MMXI (2011 as roman numeral) Roman numerals stem from the numeral system of ancient Rome. They are based on certain 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: I, II, III, IV, V, VI, VII, VIII, IX, and X. The Roman numeral system is decimal1 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. Numeral systems by culture Hindu-Arabic numerals Western Arabic Eastern Arabic Indian family Burmese Khmer Mongolian Thai East Asian numerals Chinese Japanese Suzhou Korean Vietnamese Counting rods Alphabetic numerals Abjad Armenian Āryabhaṭa Cyrillic Ge'ez Greek (Ionian) Hebrew Other systems Aegean Attic Babylonian Brahmi Egyptian Etruscan Inuit Mayan Quipu Roman Sumerian Urnfield List of numeral system topics Positional systems by base Decimal (10) 1, 2, 3, 4, 5, 6, 8, 12, 16, 20, 30, 36, 60 more… v · d · e Entrance to section LII of the Colosseum, with numerals still visible Contents 1 Symbols 2 Origins 3 Zero 4 Fractions 5 IIII and IV 5.1 Calendars and clocks 6 Subtractive principle 7 Modern usage 7.1 Music theory 7.2 Modern non-English-speaking usage 8 Alternate forms 8.1 Medieval Roman numerals 9 Modern Roman numerals 9.1 Unicode 10 Programming Conversion 11 Games 12 See also 13 References 14 External links // 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 1,000 (one thousand) (mille) Symbols are iterated to produce multiples of the decimal (1, 10, 100, 1,000) 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 used only what are called capital (upper case) letters in modern usage. In the Middle Ages, minuscule (lower case) letters were developed, and these are now also commonly called 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 an additional symbol, but merely a swash variant of i. It is used today, especially in medical prescriptions, to prevent tampering with or misinterpretation of a number after it is written.23 For large numbers (4,000 and above), a bar can be placed above a base numeral, or parentheses placed around it, to indicate multiplication by 1,000, although the Romans themselves often just wrote out the "M"s:4 Symbol Value V five thousand X ten thousand L fifty thousand C one hundred thousand D five hundred thousand 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), 29 is XXIX (twenty and nine), and 2011 is MMXI (two thousand and ten and one). 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, and 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 and 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 - ᗐ. 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; an alternative symbol for "thousand" looks like this (I), and half of a thousand or "five hundred" is the right half of the symbol, or I), and this may have been converted into D.6 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, ↀ, 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 ↁ , ↂ, etc. See alternate forms below. In the other, ↀ became ∞ and ⋈, eventually changing to M under the influence of the Latin word mille "thousand". For an alternative discussion of the origin of the roman numeral system, for small numbers, see "The River Mathematics" [Alfred Hooper. New York, H. Holt and company, 1945] Hooper contends that the digits are related to hand signals. For example, the numbers I, II, III, IIII correspond to the number of fingers held up for another to see. V, 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=(V,I), 7=(V,II), 8=(V,III), 9=(V,IIII), 10=(V,V) and X results from either crossing of the thumbs, or holding both hands up in a cross. 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" 3/12 = 1/4 ••• or ∴ quadrans, quadrantis "quarter" 4/12 = 1/3 •••• or :: triens, trientis "third" 5/12 ••••• or :•: quincunx, quincuncis "five-ounce" (quinque unciae → quincunx) 6/12 = 1/2 S semis, semissis "half" 7/12 S• septunx, septuncis "seven-ounce" (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" (de-quadrans → dodrans) or "ninth ounce" (nona uncia → nonuncium) 10/12 = 5/6 S•••• or S:: dextans, dextantis or decunx, decuncis "less a sixth" (de-sextans → dextans) or "ten ounces" (decem unciae → decunx) 11/12 S••••• or S:•: deunx, deuncis "less an ounce" (de-uncia → 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 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 IVcitation needed. 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 IX and IV. A third document in the same manuscript uses IX and a mix of IIII and IV. 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 East 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 labelled 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.7 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,8 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. Wikimedia Commons has media related to: Clocks with Roman numerals 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.9 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, showing draft in feet. 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: Names of monarchs and Popes, e.g. Elizabeth II, Benedict XVI. These are ordinal numbers; e.g. "II" is pronounced "the second". This tradition began in England with the Norman Conquest. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor. The year of production of television shows and films. Hour marks on some clockfaces and timepieces. The year of construction on some building faces and cornerstones. Publication dates of books (particularly older ones); page numbering of preliminary pages; volume numbers on spines and chapter numbers. Film series and sequels of novels and video games (such as Final Fantasy), typically emulating use in older books. Outlines use I, II, III and i, ii, iii as part of their organizational structure. A recurring grand event, such as the Olympic Games, Super Bowl, WrestleMania, or the Sprint All-Star Race. Historic events, such as World War II Names of Army Corps. Crossword puzzle clues, particularly cryptic crosswords. Names of cranial nerves. Guitar chord diagrams. Parts of laws, such as Titles (e.g. Civil Rights Act of 1964) or Schedules (e.g. Controlled Substances Act). Sports teams, indicating the number of players in the squad. In rugby union, the 1st XV of a particular club would be the 1st and best team the club has, likewise for the XIII in rugby league, and XI for football (soccer), field hockey and cricket. Some countries use Roman numerals to number centuries (instead of "18th century", "XVIII century" is used). This is uncommon in the English-speaking world.citation needed Some countries use Roman numerals to indicate months, to avoid confusion due to differing date notation order. For example, 2/10/1948 can mean 10 February 1948 or 2 October 1948; writing 2/X/1948 will make it clear that the date meant was actually the second one. This is also the convention used on some postmarks. Call signs of some American television stations (usually based on the station's channel number; such as WXII, KXII, WXIX, WPVI, etc.) Some RAF squadrons have two names; there is the standard number name and a Roman numeral name. For example the attack on the German battleship Tirpitz was carried out by No. 617 Squadron RAF (The Dambusters) and No. IX Squadron RAF. The former is never known as DCXVII while the latter incorporates IX in its squadron badge. 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 that 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 deprecated 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. In Petroleum Industry, Roman numeral M is commonly used in natural gas units, such as MSCF (Thousand Standard Cubic Feet) and MBTU (Thousand British Thermal Unit). Music theory C major scale with roman numerals Play (help·info). 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. Since the 1970s, upper-case Roman numerals indicate major triads while lower-case Roman numerals indicate minor triads, as the following chart illustrates. Some writers, (e.g. Schoenberg) 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. Some writers use upper-case Roman numerals to indicate the chord is diatonic in the major scale, and lower-case Roman numerals to indicate that the chord is diatonic in the minor scale. 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 Also: 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 Scale degree (minor mode) tonic supertonic mediant subdominant dominant submediant subtonic In performance practice, 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. Other systems of notation for chords include:10 plain staff notation, used in classical music,11 figured bass, much used in the Baroque era, and macro symbols, sometimes used in modern musicology. 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, Catalan and Serbian 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 adopted 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 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: I for one thousand V for five thousand |I| for one hundred thousand |V| for five hundred thousand 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. 1630 on the Westerkerk in Amsterdam Roman numerals, 16th century 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 IƆ and CIƆ, respectively. 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   CCIƆƆƆƆ = 15,000 CCCIƆƆƆƆƆ = 105,000 3 extra Ɔs IƆƆƆ = 50,000     CCCIƆƆƆƆƆƆ = 150,000 Sometimes CIƆ was reduced to a lemniscate symbol (ↀ) 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 ↁ; and 10,000 (CCIƆƆ) was reduced to ↂ. 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.12 Modern number Medieval abbreviation Notes 5 A Resembles an upside-down V. Also said to equal 500. 6 ↅ Either a ligature of VI, or the Greek letter stigma (Ϛ), having the same numerical value.13 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. 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 5−1, 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 5+1 VII 7 VIII 8 IIX was used rarely in the Middle Ages. IX 9 10−1 X 10 VV was used rarely in the Middle Ages. XI 11 10+1 XII 12 XIII 13 XIV 14 10+(5-1) XV 15 XVI 16 XVII 17 XVIII 18 XIX 19 XX 20 XXI 21 XXV 25 XXX 30 XXXV 35 XL 40 50−10 XLV 45 XLIX 49 Per rule above, IL would not be generally accepted. L 50 LX 60 50+10 LXIX 69 50+10+(10-1) LXX 70 The abbreviation for the Septuagint LXXVI 76 50+10+10+(5+1) LXXX 80 XC 90 100−10 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. CX 110 100+10 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 MCMXCIX 1,999 Shortcuts like IMM and MIM disagree with the rule stated above MM 2,000 MMI 2,001 MMX 2,010 MMXII 2,012 1000+1000+10+1+1 MMD 2,500 MMM 3,000 MMMDCCCLXXXVIII 3,888 1000+1000+1000+500+100+100+100+50+10+10+10+5+1+1+1 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 MMMMcitation 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 MMMDCCCLXXXVMMMDCCCLXXXVIII 3,888,888 Longest number (most symbols, about half with one line above them) MMMCMXCIXMMMCMXCIX 3,999,999 Largest number 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 Forms14 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 (Ⅻ 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 archaic14 forms of 1000, 5000, 10,000, large reversed C (Ɔ), late 6 (ↅ, similar to Greek Stigma: Ϛ), early 50 (ↆ, similar to down arrow ↓⫝⊥13), 50,000, and 100,000. Note that the small reversed c, ↄ is not intended to be used in roman numerals, but as lower case Claudian letter Ↄ, Table of Roman numerals in Unicode Code x= 0 1 2 3 4 5 6 7 8 9 A B C D E F Value15 1 2 3 4 5 6 7 8 9 10 11 12 50 100 500 1,000 U+216x Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ Ⅻ Ⅼ Ⅽ Ⅾ Ⅿ U+217x ⅰ ⅱ ⅲ ⅳ ⅴ ⅵ ⅶ ⅷ ⅸ ⅹ ⅺ ⅻ ⅼ ⅽ ⅾ ⅿ Value 1000 5000 10,000 – – 6 50 50,000 100,000 U+218x ↀ ↁ ↂ Ↄ ↄ ↅ ↆ ↇ ↈ 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. If using blackletter or script typefaces, Roman numerals are set in Roman type. Such typefaces may contain Roman numerals matching the style of the typeface in the Unicode range U+2160–217F; if they don't exist, a matching Antiqua typeface is used for Roman numerals. Programming Conversion The following is a C++ algorithm for translating a decimal (up to 3999) into a Roman Numerical System: #include <string> using std::string; string decimal2roman(int input) { const string roman13 = { "M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"}; const int decimal13 = {1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1}; string romanvalue = ""; for (int i = 0; i < 13; i++) { while (input >= decimali) { input -= decimali; romanvalue += romani; } } return romanvalue; } 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. See also Roman arithmetic Roman abacus Kharosthi#Numerals Urnfield culture numerals References ^ Or more precisely, "a decimal system in which the number 5 is an auxiliary base" (Ifrah 200:193) ^ Sturmer, Julius W. Course in Pharmaceutical and Chemical Arithmetic, 3rd ed. (LaFayette, IN: Burt-Terry-Wilson, 1906). p25 Retrieved on 2010-03-15. ^ 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. ^ Roman numerals: How they work: Larger numbers ^ 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. ^ "Asimov On Numbers" - Isaac Asimov - published by Pocket Books, a division of Simon & Schuster, Inc. 1966, 1977 - page 9. ^ W.I. Milham, Time & Timekeepers (New York: Macmillan, 1947) p. 196 ^ FAQ: Roman IIII vs. IV on Clock Dials - Donn Lathrop's page on IIII vs. IV - Copyright © UBR, Inc., 1996-2007. ^ Paul Lewis, Clocking the fours: A new theory about IIII ^ Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p. 77. Seventh Edition. ISBN 978-0-07-294262-0. ^ Arnold Schoenberg, Structural Functions of Harmony, Faber and Faber, 1983, p.1-2. ^ Capelli, A. Dictionary of Latin Abbreviations. 1912. ^ a b Perry, David J. Proposal to Add Additional Ancient Roman Characters to UCS. ^ a b Unicode Number Forms ^ For the first two rows Menninger, Karl (1992). Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications. ISBN 978-0-486-27096-8.  External links Look up Appendix:Roman numerals or roman numeral in Wiktionary, the free dictionary. 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