ROMAN NUMERALS

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 decimal [1]  but not directly positional and does not

include a zero. It is a cousin of the Etruscan numerals, and the letters derive from

earlier non-alphabetical symbols; over time the Romans came to identify the

symbols with letters of the Latin alphabet. The system was modified slightly during

theMiddle 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.

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 ofi. It is used today, especially in medical

prescriptions, to prevent tampering with or misinterpretation of a number after it is

written.[2][3]

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 MM

MMMM IV V VI VII VIII IX

Ten thousands X XX XXX XL L LX LXX LXXX XC

Hundred

thousandsC 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 duodecimalsystem 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 unitas, 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:

FractionRoman

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 =

5/6S•••• 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 IV[citation 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 undevigintior "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.

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 W XII , K XII , W XIX , WP VI , 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 ofJupiter 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

In music theory, while scale degrees are typically represented with Arabic numerals,

often modified with a caret or circumflex, thetriads 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

subdominan

tdominant

submedian

tleading tone

Roman

numerali ii° (♭)III iv v (♭)VI (♭)VII vii°

Scale degree

(minor

mode)

tonic supertonic mediant subdominantdominan

tsubmediant

subtoni

c

leading

tone

Also:

Roman numeral I II III IV V VI VII

Scale degree

(major mode)tonic supertonic mediant

subdominan

tdominant

submedian

tleading tone

Roman numeral i ii iii iv v vi vii

Scale degree

(minor mode)tonic

supertoni

cmediant subdominant

dominan

tsubmediant 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 modernmusicology.

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, Croat

ian, Catalan and Serbian languages use capital Roman numerals to denote centuries.

For example, XVIIIrefers 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 Amsterdamare 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 =

1,000CCIƆƆ = 10,000 CCCIƆƆƆ = 100,000

1 extra Ɔ IƆ = 500CIƆƆ =

1,500

CCIƆƆƆ =

10,500CCCIƆƆƆƆ = 100,500

2 extra Ɔs IƆƆ = 5,000  CCIƆƆƆƆ =

15,000

CCCIƆƆƆƆƆ =

105,000

3 extra ƆsIƆƆƆ =

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 ↅEither 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 KThis 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 0N for nulla was used at least once (by Bede about

725).

I 1

II 2

III 3

IV 45−1, 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 49Per 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 499Per rule above, ID would not be generally

accepted.

D 500

DC 600

DCLXVI 666Using every symbol except M in descending order

gives the beast number.

DCC 700

DCCC 800

CM 900

CMXCIX 999Per rule above, IM would not be generally

accepted.

M 1,000

MCDXLIV 1,444 Smallest pandigital number (each symbol is used)

MDCLXVI 1,666Largest efficient pandigital number (each symbol

occurs exactly once)

MCMXC 1,990Shortcuts like XMM and MXM disagree with the

rule stated above

MCMXCIX 1,999Shortcuts 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 3,999Largest number without an overline at any

symbol.

IV 4,000 sometimes MMMM[citation needed] or MV

V 5,000

VMDCLXVI 6,666 This number uses every symbol up to V once.

X 10,000

L 50,000

C100,00

0

D500,00

0

M1,000,0

00

MCDXLIV1,444,0

00

Smallest pandigital number (each symbol is used

with one line above every symbol)

MDCLXVI1,666,0

00

Largest efficient pandigital number (each symbol

is used with one line above every symbol)

MM2,000,0

00

MMMDCCCLXXXVMMMDCCC 3,888,8 Longest number (most symbols, about half with

LXXXVIII 88 one line above them)

MMMCMXCIXCMXCIX3,999,9

99Largest 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 Forms[14] 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 archaic[14] 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

Value[15] 1 2 3 4 5 6 7 8 9 10 11 12 50 10050

01,000

U+21

6xⅠ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ Ⅻ Ⅼ Ⅽ Ⅾ Ⅿ

U+21

7xⅰ ⅱ ⅲ ⅳ ⅴ ⅵ ⅶ ⅷ ⅸ ⅹ ⅺ ⅻ ⅼ ⅽ ⅾ ⅿ

Value 1000500

010,000 – – 6 50 50,000

100,00

0

U+21

8xↀ 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 roman[13] = { "M", "CM", "D", "CD", "C", "XC",

"L", "XL", "X", "IX", "V", "IV", "I"};

const int decimal[13] = {1000, 900, 500, 400, 100, 90,

50, 40, 10, 9, 5, 4, 1};

string romanvalue = "";

for (int i = 0; i < 13; i++) {

while (input >= decimal[i]) {

input -= decimal[i];

romanvalue += roman[i];

}

}

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.