Roman numerals

Roman numerals is a  originating in ancient, adapted from. The system used in was slightly modified in the  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 or the.

For arithmetics involving Roman numerals, see and.

Symbols
Multiple symbols may be combined to produce numbers in between these values, subject to certain rules on. 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. Sometimes, especially in s, a final i becomes j, such as iij for 3 or vij for 7. This was originally done to prevent forgery. Again, for the numbers not assigned a specific symbol, the above given symbols are combined:

For large numbers (4000 and above), a bar is placed above a base numeral to indicate by 1000:
 * II or ii for.
 * III or iii for.
 * IV, iv, IIII, or iiii for
 * VI or vi for
 * VII or vii for
 * VIII or viii for
 * IX or ix for
 * XXXII or xxxii for
 * XLV or xlv for
 * $\overline{V}$ for
 * $\overline{X}$ for
 * $\overline{L}$ for fifty thousand
 * $\overline{C}$ for
 * $\overline{D}$ for five hundred thousand
 * $\overline{M}$ for

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 independent symbols. The, 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 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, which continued to be used by and n shepherds into the 19th century.

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 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 . 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, 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, was then abbreviated to 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 superposed 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 CD (the latter more accurately a mirror image of a D, which is not supported by Unicode, adjacent to a regular D), 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,, 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  below.
 * In the other, became  and, eventually changing to M under the influence of the Latin word mille "thousand".

Zero
In general, the number did not have its own Roman numeral, but a primitive form (nulla) was known by medieval  (responsible for calculating the date of ). They included zero (via the word nulla meaning "none") as one of nineteen s, or the age of the moon on. The first three epacts were nullae, xi, and xxii (written in or lower case). The first known computist to use zero was in 525. Only one instance of a Roman numeral for zero is known. About 725, or one of his colleagues used the letter, 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 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 in the early. On the other hand, it may have been the lack of positional notation that prevented the Romans from developing a zero.

Fractions


Though the Romans used a system for s, reflecting how they counted in Latin, they used a  system for s, because the  of twelve (12 = 3×4) makes it easier to handle the common s of 1/3 and 1/4 than does a system based on ten (10 = 2×5). On s, many of which had values that were duodecimal fractions of the unit, 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 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:

The arrangement of the dots was variable and not necessarily linear. Five dots arranged like :·: (as on dice faces ) are known as a from the name of the Roman fraction/coin. The Latin words sextans and quadrans are the source of the English words and.

Other Roman fractions include:
 * 1/8 sescuncia, sescunciae (from  + uncia, i.e. 1½ uncias), represented by a sequence of the symbols for the semuncia and the uncia.
 * 1/24 semuncia, semunciae (from  + uncia, i.e. ½ uncia), represented by several variant glyphs deriving from the shape of Greek letter, one variant resembling the pound sign  without the horizontal line(s) and another resembling Cyrillic letter.
 * 1/36 binae sextulae, binarum sextularum ("two sextulas") or duella, duellae, represented by a sequence of two reversed S.
 * 1/48 sicilicus, sicilici, represented by a reversed C.
 * 1/72 sextula, sextulae (1/6 of an uncia), represented by a reversed S.
 * 1/144 dimidia sextula, dimidiae sextulae ("half a sextula"), represented by a reversed S crossed by a horizontal line.
 * 1/288 scripulum, scripuli, represented by a symbol resembling Cyrillic letter.
 * 1/1728 siliqua, siliquae, represented by a symbol resembling closing guillemets ».

IIII vs. 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, whose Latin name, IVPITER, begins with IV. The (which uses IV instead of IIII) has become universally used only in modern times. For example,, 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. 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, without conveying the benefits of a full system.

Likewise, on some buildings it is possible to see MDCCCCX, for example, representing 1910 instead of MCMX – notably in. The Leader Building in, at the corner of Superior Avenue and E.6th Street, is marked MDCCCCXII, representing 1912. Another notable example is on '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), 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.
 * , king of France, who preferred IIII over IV, ordered his clockmakers to produce clocks with IIII and not IV, and thus it has remained.

Chemistry
As it relates to the, 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 monarchs 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.
 * Outlines use I, II, III and i, ii, iii as part of their organizational structure..
 * The number is shown using Roman numerals.

There are many other places as well.

XCIX vs. IC
Rules regarding Roman numerals often state that a symbol representing 10n may not precede any symbol larger than 10n +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 s, 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, though the s of major buildings still occasionally use them. Roman numerals are today still used on building faces for dates: can be represented as MMVII. They are also sometimes used in the of movies and television programs to denote the year of production, particularly programs made by the  and.

Other modern usage


Roman numerals remained in common use until about the 14th century, when they were replaced by (thought to have been introduced to Europe from, by way of  traders and arithmetic treatises, around the 11th century). The use of Roman numerals today is mostly restricted to numbers, such as volumes or chapters in a book or the numbers identifying monarchs or popes (eg., , 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. and ), sporting events (eg. the, the , and 's ), historic events (eg. , ), and computer or videogames (eg. , , ). 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, the 1st XV of a particular club would be the 1st and best team the club has, likewise for the XIII in , and XI for , and.

In, Roman numerals were used to denote the in the. 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, the s or "moons" of the s are traditionally designated by capital Roman numerals, at first by order from the center of the planet, as the four s of are numbered, and later by order of discovery; e.g.,  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. , and not astronomy per se, has adopted the use for numbering the planets around a star; e.g., Planet Earth is called " III".

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

In, Roman numerals are used to designate degrees of the.

In, while s are typically represented with Arabic numerals, often modified with a or , the s that have these degrees as their roots are often identified by Roman numerals (as in s). See also s. Upper-case Roman numerals indicate major triads while lower-case Roman numerals indicate minor triads, as the following chart illustrates. In the the triad on the seventh scale degree, the leading tone triad, is.

Roman numerals often appear in puzzles. For example, "DLII" could be the answer to clues such as "Ovid's 552" or "half of MCIV".

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, the , the , the , the , the and the  languages use capital Roman numerals to denote centuries. For example, XVIII refers to the, 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 secolo XV, the .) Some scholars in English-speaking countries have adopted the former method, among them.

In, , and in , and  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, the month is written in Roman numerals while the day is in Arabic numerals: 14-VI-1789 is. This is how dates are inscribed on, 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 to. Note, though, that Spanish journalists use another format with the month's initial for certain dates even if it may be ambiguous: marks the bombing of trains in Madrid on  de 2004, not .

In, especially the 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. 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.

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. ( has since specified that dates should be given in all Arabic numerals, in formats.)

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

In, Roman numerals are used for. Likewise apartments in central 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, 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 tax office in Gdańsk) and courts ("I Wydział Cywilny Sądu Okręgowego" - District Court, 1st Civil Division) - use Roman numerals. Institutions that use "Instutition 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. The in  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:
 * $\overline{I}$ for
 * $\overline{V}$ for
 * $\overline{I}$| for
 * $\overline{V}$| 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. $\overline{MCMLXVII}$, and in certain font-faces, particularly , 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:

Sometimes was reduced to an  symbol  for denoting 1,000. 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 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  .)

Table of Roman numerals
The "modern" Roman numerals, post-, are shown below:

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
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  for numbers up to 12 ( or XII), mainly intended for the clock faces for  with large East-Asian character sets such as  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.

The characters in the range U+2160–217F are present only for 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 that contains appropriate glyphs for them.

Games
After the, the Roman system could also be used to write s. 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 s 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