# Roman numerals

### 2008/9 Schools Wikipedia Selection. Related subjects: Mathematics

**Roman numerals** are 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.

Numeral systems by culture | |
---|---|

Hindu-Arabic numerals | |

Indian Eastern Arabic Khmer |
Indian family Brahmi Thai |

East Asian numerals | |

Chinese Suzhou Counting rods |
Japanese Korean |

Alphabetic numerals | |

Abjad Armenian Cyrillic Ge'ez |
Hebrew Greek (Ionian) Āryabhaṭa |

Other systems | |

Attic Babylonian Egyptian Etruscan |
MayanRomanUrnfield |

List of numeral system topics | |

Positional systems by base | |

Decimal (10) | |

2, 4, 8, 16, 32, 64 | |

1, 3, 9, 12, 20, 24, 30, 36, 60, more… | |

## Symbols

Symbol | Value |
---|---|

I | 1 (one) (unus) |

V | 5 ( five) (quinque) |

X | 10 ( ten) (decem) |

L | 50 ( fifty) (quinquaginta) |

C | 100 ( one hundred) (centum) |

D | 500 ( five hundred) (quingenti) |

M | 1000 ( one thousand) (mille) |

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*. Sometimes, especially in medical prescriptions, 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:

- II or ii for two.
- III or iii for three.
- IV or iv for four
- V or v for five
- VI or vi for six
- VII or vii for seven
- VIII or viii for eight
- IX or ix for nine
- X for 10
- XI or xi for eleven
- XXXII or xxxii for thirty-two
- XLV or xlv for forty-five

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

- V for five thousand
- X for ten thousand
- L for fifty thousand
- C for one hundred thousand
- D for five hundred thousand
- M for one million

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

Thus I descends not from the letter I but from a notch scored across the stick. Every fifth notch was double cut (i.e. ⋀, ⋁, ⋋, ⋌, *etc.*), and every tenth was cross cut (X), IIIIΛIIIIXIIIIΛIIIIXII…, much like European tally marks today. This produced a positional system: *Eight* on a counting stick was eight tallies, IIIIΛIII, or the eighth of a longer series of tallies; either way, it could be abbreviated ΛIII (or VIII), as the existence of a Λ implies four prior notches. By extension, *eighteen* was the eighth tally after the first ten, which could be abbreviated X, and so was XΛIII. Likewise, number *four* on the stick was the I-notch that could be felt just before the cut of the Λ (V), so it could be written as either IIII or IΛ (IV). Thus the system was neither additive nor subtractive in its conception, but * ordinal*. When the tallies were transferred to writing, the marks were easily identified with the existing Roman letters I, V, X.

The tenth V or X along the stick received an extra stroke. Thus 50 was written variously as N, И, K, Ψ, ⋔, *etc.*, but perhaps most often as a chicken-track shape like a superimposed V and I - 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 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, 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".

## 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 *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.

## Fractions

Though the Romans used a decimal system for whole numbers, reflecting how they counted in Latin, they used a duodecimal system for fractions, because the divisibility of twelve (12 = 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" (quinquae 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, dodrantisor nonuncium, nonuncii |
"less a quarter" (de-quadrans → dodrans)or "ninth ounce" (nona uncia → nonuncium) |

10/12 = 5/6 | S•••• or S:: |
dextans, dextantisor 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 dice faces ⚄) 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
(from**sescuncia, sescunciae***sesqui-*+*uncia*, i.e. 1½ uncias), represented by a sequence of the symbols for the semuncia and the uncia. - 1/24
(from**semuncia, semunciae***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
("two sextulas") or**binae sextulae, binarum sextularum**, represented by a sequence of two reversed S.**duella, duellae** - 1/48
, represented by a reversed C.**sicilicus, sicilici** - 1/72
(1/6 of an uncia), represented by a reversed S.**sextula, sextulae** - 1/144
("half a sextula"), represented by a reversed S crossed by a horizontal line.**dimidia sextula, dimidiae sextulae** - 1/288
, represented by a symbol resembling Cyrillic letter Э.**scripulum, scripuli** - 1/1728
, represented by a symbol resembling closing guillemets ».**siliqua, siliquae**

## 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 Roman god Jupiter, whose Latin name, IVPPITER, 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 *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.

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. In Dubrovnik, Croatia, a commemorative inscription marking the 1000th anniversary of King Tomislav’s coronation (Croatia’s first King), appears as DCCCCXXV - MDCCCCXXV (925 -1925).

### 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 the exception of square faced watches and clocks, where the opposite number is X).
- 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, 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. (However,*nine*is written IX on clocks, and the IV notation is ordinal rather than subtractive in origin.) - As noted above, it has been suggested that since IV is the first two letters of IVPITER (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, 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 nomenclature of inorganic compounds, only IV should be used. For example MnO_{2} should be named manganese (IV) oxide; manganese (IIII) oxide is unacceptable.

## XCIX vs. IC

Rules regarding Roman numerals often state that a symbol representing 10^{n} may not precede any symbol larger than 10^{n+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 (using decimal places -- 90 (XC) then 9 (IX)), not as the "shortcut" IC.

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.

However, these rules are not universally followed.

Modern Roman numerals are written by expressing each digit separately starting with the left most digit and skipping any digit with a value of zero. To see this in practice, consider the above example of 1990. In Roman numerals 1990 is rendered: 1000=M, 900=CM, 90=XC; resulting in MCMXC. 2008 is written as 2000=MM, 8=VIII; or MMVIII.

## 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 periods, 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: 2008 can be represented as MMVIII. They are also sometimes used in the credits of movies and television programs to denote the year of production, particularly programs made by the BBC and CBS.

## 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, if any, credits shown at the end of a television show or film.
- Some faces of clocks and timepieces show hours in Roman numerals.
- Names of monarchs and Popes 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 Super Bowl number is shown using Roman numerals.
- The Sprint All-Star Race is shown using Roman numerals.
- Film series and sequels are often numbered with Roman numerals.
- Army Corps are typically named using Roman numerals.
- Names of phases of ice.
- Names of cranial nerves.

There are many other places as well.

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, 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 WWE'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 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 centre 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". This is particularly amusing in the case of Callisto, because, as mentioned above, the notation IV was mostly disused by the Romans for its similarity to the first two letters of Jupiter. With recent discoveries—Jupiter currently has 63 known satellites—as well as computerization, this is somewhat disparaged for the minor worlds, at least in computerized listings. Science fiction, and not astronomy *per se*, has adopted the use for numbering the planets around a star; e.g., Planet Earth is called " Sol III".

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

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

In music theory, while scale degrees are typically represented with Arabic numerals, often modified with a caret or circumflex, the triads that have these degrees as their roots are often identified by Roman numerals (as in chord symbols). See also diatonic functions. Upper-case Roman numerals indicate major triads while lower-case Roman numerals indicate minor triads, as the following chart illustrates. 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.

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 | (b)VII | vii^{°} |

Scale degree(minor mode) |
tonic | supertonic | mediant | subdominant | dominant | submediant | subtonic | leading tone |

In law, the Controlled Substances Act's five drug schedules are represented with Roman numerals.

Roman numerals often appear in crossword 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 Catalan, the French, the Hungarian, the Portuguese, the Polish, the Romanian, the Russian and the Spanish 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 Poland, Russia, and in Portuguese and Romanian 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 May 1 to August 31.

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 9:30AM 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.

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 | — |

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

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

In 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 '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 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 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 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 I followed by an *apostrophus* (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 an 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*. This practice is now merely an antiquarian's note; it is never used.

### 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 they have fallen into disfavor and primarily out of use.

Modern number |
Medieval abbreviation |
Notes |
---|---|---|

5 | A | Resembles an upside-down V. Also said to equal 500. |

7 | S, Z | Presumed abbreviation of septem, Latin for 7. |

11 | O | |

40 | F | Presumed abbreviation of English forty. |

70 | S | Also could stand for 7, and has same etymology. |

80 | R | |

90 | N | Presumed abbreviation of nonaginta, Latin for 90. |

150 | Y | Possibly derived from the lowercase y's shape. |

151 | K | This unusual abbreviation's origin is unknown; it has also been said to stand for 250. |

160 | T | Possibly derived from Greek tetra, as 4 x 40 = 160. |

200 | H | |

250 | E | |

300 | B | |

400 | P, G | |

500 | Q | Redundant with D, abbreviation for quingenti, Latin for 500. |

800 | W | More properly, the Greek ω, as W was a fairly new creation. |

900 | ĵ, ↑ | Resembled a crooked up arrow. |

2000 | Z |

## Modern Roman numerals

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

Standard | Arabic | Notes |
---|---|---|

none | 0 | N was used at least once (by Bede about 725). |

I | 1 | |

II | 2 | |

III | 3 | |

IV | 4 | IIII is still used on clock and card faces. See Calendars and clocks above. |

V | 5 | IIIII was used rarely in the Middle Ages. |

VI | 6 | |

VII | 7 | |

VIII | 8 | IIX was used rarely in the Middle Ages. |

IX | 9 | 10-1 |

X | 10 | VV was used rarely in the Middle Ages. |

XI | 11 | |

XII | 12 | |

XIII | 13 | |

XIV | 14 | |

XV | 15 | |

XVI | 16 | |

XVII | 17 | |

XVIII | 18 | |

XIX | 19 | |

XX | 20 | |

XXV | 25 | |

XXX | 30 | |

XL | 40 | 50-10 |

L | 50 | |

LX | 60 | |

LXIX | 69 | |

LXX | 70 | The abbreviation for the Septuagint |

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". |

CC | 200 | |

CCC | 300 | |

CD | 400 | 500-100 |

D | 500 | |

DC | 600 | |

DCLXVI | 666 | Using every symbol but M in order gives the beast number. |

DCC | 700 | |

DCCC | 800 | |

CM | 900 | 1000-100 |

M | 1000 | MIX=1009 |

MCDXLIV | 1444 | Smallest pandigital number (each symbol is used) |

MDCLXVI | 1666 | Largest efficient pandigital number (each symbol occurs exactly once) |

MCMXLV | 1945 | |

MCMXCVII | 1997 | |

MCMXCIX | 1999 | Shortcuts like IMM and MIM disagree with the rule stated above |

MM | 2000 | |

MMVIII | 2008 | |

MMD | 2500 | |

MMM | 3000 | |

MMMM | 4000 | Not MV |

V | 5000 | |

VMDCLXVI | 6666 | This number uses every symbol up to V once. |

X | 10000 | |

L | 50000 | |

C | 100000 | |

D | 500000 | |

M | 1000000 |

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 ⅯⅭⅯⅬⅩⅩⅩⅧ. 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 alternate forms of 1000, 5000, and 10000.

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

U+2160 | Ⅰ | Ⅱ | Ⅲ | Ⅳ | Ⅴ | Ⅵ | Ⅶ | Ⅷ | Ⅸ | Ⅹ | Ⅺ | Ⅻ | Ⅼ | Ⅽ | Ⅾ | Ⅿ |

U+2170 | ⅰ | ⅱ | ⅲ | ⅳ | ⅴ | ⅵ | ⅶ | ⅷ | ⅸ | ⅹ | ⅺ | ⅻ | ⅼ | ⅽ | ⅾ | ⅿ |

U+2180 | ↀ | ↁ | ↂ | Ↄ | ↄ |

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 regular Latin letters are preferred. Displaying these characters requires a program that can handle Unicode and a font that contains appropriate glyphs for them.

## Games

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

## 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.

**L**ucky**C**ows**D**rink**M**ilk**L**ucy**C**an't**D**rink**M**ilk**L**azy**C**ows**D**on't**M**oo**L**ittle**C**ats**D**rink**M**ilk**LCD****M**onitor

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

**M**y**D**ear**C**at**L**oves**X**tra**V**itamins**I**ntensely