,000, large reversed C (Ɔ), late 6 (, similar to Greek Stigma: Ϛ), early 50 (, similar to down arrow ↓⫝⊥[9]), 50,000, and 100,000. Note that the small reversed c, is not intended to be used in roman numerals, but as lower case Claudian letter ,

Table of Roman numerals in Unicode
Code 0 1 2 3 4 5 6 7 8 9 A B C D E F
Value[11] 1 2 3 4 5 6 7 8 9 10 11 12 50 100 500 1,000
U+2160
U+2170
Value 1000 5000 10,000 6 50 50,000 100,000
U+2180

The characters in the range U+2160–217F are present only for compatibility with other character set standards which provide these characters. For ordinary uses, the standard Latin letters are preferred. Displaying these characters requires a program that can handle Unicode and a font that contains appropriate glyphs for them.

Games

After the Renaissance, the Roman system could also be used to write chronograms. It was common to put in the first page of a book some phrase, so that when adding the I, V, X, L, C, D, M present in the phrase, the reader would obtain a number, usually the year of publication. The phrase was often (but not always) in Latin, as chronograms can be rendered in any language that utilises the Roman alphabet.

References

1. ^ Or more precisely, "a decimal system in which the number 5 is an auxiliary base" (Ifrah 200:193)
2. ^ Sturmer, Julius W. Course in Pharmaceutical and Chemical Arithmetic, 3rd ed. (LaFayette, IN: Burt-Terry-Wilson, 1906). p25 Retrieved on 2010-03-15.
3. ^ Bastedo, Walter A. Materia Medica: Pharmacology, Therapeutics and Prescription Writing for Students and Practitioners, 2nd ed. (Philadelphia, PA: W.B. Saunders, 1919) p582 Retrieved on 2010-03-15.
4. ^ Roman numerals: How they work: Larger numbers
5. ^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by David Bellos, E. F. Harding, Sophie Wood, Ian Monk. John Wiley & Sons, 2000.
6. ^ W.I. Milham, Time & Timekeepers (New York: Macmillan, 1947) p. 196
7. ^ Paul Lewis, Clocking the fours: A new theory about IIII
8. ^ Capelli, A. Dictionary of Latin Abbreviations. 1912.
9. ^ a b Perry, David J. Proposal to Add Additional Ancient Roman Characters to UCS.
10. ^ a b Unicode Number Forms
11. ^ For the first two rows
• Menninger, Karl (1992). Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications. ISBN 0-486-27096-3.

The basic modern Latin alphabet
Aa Bb Cc Dd Ee Ff Gg Hh Ii Jj Kk Ll Mm Nn Oo Pp Qq Rr Ss Tt Uu Vv Ww Xx Yy Zz

numerals ISO/IEC 646

Simple English

A Roman numeral is the name for a number when it is written in the way the Romans used to write numbers. Roman numerals are not used very often today in the west. They are used to write the names of kings and queens, or popes. For example: Queen Elizabeth II. They may be used to write the year a book or movie was made.

The base

I - 1

V - 5

X - 10

L - 50

C - 100

D - 500

M - 1000

If a lower value symbol is before a higher value one, it is subtracted. Otherwise it is added.

So 'IV' is '4' and 'VI' is '6'.

For the numbers above X, only the symbol right before it may be subtracted: so 99 is: XCIX (and not IC).

Writing numbers

Numbers are written as Roman numerals in this way:

I = 1

II = 2

III = 3

IV = 4

V =5

VI = 6

VII = 7

VIII = 8

IX = 9

X = 10

XI = 11

XV = 15

XVI = 16

XIX = 19

XX = 20

XXX = 30

XL = 40

L = 50

LX = 60

LXI = 61

XC = 90

C = 100

CD = 400

D = 500

CM = 900

CMXC = 990

CMXCIX = 999

M = 1,000

MCMXCIX = 1,999

MM = 2,000

MMVII = 2007

MMVIII = 2008

MMIX = 2009

MMX = 2010

Notation

The System that is in use today is: Whenever the same symbol is written four times, it is replaced by subtracting it from the next higher number (5,50,50,500). That way, IV is written instead of IIII (4), XL instead of XXXX (40), etc.

Usually only one number is subtracted, not two. So 8 is always VIII and never IIX

Especially on clocks and watches, IIII can sometimes still be found. This is done partly because the IIII for the 4 o'clock position aesthetically balances the VIII for the 8 o'clock position.

Proper form is to subtract only a value with the next lower power of 10. Thus, 900 is written CM, but 990 would not be XM - properly, it is CM for the 900 portion and XC for the 90 portion, or CMXC. Similarly, 999 would not be IM but rather CMXCIX - CM for the 900 portion, XC for the 90 portion, and IX for the 9 portion. Only values with 1's are ever used to subtract; 45 is properly XLV, not VL.

Notations in Roman numerals for numbers higher than 3,001 are rarely seen. One system utilizes V and X with bars over them to signify 5,000 and 10,000, respectively.

What they are used for

• In the Baltics and Russia, the days of the week, are often written as Roman numbers, 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. Example: 26.XI.2007 = November 26, 2007.
• When movies or books are published, the year of publication or year of copyright may be done 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 trimesters are sometimes counted with Roman numerals.
• In Poland, roman numerals are used to denote the month in dates and as a short method of writing ordinals (i.e. VI to be 6th)
• NFL Football Superbowl numbering