Roman Numerals

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Roman numerals is a numeral system originating in ancient Rome, adapted from Etruscan numerals. The system used in classical antiquity was slightly modified in the Middle Ages to produce the system we use today. It is based on certain letters which are given values as numerals.

Roman numerals are commonly used today in numbered lists (in outline format), clockfaces, pages preceding the main body of a book, chord triads in music analysis, the numbering of movie publication dates, successive political leaders or children with identical names, and the numbering of some sport events, such as the Olympic Games or the Super Bowl.

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

Symbols There are seven basic Roman numerals.

{| class="wikitable"! Symbol! Value|-| I) ()|-| [V) ()|-| [X) ()|-| [L) ()|-| [C) ()|-| [D) ()|-| [M) ()|}

Multiple symbols may be combined to produce numbers in between these values, subject to certain rules on [repetition. In cases where it may be shorter, it is sometimes allowable to place a smaller, subtractive, symbol before a larger value, so that, for example, one may write IV or iv for four, rather than iiii. Again, for the numbers not assigned a specific symbol, the above given symbols are combined:

II or ii for 2 (number)
III or iii for 3 (number). The final character is sometimes "j" instead of "i", often in medical prescriptions.
IV, iv, IIII, or iiii for 4 (number)
VI or vi for 6 (number)
VII or vii for 7 (number)
VIII or viii for 8 (number)
IX or ix for 9 (number)
XXXII or xxxii for 32 (number)
XLV or xlv for 45 (number)

For large numbers (4000 and above), a bar is placed above a base numeral to indicate multiplication by 1000:

for 5000 (number)
for 10000 (number)
for fifty thousand
for 100000 (number)
for five hundred thousand
for 1000000 (number)

For very large numbers, there is no standard format, although sometimes a double bar or underline is used to indicate multiplication by 1,000,000. That means an underlined X (X) is ten million.

Origins Although the Roman numerals are now written with letters of the Roman alphabet, they were originally separate symbols. The Etruscans, for example, used I Λ X 8 ⊕ for I V X L C M.

They appear to derive from notches on tally sticks, such as those used by Italy and Dalmatian shepherds into the 19th century. Thus, the I descends from a notch scored across the stick. Every fifth notch was double cut (i.e. , , , , etc.), and every tenth was cross cut (X), much like European tally marks today. This produced a positional system: Eight on a counting stick was eight tallies, IIIIΛIII, but this could be abbreviated ΛIII (or VIII), as the existence of a Λ implies four prior notches. Likewise, number four on the stick was the I-notch that could be felt just before the cut of the V, so it could be written as either IIII or IV. Thus the system was neither additive nor subtractive in its conception, but ordinal number. When the tallies were later transferred to writing, the marks were easily identified with the existing Roman letters I, V, X.

(A 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.)

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 Caesar 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, was written variously as >I< or , was then shortened to or C, with C finally winning out because, as a letter, it stood for (Latin for "hundred").

The hundredth V or X was marked with a box or circle. Thus 500 was like a superposed on a or (that is, like a Þ with a cross bar), becoming a struck-through D or a Ð by the time of Augustus, under the graphic influence of the letter D. It was later identified the letter D, perhaps as an abbreviation of "half-thousand". Meanwhile, 1000 was a circled X: , , ⊕, and by Augustinian times was partially identified with the Greek letter Φ. It then evolved along several independent routes. Some variants, such as Ψ and CD (more accurately a reversed D adjacent to a regular D), were historical dead ends (although one folk etymology later identified D for 500 as half of Φ for 1000 because of this CD variant), while two variants of survive to this day. One, , led to the convention of using parentheses to indicate multiplication by 1000 (later extended to double parentheses as in , , etc.); in the other, became and , eventually changing to M under the influence of the word ("thousand").

Zero In general, the number 0 (number) did not have its own Roman numeral, but a primitive form (nulla) was known by medieval computus (responsible for calculating the date of Easter). They included zero (via the Latin word meaning "none") as one of nineteen epacts, or the age of the moon on March 22. The first three epacts were nullae, 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 nullae, in a table of epacts, all written in Roman numerals.

A notation for the value zero is quite distinct from the role of the digit zero in a positional notation system. The lack of a zero digit may have prevented Roman numerals from being developed into a positional notation, and led to their gradual replacement by Hindu-Arabic numerals in the early second millennium. On the other hand, it may have been the lack of positional notation that prevented the Romans from developing a zero.

Fractions

Even though the Romans used a decimal system for whole numbers, reflecting Latin, they used a duodecimal system for rational numbers, because the divisibility of twelve (12 = 3×4) makes it easier to handle the common Fraction (mathematics)s of 1/3 and 1/4 than in a system based on ten (10 = 2×5). On coins, many of which had values that were duodecimal fractions of the unit , they used a notational system similar to that of whole numbers, but based on twelfths and one halves rather than units and fives. A dot • indicated an (one twelfth, the source of the English words inch and ounce), and dots were added together up to five twelfths. Then one half (six twelfths) was notated using the letter S for ("half"). Dots were added to S for the 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 its own name, which was also the name used for the corresponding coin:

{] 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 (from sesqui- + uncia, i.e. 1 uncias), represented by a sequence of the symbols for the semuncia and the uncia.
1/24 (from semi- + uncia, i.e. of an uncia), represented by several variant glyphs deriving from the shape of Greek letter sigma , one variant resembling the pound sign without the horizontal line(s) and another resembling Cyrillic letter .
1/36 ("two sextulas") or , represented by a sequence of two reversed S.
1/48 , represented by a reversed C.
1/72 (1/6 of an uncia), represented by a reversed S.
1/144 ("half a sextula"), represented by a reversed S crossed by a horizontal line.
1/288 , represented by a symbol resembling Cyrillic letter .
1/1728 , represented by a symbol resembling closing guillemets ».

IIII vs. IV , London. The numeral translates to 1910.|thumbThe notation of Roman numerals has varied through the centuries. Originally, it was common to use IIII to represent four, because IV represented the Roman mythology Jupiter (mythology), whose Latin name, IVPITER, begins with IV. The subtractive notation (which uses IV instead of IIII) has become universally used 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 or “two from twenty”; the number 19 was 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.

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. Another notable example is on Harvard Medical School's Gordon Hall, which reads MDCCCCIIII for 1904.

Another likely tale is that the low literacy rate made it difficult for some to do subtraction, where the IIII notation could simply be counted.

Calendars and clocks 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:

The four-character form IIII creates a visual symmetry with the VIII on the other side, which IV would not.
With IIII, the number of symbols on the clock totals twenty I's, four V's, and four X's, so clock makers need only a single mold with a V, five I's, 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 IX’s are rotated 180° to form XI and XII. The alternative with IV uses seventeen I's, five V's, and four X's, possibly requiring the clock maker to have several different molds.

IIII was the preferred way for the ancient Romans to write four, since they to a large extent avoided subtraction.
As noted above, it has been suggested that since IV is the first two letters of Jupiter (god) (Jupiter), the main god of the Romans, it was not appropriate to use.
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.
IV is difficult to read upside down and on an angle, particularly at that location on the clock.
Louis XIV of France, king of France, preferred IIII over IV, ordered his clockmakers to produce clocks with IIII and not IV, and thus it has remained.W.I. Milham, Time & Timekeepers (New York: Macmillan, 1947) p. 196

Chemistry As it relates to the IUPAC nomenclature of inorganic chemistry, only IV should be used. For example MnO2 should be named manganese (IV) oxide; manganese (IIII) oxide is unacceptable.

Modern usage The Roman number system is generally regarded as obsolete in modern usage, but is still seen in certain institutions to this day.Below are a few examples of its current use.

The year and/or credits given at the end of a television show or film.
Some faces of clocks and timepieces show hours in Roman numerals.
Names of monarchies are still displayed in Roman numerals, e.g. George VI.
Postmarks often display Roman numerals.
Books (particularly older ones) are dated in Roman numerals, and display preliminary pages in Roman numbers. Volume numbers on spines can also be in Roman numerals.

There are many other places as well.

XCIX vs. IC? Rules regarding Roman numerals often state that a symbol representing 10x may not precede any symbol larger than 10x+1. For example, C cannot be preceded by I or V, only by X (or, of course, by a symbol representing a value equal to or larger than C). Thus, one should represent the number ninety-nine as XCIX, not as the "shortcut" IC. However, these rules are not universally followed.

This problem manifested in such questions as why 1990 was not written as MXM instead of the universal usage MCMXC, or why 1999 was not written simply IMM or MIM as opposed to the universal MCMXCIX.

Year in Roman numerals In seventeenth century Europe, using Roman numerals for the year of publication for books was standard; there were many other places it was used as well. Publishers attempted to make the number easier to read by those more accustomed to Arabic positional numerals. On British title pages, there were often spaces between the groups of digits: M DCC LX I (relating to 1000 700 60 1 or 1761) is one example. This may have come from the French, who separated the groups of digits with full stops, as: M.DCC.LXI. or M. DCC. LXI. Notice the period at the end of the sequence; many countries did this for Roman numerals in general, but not necessarily Britain. (Periods were also common on each side of numerals in running text, as in "commonet .iij. viros illos".)

These practices faded from general use before the start of the twentieth century, though the cornerstones of major buildings still occasionally use them. Roman numerals are today still used on building faces for dates: 2007 can be represented as MMVII. They are also sometimes used in the closing credits of movies and television programs to denote the year of production, particularly programs made by the BBC and CBS.

Other modern usage , Greenwich with Roman numbers up to XXIII (and 0), in Greenwich

Roman numerals remained in common use until about the 14th century, when they were replaced by 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 use of Roman numerals today is mostly restricted to ordinal numbers, such as volumes or chapters in a book or the numbers identifying monarchs or popes (eg. Elizabeth II of the United Kingdom, Pope Benedict XVI, etc.).

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.

Modern English usage also employs Roman numerals in many books (especially anthologies), movies (eg. Star Trek and Star Wars), sporting events (eg. the Olympic Games, the Super Bowl, and World Wrestling Entertainment's WrestleMania), historic events (eg. World War I, World War II), and computer or videogames (eg. Final Fantasy, King's Quest, Tales Of Symphonia). The common unifying theme seems to be stories or events that are episodic or annual in nature, with the use of classical numbering suggesting importance or timelessness.

Sports teams can be referred to as the number of players in the squad with roman numerals. 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.

In chemistry, Roman numerals were used to denote the periodic table 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.

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 moonss of Jupiter are numbered, and later by order of discovery; e.g., Callisto (moon) was "Jupiter IV" or "J IV". 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 earthquake seismology, Roman numerals are used to designate degrees of the Mercalli intensity scale.

In music theory, while scale degrees are typically represented with Arabic numerals, often modified with a caret or circumflex, the triad (music)s 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. In the major mode the triad on the seventh scale degree, the leading tone triad, is diminished chord.

{| class="wikitable"|Roman numeral ||align=center| I ||align=center| ii ||align=center| iii ||align=center| IV ||align=center| V ||align=center| vi ||align=center| vii°|-|Scale degree
(major mode) || tonic (music) || supertonic ] || subdominant ] || submediant ]/[subtonic puzzles. For example, the answer to the clue "half of MCIV" would be "DLII", or the answer to the clue "Ovid's 552" would also be "DLII".

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 which are unknown in English-speaking regions.

The Catalan language, the French language, the Portuguese language, the Polish language, the Romanian language, the Russian language and the Spanish language 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 usually take the opposite approach, basing names of centuries on the digits of the years; for example is the common Italian name for , the fifteenth century.) Some scholars in English-speaking countries have adopted the former method, among them L. Sprague de Camp.

In Poland, Russia, and in Spanish language, Portuguese language and Romanian language 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 Kremlin Wall Necropolis, 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 May 1 to August 31.Note, though, that Spanish journalists use another format with the month's initial for certain dates even if it may be ambiguous: 11-M marks the bombing of trains in Madrid on 11 March de 2004, not 11 May.

In Eastern Europe, especially the Baltic Sea 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 9:30AM to 5:30PM on Mondays, Wednesdays, and Thursdays; 9:30AM to 7:00PM on Tuesdays and Fridays; and 9:30AM to 1:00PM on Saturdays; and which is closed on Sundays.{] 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 Romania, 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 ''.

In Poland, Roman numerals are used for ordinals in names of some institutions. In particular high schools ("" - 5th High School in Kraków), tax offices ("" - 2nd tax office in Gdańsk) and courts ("" - District Court, 1st Civil Division) - use Roman numerals. Institutions that use "" notation always use Arabic numerals. These include elementary ("") and middle schools ("").

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:

for 1000 (number)
for 5000 (number)
|| for 100000 (number)
|| 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. , and in certain font-faces, particularly Times New Roman, the capital letters when used without spaces simulates the appearance of the under/over bar, eg. MCMLXVII, which is often exaggerated when written by hand.

Sometimes 500, usually D, was written as followed by an apostrophus, resembling a backwards C (), while 1,000, usually M, was written as . 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 , respectively.

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

{] 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 hyperbole used to represent very large numbers. Similarly, 5,000 () was reduced to ; and 10,000 () 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. This practice is now merely an antiquarian's note; it is never used. (It did, however, lead to the Dutch language diphthong IJ (letter).)

Table of Roman numerals The "modern" Roman numerals, post-Victorian era, are shown below:{]|N was used at least once (by Bede about 725).]||-|colspan=2|II|2 (number)||-|colspan=2|III|3 (number)||-|colspan=2|IV|4 (number)|IIII is still used on clock and card faces.|-|colspan=2|V|5 (number)|IIIII was used rarely in the Middle Ages.|-|colspan=2|VI|6 (number)||-|colspan=2|VII|7 (number)||-|colspan=2|VIII|8 (number)|IIX was used rarely in the Middle Ages.|-|colspan=2|IX|9 (number)||-|colspan=2|X|10 (number)|VV was used rarely in the Middle Ages.|-|colspan=2|XI|11 (number)||-|colspan=2|XII|12 (number)||-|colspan=2|XIII|13 (number)||-|colspan=2|XIV|14 (number)||-|colspan=2|XV|15 (number)||-|colspan=2|XVI|16 (number)||-|colspan=2|XVII|17 (number)||-|colspan=2|XVIII|18 (number)||-|colspan=2|XIX|19 (number)||-|colspan=2|XX|20 (number)||-|colspan=2|XXV|25 (number)||-|colspan=2|XXX|30 (number)||-|colspan=2|XL|40 (number)||-|colspan=2|L|50 (number)||-|colspan=2|LX|60 (number)||-|colspan=2|LXIX|69 (number)||-|colspan=2|LXX|70 (number)|The abbreviation for the Septuagint||-|colspan=2|XC|[90 (number)||-|colspan=2|XCIX|99 (number)|As opposed to the "shortcut" way IC seen #XCIX or IC?.|-|colspan=2|C|100 (number)|This is the origin of using the slang term "C-bill" or "C-note" for "U.S. hundred dollar bill".|-|colspan=2|CC|200 (number)||-|colspan=2|CCC|300 (number)||-|colspan=2|CD|400 (number)||-|colspan=2|D|500 (number)||-|colspan=2|DC|600 (number)||-|colspan=2|DCLXVI|666 (number)|Using every basic symbol but M once gives the Number of the Beast (numerology).|-|colspan=2|DCC|700 (number)||-|colspan=2|DCCC|800 (number)||-|colspan=2|CM|900 (number)||-|colspan=2|M|1000 (number)|MIX=1009|-|colspan=2|MCDXLIV|1000 (number)|Smallest pandigital number (each symbol is used)]|Largest efficient pandigital number (each symbol occurs exactly once)|-|colspan=2|MCMXLV|1000 (number)||-|colspan=2|MCMXCVII|1997 (number)|-|colspan=2|MCMXCIX|1000 (number)|Shortcuts like IMM and MIM disagree with the rule stated #XCIX or IC|-|colspan=2|MM|2000 (number)||-|colspan=2|MMVII|2007 (number)||-|colspan=2|MMD|2500 (number)||-|colspan=2|MMM|3000 (number)||-|MMMM||4000 (number)|Not M|-|||5000 (number)|I followed by two reversed C, an adapted Greek alphabet sign|-|colspan=2|MDCLXVI|6000 (number)|This number uses every symbol up to once.|-|colspan=2||[10000 (number)|10000||}

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 range from U+2160 to U+2183. For example, MCMLXXXVIII could alternatively be written as. 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 alternate forms of 1000, 5000, and 10000.

{] with other character set standards which provide these characters. For ordinary uses, the regular Latin letters are preferred. Displaying these characters requires a program that can handle Unicode and a typeface 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.

Mnemonic devices There are several mnemonics that can be useful in remembering the Roman numeral system.

The following mnemonics recall the order of Roman numeral values above ten, with L being 50, C being 100, D being 500, and M being 1000.

Lucky Cows Drink Milk
Lucy Can't Drink Milk
Lazy Cows Don't Moo
Little Cats Drink Milk
Little Children Do Math
LCD Monitor

A longer mnemonic helps to recall the order of Roman numerals from large to small.

My Dear Cat Loves Xtra Vitamins Intensely

References