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Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each letter with a fixed integer value, modern style uses only these seven:

I	V	X	L	C	D	M
1	5	10	50	100	500	1000

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some applications to this day.

One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as:

The notations IV and IX can be read as «one less than five» (4) and «one less than ten» (9), although there is a tradition favouring representation of «4» as «IIII» on Roman numeral clocks.^[1]

Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. MCM, signifying «a thousand, and a hundred less than another thousand», means 1900, so 1912 is written MCMXII. For the years of this century, MM indicates 2000. The current year is MMXXIII (2023).

Description

Roman numerals use different symbols for each power of ten and no zero symbol, in contrast with the place value notation of Arabic numerals (in which place-keeping zeros enable the same digit to represent different powers of ten).

This allows some flexibility in notation, and there has never been an official or universally accepted standard for Roman numerals. Usage in ancient Rome varied greatly and became thoroughly chaotic in medieval times. Even the post-renaissance restoration of a largely «classical» notation has failed to produce total consistency: variant forms are even defended by some modern writers as offering improved «flexibility».^[2] On the other hand, especially where a Roman numeral is considered a legally binding expression of a number, as in U.S. Copyright law (where an «incorrect» or ambiguous numeral may invalidate a copyright claim, or affect the termination date of the copyright period)^[3] it is desirable to strictly follow the usual style described below.

Standard form

The following table displays how Roman numerals are usually written:^[4]

Individual decimal places

	Thousands	Hundreds	Tens	Units
1	M	C	X	I
2	MM	CC	XX	II
3	MMM	CCC	XXX	III
4		CD	XL	IV
5		D	L	V
6		DC	LX	VI
7		DCC	LXX	VII
8		DCCC	LXXX	VIII
9		CM	XC	IX

The numerals for 4 (IV) and 9 (IX) are written using «subtractive notation»,^[5] where the first symbol (I) is subtracted from the larger one (V, or X), thus avoiding the clumsier IIII and VIIII.^[a] Subtractive notation is also used for 40 (XL), 90 (XC), 400 (CD) and 900 (CM).^[6] These are the only subtractive forms in standard use.

A number containing two or more decimal digits is built by appending the Roman numeral equivalent for each, from highest to lowest, as in the following examples:

•    39 = XXX + IX = XXXIX.
•   246 = CC + XL + VI = CCXLVI.
•   789 = DCC + LXXX + IX = DCCLXXXIX.
• 2,421 = MM + CD + XX + I = MMCDXXI.

Any missing place (represented by a zero in the place-value equivalent) is omitted, as in Latin (and English) speech:

•   160 = C + LX = CLX
•   207 = CC + VII = CCVII
• 1,009 = M + IX = MIX
• 1,066 = M + LX + VI = MLXVI^[7][8]

In practice, Roman numerals for numbers over 1000 ^[b] are currently used mainly for year numbers, as in these examples:

• 1776 = M + DCC + LXX + VI = MDCCLXXVI (the date written on the book held by the Statue of Liberty).
• 1918 = M + CM + X + VIII = MCMXVIII (the first year of the Spanish flu pandemic)
• 1954 = M + CM + L + IV = MCMLIV (as in the trailer for the movie The Last Time I Saw Paris)^[3]
• 2014 = MM + X + IV = MMXIV (the year of the games of the XXII (22nd) Olympic Winter Games (in Sochi, Russia))

The largest number that can be represented in this notation is 3,999 (MMMCMXCIX), but since the largest Roman numeral likely to be required today is MMXXIII (the current year) there is no practical need for larger Roman numerals. Prior to the introduction of Arabic numerals in the West, ancient and medieval users of the system used various means to write larger numbers; see large numbers below.

Other forms

Forms exist that vary in one way or another from the general standard represented above.

Other additive forms

While subtractive notation for 4, 40 and 400 (IV, XL and CD) has been the usual form since Roman times, additive notation to represent these numbers (IIII, XXXX and CCCC)^[9] continued to be used, including in compound numbers like XXIIII,^[10] LXXIIII,^[11] and CCCCLXXXX.^[12] The additive forms for 9, 90, and 900 (VIIII,^[9] LXXXX,^[13] and DCCCC^[14]) have also been used, although less often.

The two conventions could be mixed in the same document or inscription, even in the same numeral. For example, on the numbered gates to the Colosseum, IIII is systematically used instead of IV, but subtractive notation is used for XL; consequently, gate 44 is labelled XLIIII.^[15][16]

Modern clock faces that use Roman numerals still very often use IIII for four o’clock but IX for nine o’clock, a practice that goes back to very early clocks such as the Wells Cathedral clock of the late 14th century.^[17][18][19] However, this is far from universal: for example, the clock on the Palace of Westminster tower (commonly known as Big Ben) uses a subtractive IV for 4 o’clock.^[18]

Isaac Asimov once mentioned an «interesting theory» that Romans avoided using IV because it was the initial letters of IVPITER, the Latin spelling of Jupiter, and might have seemed impious.^[20] He did not say whose theory it was.

Several monumental inscriptions created in the early 20th century use variant forms for «1900» (usually written MCM). These vary from MDCCCCX for 1910 as seen on Admiralty Arch, London, to the more unusual, if not unique MDCDIII for 1903, on the north entrance to the Saint Louis Art Museum.^[21]

Especially on tombstones and other funerary inscriptions 5 and 50 have been occasionally written IIIII and XXXXX instead of V and L, and there are instances such as IIIIII and XXXXXX rather than VI or LX.^[22][23]

Other subtractive forms

There is a common belief that any smaller digit placed to the left of a larger digit is subtracted from the total, and that by clever choices a long Roman numeral can be «compressed». The best known example of this is the ROMAN() function in Microsoft Excel, which can turn 499 into CDXCIX, LDVLIV, XDIX, VDIV, or ID depending on the «Form» setting.^[24] There is no indication this is anything other than an invention by the programmer, and the universal-subtraction belief may be a result of modern users trying to rationalize the syntax of Roman numerals.

There is, however, some historic use of subtractive notation other than that described in the above «standard»: in particular IIIXX for 17,^[25] IIXX for 18,^[26] IIIC for 97,^[27] IIC for 98,^[28][29] and IC for 99.^[30] A possible explanation is that the word for 18 in Latin is duodeviginti, literally «two from twenty», 98 is duodecentum (two from hundred), and 99 is undecentum (one from hundred).^[31] However, the explanation does not seem to apply to IIIXX and IIIC, since the Latin words for 17 and 97 were septendecim (seven ten) and nonaginta septem (ninety seven), respectively.

There are multiple examples of IIX being used for 8. There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than VIII. XIIX was used by officers of the XVIII Roman Legion to write their number.^[32][33] The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius (c. 45 BC – 9 AD). On the publicly displayed official Roman calendars known as Fasti, XIIX is used for the 18 days to the next Kalends, and XXIIX for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the Fasti Antiates Maiores.^[34]

Rare variants

While irregular subtractive and additive notation has been used at least occasionally throughout history, some Roman numerals have been observed in documents and inscriptions that do not fit either system. Some of these variants do not seem to have been used outside specific contexts, and may have been regarded as errors even by contemporaries.

• IIXX was how people associated with the XXII Roman Legion used to write their number. The practice may have been due to a common way to say «twenty-second» in Latin, namely duo et vice(n)sima (literally «two and twentieth») rather than the «regular» vice(n)sima secunda (twenty second).^[35] Apparently, at least one ancient stonecutter mistakenly thought that the IIXX of «22nd Legion» stood for 18, and «corrected» it to XVIII.^[35]

• There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as XVIXIII, corresponding to the common reading «sixteen thirteen» of such year numbers in English, or 1519 as XV^CXIX as in French quinze-cent-dix-neuf (fifteen-hundred and nineteen), and similar readings in other languages.^[37]
• In some French texts from the 15th century and later one finds constructions like IIII^XXXIX for 99, reflecting the French reading of that number as quatre-vingt-dix-neuf (four-score and nineteen).^[37] Similarly, in some English documents one finds, for example, 77 written as «iii^xxxvii» (which could be read «three-score and seventeen»).^[38]
• A medieval accounting text from 1301 renders numbers like 13,573 as «XIII. M. V. C. III. XX. XIII«, that is, «13×1000 + 5×100 + 3×20 + 13».^[39]
• Other numerals that do not fit the usual patterns – such as VXL for 45, instead of the usual XLV — may be due to scribal errors, or the writer’s lack of familiarity with the system, rather than being genuine variant usage.

Non-numeric combinations

As Roman numerals are composed of ordinary alphabetic characters, there may sometimes be confusion with other uses of the same letters. For example, «XXX» and «XL» have other connotations in addition to their values as Roman numerals, while «IXL» more often than not is a gramogram of «I excel», and is in any case not an unambiguous Roman numeral.^[40]

Zero

As a non-positional numeral system, Roman numerals have no «place-keeping» zeros. Furthermore, the system as used by the Romans lacked a numeral for the number zero itself (that is, what remains after 1 is subtracted from 1). The word nulla (the Latin word meaning «none») was used to represent 0, although the earliest attested instances are medieval. For instance Dionysius Exiguus used nulla alongside Roman numerals in a manuscript from 525 AD.^[41][42] About 725, Bede or one of his colleagues used the letter N, the initial of nulla or of nihil (the Latin word for «nothing») for 0, in a table of epacts, all written in Roman numerals.^[43]

The use of N to indicate «none» long survived in the historic apothecaries’ system of measurement: used well into the 20th century to designate quantities in pharmaceutical prescriptions.^[44]

Fractions

The base «Roman fraction» is S, indicating 1⁄2.
The use of S (as in VIIS to indicate 71⁄2) is attested in some ancient inscriptions^[45]
and also in the now rare apothecaries’ system (usually in the form SS):^[44] but while Roman numerals for whole numbers are essentially decimal S does not correspond to 5⁄10, as one might expect, but 6⁄12.

The Romans used a duodecimal rather than a decimal system for fractions, as the divisibility of twelve (12 = 2² × 3) makes it easier to handle the common fractions of 1⁄3 and 1⁄4 than does a system based on ten (10 = 2 × 5). Notation for fractions other than 1⁄2 is mainly found on surviving Roman coins, many of which had values that were duodecimal fractions of the unit as. Fractions less than 1⁄2 are indicated by a dot (·) for each uncia «twelfth», the source of the English words inch and ounce; dots are repeated for fractions up to five twelfths. Six twelfths (one half), is 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.^[46] 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.

Each fraction from 1⁄12 to 12⁄12 had a name in Roman times; these corresponded to the names of the related coins:

Fraction	Roman numeral	Name (nominative and genitive)	Meaning
1⁄12	·	Uncia, unciae	«Ounce»
2⁄12 = 1⁄6	·· or :	Sextans, sextantis	«Sixth»
3⁄12 = 1⁄4	··· or ∴	Quadrans, quadrantis	«Quarter»
4⁄12 = 1⁄3	···· or ∷	Triens, trientis	«Third»
5⁄12	····· or ⁙	Quincunx, quincuncis	«Five-ounce» (quinque unciae → quincunx)
6⁄12 = 1⁄2	S	Semis, semissis	«Half»
7⁄12	S·	Septunx, septuncis	«Seven-ounce» (septem unciae → septunx)
8⁄12 = 2⁄3	S·· or S:	Bes, bessis	«Twice» (as in «twice a third»)
9⁄12 = 3⁄4	S··· or S∴	Dodrans, dodrantis or nonuncium, nonuncii	«Less a quarter» (de-quadrans → dodrans) or «ninth ounce» (nona uncia → nonuncium)
10⁄12 = 5⁄6	S···· or S∷	Dextans, dextantis or decunx, decuncis	«Less a sixth» (de-sextans → dextans) or «ten ounces» (decem unciae → decunx)
11⁄12	S····· or S⁙	Deunx, deuncis	«Less an ounce» (de-uncia → deunx)
12⁄12 = 1	I	As, assis	«Unit»

Other Roman fractional notations included the following:

Fraction	Roman numeral	Name (nominative and genitive)	Meaning
1⁄1728=12−3	𐆕	Siliqua, siliquae
1⁄288	℈	Scripulum, scripuli	«scruple»
1⁄144=12−2	𐆔	Dimidia sextula, dimidiae sextulae	«half a sextula»
1⁄72	𐆓	Sextula, sextulae	«1⁄6 of an uncia»
1⁄48	Ↄ	Sicilicus, sicilici
1⁄36	𐆓𐆓	Binae sextulae, binarum sextularum	«two sextulas» (duella, duellae)
1⁄24	Σ or 𐆒 or Є	Semuncia, semunciae	«1⁄2 uncia» (semi- + uncia)
1⁄8	Σ· or 𐆒· or Є·	Sescuncia, sescunciae	«1+1⁄2 uncias» (sesqui- + uncia)

Large numbers

During the centuries that Roman numerals remained the standard way of writing numbers throughout Europe, there were various extensions to the system designed to indicate larger numbers, none of which were ever standardised.

Apostrophus

One of these was the apostrophus,^[47] in which 500 was written as IↃ, while 1,000 was written as CIↃ.^[20] This is a system of encasing numbers to denote thousands (imagine the Cs and Ↄs as parentheses), which has its origins in Etruscan numeral usage.

Each additional set of C and Ↄ surrounding CIↃ raises the value by a factor of ten: CCIↃↃ represents 10,000 and CCCIↃↃↃ represents 100,000. Similarly, each additional Ↄ to the right of IↃ raises the value by a factor of ten: IↃↃ represents 5,000 and IↃↃↃ represents 50,000. Numerals larger than CCCIↃↃↃ do not occur.^[48]

Sometimes CIↃ was reduced to ↀ for 1,000. Similarly, IↃↃ for 5,000 was reduced to ↁ; CCIↃↃ for 10,000 to ↂ; IↃↃↃ for 50,000 to ↇ (ↇ); and CCCIↃↃↃ (ↈ) for 100,000 to ↈ.
^[49]

IↃ and CIↃ most likely preceded, and subsequently influenced, the adoption of «D» and «M» in Roman numerals.

John Wallis is often credited for introducing the symbol for infinity ⟨∞⟩, and one conjecture is that he based it on ↀ, since 1,000 was hyperbolically used to represent very large numbers.

Vinculum

Another system was the vinculum, in which conventional Roman numerals were multiplied by 1,000 by adding a «bar» or «overline».^[49] It was a common alternative to the apostrophic ↀ during the Imperial era: both systems were in simultaneous use around the Roman world (M for ‘1000’ was not in use until the Medieval period).^[50]
[51]
The use of vinculum for multiples of 1,000 can be observed, for example, on the milestones erected by Roman soldiers along the Antonine Wall in the mid-2nd century AD.^[52] The vinculum for marking 1,000s continued in use in the Middle Ages, though it became known more commonly as titulus.^[53]

Some modern sources describe the vinculum as if it were a part of the current «standard».^[54] However, this is largely hypothetical, since no common modern usage requires numbers larger than the current year (MMXXIII). Nonetheless, here are some examples, to give an idea of how it might be used:

• IV = 4,000
• IVDCXXVII = 4,627
• XXV = 25,000
• XXVCDLIX = 25,459

This use of lines is distinct from the custom, once very common, of adding both underline and overline (or very large serifs) to a Roman numeral, simply to make it clear that it is a number, e.g.
for 1967. There is some scope for confusion when an overline is meant to denote multiples of 1,000, and when not. The Greeks and Romans often overlined letters acting as numerals to highlight them from the general body of the text, without any numerical significance. This stylistic convention was, for example, also in use in the inscriptions of the Antonine Wall,^[55] and the reader is required to decipher the intended meaning of the overline from the context.

Another medieval usage was the addition of vertical lines (or brackets) before and after the numeral to multiply it by 10:^{[citation needed]} thus M for 10,000 as an alternative form for X. In combination with the overline the bracketed forms might be used to raise the multiplier to ten thousand, thus:

• VIII for 80,000
• XX for 200,000

This same syntax may also have indicated multiplication by 100^{[citation needed]} so the above two examples are 800,000 and 2,000,000.

Origin

The system is closely associated with the ancient city-state of Rome and the Empire that it created. However, due to the scarcity of surviving examples, the origins of the system are obscure and there are several competing theories, all largely conjectural.

Etruscan numerals

Rome was founded sometime between 850 and 750 BC. At the time, the region was inhabited by diverse populations of which the Etruscans were the most advanced. The ancient Romans themselves admitted that the basis of much of their civilization was Etruscan. Rome itself was located next to the southern edge of the Etruscan domain, which covered a large part of north-central Italy.

The Roman numerals, in particular, are directly derived from the Etruscan number symbols: ⟨𐌠⟩, ⟨𐌡⟩, ⟨𐌢⟩, ⟨𐌣⟩, and ⟨𐌟⟩ for 1, 5, 10, 50, and 100 (They had more symbols for larger numbers, but it is unknown which symbol represents which number). As in the basic Roman system, the Etruscans wrote the symbols that added to the desired number, from higher to lower value. Thus the number 87, for example, would be written 50 + 10 + 10 + 10 + 5 + 1 + 1 = 𐌣𐌢𐌢𐌢𐌡𐌠𐌠 (this would appear as 𐌠𐌠𐌡𐌢𐌢𐌢𐌣 since Etruscan was written from right to left.)^[56]

The symbols ⟨𐌠⟩ and ⟨𐌡⟩ resembled letters of the Etruscan alphabet, but ⟨𐌢⟩, ⟨𐌣⟩, and ⟨𐌟⟩ did not. The Etruscans used the subtractive notation, too, but not like the Romans. They wrote 17, 18, and 19 as 𐌠𐌠𐌠𐌢𐌢, 𐌠𐌠𐌢𐌢, and 𐌠𐌢𐌢, mirroring the way they spoke those numbers («three from twenty», etc.); and similarly for 27, 28, 29, 37, 38, etc. However, they did not write 𐌠𐌡 for 4 (nor 𐌢𐌣 for 40), and wrote 𐌡𐌠𐌠, 𐌡𐌠𐌠𐌠 and 𐌡𐌠𐌠𐌠𐌠 for 7, 8, and 9, respectively.^[56]

Early Roman numerals

The early Roman numerals for 1, 10, and 100 were the Etruscan ones: ⟨𐌠⟩, ⟨𐌢⟩, and ⟨𐌟⟩. The symbols for 5 and 50 changed from ⟨𐌡⟩ and ⟨𐌣⟩ to ⟨V⟩ and ⟨ↆ⟩ at some point. The latter had flattened to ⟨⊥⟩ (an inverted T) by the time of Augustus, and soon afterwards became identified with the graphically similar letter ⟨L⟩.^[48]

The symbol for 100 was written variously as ⟨𐌟⟩ or ⟨ↃIC⟩, and was then abbreviated to ⟨Ↄ⟩ or ⟨C⟩, with ⟨C⟩ (which matched the Latin letter C) finally winning out. It might have helped that C was the initial letter of CENTUM, Latin for «hundred».

The numbers 500 and 1000 were denoted by V or X overlaid with a box or circle. Thus 500 was like a Ↄ superimposed on a Þ. It became 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» was a CIↃ, and half of a thousand or «five hundred» is the right half of the symbol, IↃ, and this may have been converted into D.^[20]

The notation for 1000 was a circled or boxed X: Ⓧ, ⊗, ⊕, and by Augustinian times was partially identified with the Greek letter Φ phi. Over time, the symbol changed to Ψ and ↀ. The latter symbol further evolved into ∞, then ⋈, and eventually changed to M under the influence of the Latin word mille «thousand».^[48]

According to Paul Kayser, the basic numerical symbols were I, X, C and Φ (or ⊕) and the intermediate ones were derived by taking half of those (half an X is V, half a C is L and half a Φ/⊕ is D).^[57]

Classical Roman numerals

The Colosseum was constructed in Rome in CE 72–80,^[58] and while the original perimeter wall has largely disappeared, the numbered entrances from XXIII (23) to LIIII (54) survive,^[59] to demonstrate that in Imperial times Roman numerals had already assumed their classical form: as largely standardised in current use. The most obvious anomaly (a common one that persisted for centuries) is the inconsistent use of subtractive notation — while XL is used for 40, IV is avoided in favour of IIII: in fact gate 44 is labelled XLIIII.

Use in the Middle Ages and Renaissance

Lower case, or minuscule, letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and since that time lower-case versions of Roman numbers have also been commonly used: i, ii, iii, iv, and so on.

Since the Middle Ages, a «j» has sometimes been substituted for the final «i» of a «lower-case» Roman numeral, such as «iij» for 3 or «vij» for 7. This «j» can be considered a swash variant of «i«. Into the early 20th century, the use of a final «j» was still sometimes used in medical prescriptions to prevent tampering with or misinterpretation of a number after it was written.^[60]

Numerals in documents and inscriptions from the Middle Ages sometimes include additional symbols, which today are called «medieval Roman numerals». Some simply substitute another letter for the standard one (such as «A» for «V«, or «Q» for «D«), while others serve as abbreviations for compound numerals («O» for «XI«, or «F» for «XL«). Although they are still listed today in some dictionaries, they are long out of use.^[61]

Number	Medieval abbreviation	Notes and etymology
5	A	Resembles an upside-down V. Also said to equal 500.
6	ↅ	Either from a ligature of VI, or from digamma (ϛ), the Greek numeral 6 (sometimes conflated with the στ ligature).[48]
7	S, Z	Presumed abbreviation of septem, Latin for 7.
9.5	X̷	Scribal abbreviation, an x with a slash through it. Likewise, IX̷ represented 8.5
11	O	Presumed abbreviation of onze, French for 11.
40	F	Presumed abbreviation of English forty.
70	S	Also could stand for 7, with the same derivation.
80	R
90	N	Presumed abbreviation of nonaginta, Latin for 90. (Ambiguous with N for «nothing» (nihil)).
150	Y	Possibly derived from the lowercase y’s shape.
151	K	Unusual, origin unknown; also said to stand for 250.[62]
160	T	Possibly derived from Greek tetra, as 4 × 40 = 160.
200	H	Could also stand for 2 (see also 𐆙, the symbol for the dupondius). From a barring of two I‘s.
250	E
300	B
400	P, G
500	Q	Redundant with D; abbreviates quingenti, Latin for 500. Also sometimes used for 500,000.[63]
800	Ω	Borrowed from Gothic.
900	ϡ	Borrowed from Gothic.
2000	Z

Chronograms, messages with dates encoded into them, were popular during the Renaissance era. The chronogram would be a phrase containing the letters I, V, X, L, C, D, and M. By putting these letters together, the reader would obtain a number, usually indicating a particular year.

Modern use

By the 11th century, Arabic numerals had been introduced into Europe from al-Andalus, by way of Arab traders and arithmetic treatises. Roman numerals, however, proved very persistent, remaining in common use in the West well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Replacement by their more convenient «Arabic» equivalents was quite gradual, and Roman numerals are still used today in certain contexts. A few examples of their current use are:

• Names of monarchs and popes, e.g. Elizabeth II of the United Kingdom, Pope Benedict XVI. These are referred to as regnal numbers and are usually read as ordinals; e.g. II is pronounced «the second». This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England during the reign of Henry VIII. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor. Some monarchs (e.g. Charles IV of Spain and Louis XIV of France) seem to have preferred the use of IIII instead of IV on their coinage (see illustration).
• Generational suffixes, particularly in the U.S., for people sharing the same name across generations, for example William Howard Taft IV. These are also usually read as ordinals.
• In the French Republican Calendar, initiated during the French Revolution, years were numbered by Roman numerals – from the year I (1792) when this calendar was introduced to the year XIV (1805) when it was abandoned.
• The year of production of films, television shows and other works of art within the work itself. Outside reference to the work will use regular Arabic numerals.

• Hour marks on timepieces. In this context, 4 is often written IIII.
• The year of construction on building façades and cornerstones.
• Page numbering of prefaces and introductions of books, and sometimes of appendices and annexes, too.
• Book volume and chapter numbers, as well as the several acts within a play (e.g. Act iii, Scene 2).
• Sequels to some films, video games, and other works (as in Rocky II, Grand Theft Auto V).
• Outlines that use numbers to show hierarchical relationships.
• Occurrences of a recurring grand event, for instance:
  • The Summer and Winter Olympic Games (e.g. the XXI Olympic Winter Games; the Games of the XXX Olympiad).
  • The Super Bowl, the annual championship game of the National Football League (e.g. Super Bowl XLII; Super Bowl 50 was a one-time exception^[64]).
  • WrestleMania, the annual professional wrestling event for the WWE (e.g. WrestleMania XXX). This usage has also been inconsistent.

Specific disciplines

In astronautics, United States rocket model variants are sometimes designated by Roman numerals, e.g. Titan I, Titan II, Titan III, Saturn I, Saturn V.

In astronomy, the natural satellites or «moons» of the planets are traditionally designated by capital Roman numerals appended to the planet’s name. For example, Titan’s designation is Saturn VI.

In chemistry, Roman numerals are often used to denote the groups of the periodic table. They are also used in the IUPAC nomenclature of inorganic chemistry, for the oxidation number of cations which can take on several different positive charges. They are also used for naming phases of polymorphic crystals, such as ice.

In education, school grades (in the sense of year-groups rather than test scores) are sometimes referred to by a Roman numeral; for example, «grade IX» is sometimes seen for «grade 9».

In entomology, the broods of the thirteen and seventeen year periodical cicadas are identified by Roman numerals.

In graphic design stylised Roman numerals may represent numeric values.

In law, Roman numerals are commonly used to help organize legal codes as part of an alphanumeric outline.

In advanced mathematics (including trigonometry, statistics, and calculus), when a graph includes negative numbers, its quadrants are named using I, II, III, and IV. These quadrant names signify positive numbers on both axes, negative numbers on the X axis, negative numbers on both axes, and negative numbers on the Y axis, respectively. The use of Roman numerals to designate quadrants avoids confusion, since Arabic numerals are used for the actual data represented in the graph.

In military unit designation, Roman numerals are often used to distinguish between units at different levels. This reduces possible confusion, especially when viewing operational or strategic level maps. In particular, army corps are often numbered using Roman numerals (for example the American XVIII Airborne Corps or the WW2-era German III Panzerkorps) with Arabic numerals being used for divisions and armies.

In music, Roman numerals are used in several contexts:

• Movements are often numbered using Roman numerals.
• In Roman Numeral Analysis, harmonic function is identified using Roman Numerals.
• Individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings.

In pharmacy, Roman numerals were used with the now largely obsolete apothecaries’ system of measurement: including SS to denote «one half» and N to denote «zero».^[44][65]

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

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

In sport the team containing the «top» players and representing a nation or province, a club or a school at the highest level in (say) rugby union is often called the «1st XV«, while a lower-ranking cricket or American football team might be the «3rd XI«.

In tarot, Roman numerals (with zero) are used to denote the cards of the Major Arcana.

In theology and biblical scholarship, the Septuagint is often referred to as LXX, as this translation of the Old Testament into Greek is named for the legendary number of its translators (septuaginta being Latin for «seventy»).

Modern use in European languages other than English

Some uses that are rare or never seen in English speaking countries may be relatively common in parts of continental Europe and in other regions (e.g. Latin America) that use a European language other than English. For instance:

Capital or small capital Roman numerals are widely used in Romance languages to denote centuries, e.g. the French XVIII^e siècle^[66] and the Spanish siglo XVIII mean «18th century». Slavic languages in and adjacent to Russia similarly favor Roman numerals (xviii век). On the other hand, in Slavic languages in Central Europe, like most Germanic languages, one writes «18.» (with a period) before the local word for «century».

Mixed Roman and Arabic numerals are sometimes used in numeric representations of dates (especially in formal letters and official documents, but also on tombstones). The month is written in Roman numerals, while the day is in Arabic numerals: «4.VI.1789″ and «VI.4.1789″ both refer unambiguously to 4 June 1789.

Roman numerals are sometimes used to represent the days of the week in hours-of-operation signs displayed in windows or on doors of businesses,^[67] and also sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by I. Sunday is represented by VII. 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. In the example case (left), the business opens from 10 AM to 7 PM on weekdays, 10 AM to 5 PM on Saturdays and is closed on Sundays. Note that the listing uses 24-hour time.

Roman numerals may also be used for floor numbering.^[68][69] For instance, 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 Italy, where roads outside built-up areas have kilometre signs, major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from I to IX for the smaller intervals. The sign IX/17 thus marks 17.9 km.

Certain romance-speaking countries use Roman numerals to designate assemblies of their national legislatures. For instance, the composition of the Italian Parliament from 2018 to 2022 (elected in the 2018 Italian general election) is called the XVIII Legislature of the Italian Republic (or more commonly the «XVIII Legislature»).

A notable exception to the use of Roman numerals in Europe is in Greece, where Greek numerals (based on the Greek alphabet) are generally used in contexts where Roman numerals would be used elsewhere.

Unicode

The «Number Forms» block of the Unicode computer character set standard has a number of Roman numeral symbols in the range of code points from U+2160 to U+2188.^[70] This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ or XII). One justification for the existence of pre-combined numbers is to facilitate the setting of multiple-letter numbers (such as VIII) on a single horizontal line in Asian vertical text. The Unicode standard, however, includes special Roman numeral code points for compatibility only, stating that «[f]or most purposes, it is preferable to compose the Roman numerals from sequences of the appropriate Latin letters».^[71]
The block also includes some apostrophus symbols for large numbers, an old variant of «L» (50) similar to the Etruscan character, the Claudian letter «reversed C», etc.

Symbol	ↀ	ↁ	ↂ	ↅ	ↆ	ↇ	ↈ
Value	1,000	5,000	10,000	6	50	50,000	100,000

See also

References

Notes

Citations

Sources

• Menninger, Karl (1992). Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications. ISBN 978-0-486-27096-8.

Further reading

• Aczel, Amir D. 2015. Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers. 1st edition. New York: Palgrave Macmillan.
• Goines, David Lance. A Constructed Roman Alphabet: A Geometric Analysis of the Greek and Roman Capitals and of the Arabic Numerals. Boston: D.R. Godine, 1982.
• Houston, Stephen D. 2012. The Shape of Script: How and Why Writing Systems Change. Santa Fe, NM: School for Advanced Research Press.
• Taisbak, Christian M. 1965. «Roman numerals and the abacus.» Classica et medievalia 26: 147–60.

External links

• «Roman Numerals (Totally Epic Guide)». Know The Romans.

Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each letter with a fixed integer value, modern style uses only these seven:

I	V	X	L	C	D	M
1	5	10	50	100	500	1000

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some applications to this day.

One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as:

The notations IV and IX can be read as «one less than five» (4) and «one less than ten» (9), although there is a tradition favouring representation of «4» as «IIII» on Roman numeral clocks.^[1]

Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. MCM, signifying «a thousand, and a hundred less than another thousand», means 1900, so 1912 is written MCMXII. For the years of this century, MM indicates 2000. The current year is MMXXIII (2023).

Description

Roman numerals use different symbols for each power of ten and no zero symbol, in contrast with the place value notation of Arabic numerals (in which place-keeping zeros enable the same digit to represent different powers of ten).

This allows some flexibility in notation, and there has never been an official or universally accepted standard for Roman numerals. Usage in ancient Rome varied greatly and became thoroughly chaotic in medieval times. Even the post-renaissance restoration of a largely «classical» notation has failed to produce total consistency: variant forms are even defended by some modern writers as offering improved «flexibility».^[2] On the other hand, especially where a Roman numeral is considered a legally binding expression of a number, as in U.S. Copyright law (where an «incorrect» or ambiguous numeral may invalidate a copyright claim, or affect the termination date of the copyright period)^[3] it is desirable to strictly follow the usual style described below.

Standard form

The following table displays how Roman numerals are usually written:^[4]

Individual decimal places

	Thousands	Hundreds	Tens	Units
1	M	C	X	I
2	MM	CC	XX	II
3	MMM	CCC	XXX	III
4		CD	XL	IV
5		D	L	V
6		DC	LX	VI
7		DCC	LXX	VII
8		DCCC	LXXX	VIII
9		CM	XC	IX

The numerals for 4 (IV) and 9 (IX) are written using «subtractive notation»,^[5] where the first symbol (I) is subtracted from the larger one (V, or X), thus avoiding the clumsier IIII and VIIII.^[a] Subtractive notation is also used for 40 (XL), 90 (XC), 400 (CD) and 900 (CM).^[6] These are the only subtractive forms in standard use.

A number containing two or more decimal digits is built by appending the Roman numeral equivalent for each, from highest to lowest, as in the following examples:

•    39 = XXX + IX = XXXIX.
•   246 = CC + XL + VI = CCXLVI.
•   789 = DCC + LXXX + IX = DCCLXXXIX.
• 2,421 = MM + CD + XX + I = MMCDXXI.

Any missing place (represented by a zero in the place-value equivalent) is omitted, as in Latin (and English) speech:

•   160 = C + LX = CLX
•   207 = CC + VII = CCVII
• 1,009 = M + IX = MIX
• 1,066 = M + LX + VI = MLXVI^[7][8]

In practice, Roman numerals for numbers over 1000 ^[b] are currently used mainly for year numbers, as in these examples:

• 1776 = M + DCC + LXX + VI = MDCCLXXVI (the date written on the book held by the Statue of Liberty).
• 1918 = M + CM + X + VIII = MCMXVIII (the first year of the Spanish flu pandemic)
• 1954 = M + CM + L + IV = MCMLIV (as in the trailer for the movie The Last Time I Saw Paris)^[3]
• 2014 = MM + X + IV = MMXIV (the year of the games of the XXII (22nd) Olympic Winter Games (in Sochi, Russia))

The largest number that can be represented in this notation is 3,999 (MMMCMXCIX), but since the largest Roman numeral likely to be required today is MMXXIII (the current year) there is no practical need for larger Roman numerals. Prior to the introduction of Arabic numerals in the West, ancient and medieval users of the system used various means to write larger numbers; see large numbers below.

Other forms

Forms exist that vary in one way or another from the general standard represented above.

Other additive forms

While subtractive notation for 4, 40 and 400 (IV, XL and CD) has been the usual form since Roman times, additive notation to represent these numbers (IIII, XXXX and CCCC)^[9] continued to be used, including in compound numbers like XXIIII,^[10] LXXIIII,^[11] and CCCCLXXXX.^[12] The additive forms for 9, 90, and 900 (VIIII,^[9] LXXXX,^[13] and DCCCC^[14]) have also been used, although less often.

The two conventions could be mixed in the same document or inscription, even in the same numeral. For example, on the numbered gates to the Colosseum, IIII is systematically used instead of IV, but subtractive notation is used for XL; consequently, gate 44 is labelled XLIIII.^[15][16]

Modern clock faces that use Roman numerals still very often use IIII for four o’clock but IX for nine o’clock, a practice that goes back to very early clocks such as the Wells Cathedral clock of the late 14th century.^[17][18][19] However, this is far from universal: for example, the clock on the Palace of Westminster tower (commonly known as Big Ben) uses a subtractive IV for 4 o’clock.^[18]

Isaac Asimov once mentioned an «interesting theory» that Romans avoided using IV because it was the initial letters of IVPITER, the Latin spelling of Jupiter, and might have seemed impious.^[20] He did not say whose theory it was.

Several monumental inscriptions created in the early 20th century use variant forms for «1900» (usually written MCM). These vary from MDCCCCX for 1910 as seen on Admiralty Arch, London, to the more unusual, if not unique MDCDIII for 1903, on the north entrance to the Saint Louis Art Museum.^[21]

Especially on tombstones and other funerary inscriptions 5 and 50 have been occasionally written IIIII and XXXXX instead of V and L, and there are instances such as IIIIII and XXXXXX rather than VI or LX.^[22][23]

Other subtractive forms

There is a common belief that any smaller digit placed to the left of a larger digit is subtracted from the total, and that by clever choices a long Roman numeral can be «compressed». The best known example of this is the ROMAN() function in Microsoft Excel, which can turn 499 into CDXCIX, LDVLIV, XDIX, VDIV, or ID depending on the «Form» setting.^[24] There is no indication this is anything other than an invention by the programmer, and the universal-subtraction belief may be a result of modern users trying to rationalize the syntax of Roman numerals.

There is, however, some historic use of subtractive notation other than that described in the above «standard»: in particular IIIXX for 17,^[25] IIXX for 18,^[26] IIIC for 97,^[27] IIC for 98,^[28][29] and IC for 99.^[30] A possible explanation is that the word for 18 in Latin is duodeviginti, literally «two from twenty», 98 is duodecentum (two from hundred), and 99 is undecentum (one from hundred).^[31] However, the explanation does not seem to apply to IIIXX and IIIC, since the Latin words for 17 and 97 were septendecim (seven ten) and nonaginta septem (ninety seven), respectively.

There are multiple examples of IIX being used for 8. There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than VIII. XIIX was used by officers of the XVIII Roman Legion to write their number.^[32][33] The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius (c. 45 BC – 9 AD). On the publicly displayed official Roman calendars known as Fasti, XIIX is used for the 18 days to the next Kalends, and XXIIX for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the Fasti Antiates Maiores.^[34]

Rare variants

While irregular subtractive and additive notation has been used at least occasionally throughout history, some Roman numerals have been observed in documents and inscriptions that do not fit either system. Some of these variants do not seem to have been used outside specific contexts, and may have been regarded as errors even by contemporaries.

• IIXX was how people associated with the XXII Roman Legion used to write their number. The practice may have been due to a common way to say «twenty-second» in Latin, namely duo et vice(n)sima (literally «two and twentieth») rather than the «regular» vice(n)sima secunda (twenty second).^[35] Apparently, at least one ancient stonecutter mistakenly thought that the IIXX of «22nd Legion» stood for 18, and «corrected» it to XVIII.^[35]

• There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as XVIXIII, corresponding to the common reading «sixteen thirteen» of such year numbers in English, or 1519 as XV^CXIX as in French quinze-cent-dix-neuf (fifteen-hundred and nineteen), and similar readings in other languages.^[37]
• In some French texts from the 15th century and later one finds constructions like IIII^XXXIX for 99, reflecting the French reading of that number as quatre-vingt-dix-neuf (four-score and nineteen).^[37] Similarly, in some English documents one finds, for example, 77 written as «iii^xxxvii» (which could be read «three-score and seventeen»).^[38]
• A medieval accounting text from 1301 renders numbers like 13,573 as «XIII. M. V. C. III. XX. XIII«, that is, «13×1000 + 5×100 + 3×20 + 13».^[39]
• Other numerals that do not fit the usual patterns – such as VXL for 45, instead of the usual XLV — may be due to scribal errors, or the writer’s lack of familiarity with the system, rather than being genuine variant usage.

Non-numeric combinations

As Roman numerals are composed of ordinary alphabetic characters, there may sometimes be confusion with other uses of the same letters. For example, «XXX» and «XL» have other connotations in addition to their values as Roman numerals, while «IXL» more often than not is a gramogram of «I excel», and is in any case not an unambiguous Roman numeral.^[40]

Zero

As a non-positional numeral system, Roman numerals have no «place-keeping» zeros. Furthermore, the system as used by the Romans lacked a numeral for the number zero itself (that is, what remains after 1 is subtracted from 1). The word nulla (the Latin word meaning «none») was used to represent 0, although the earliest attested instances are medieval. For instance Dionysius Exiguus used nulla alongside Roman numerals in a manuscript from 525 AD.^[41][42] About 725, Bede or one of his colleagues used the letter N, the initial of nulla or of nihil (the Latin word for «nothing») for 0, in a table of epacts, all written in Roman numerals.^[43]

The use of N to indicate «none» long survived in the historic apothecaries’ system of measurement: used well into the 20th century to designate quantities in pharmaceutical prescriptions.^[44]

Fractions

The base «Roman fraction» is S, indicating 1⁄2.
The use of S (as in VIIS to indicate 71⁄2) is attested in some ancient inscriptions^[45]
and also in the now rare apothecaries’ system (usually in the form SS):^[44] but while Roman numerals for whole numbers are essentially decimal S does not correspond to 5⁄10, as one might expect, but 6⁄12.

The Romans used a duodecimal rather than a decimal system for fractions, as the divisibility of twelve (12 = 2² × 3) makes it easier to handle the common fractions of 1⁄3 and 1⁄4 than does a system based on ten (10 = 2 × 5). Notation for fractions other than 1⁄2 is mainly found on surviving Roman coins, many of which had values that were duodecimal fractions of the unit as. Fractions less than 1⁄2 are indicated by a dot (·) for each uncia «twelfth», the source of the English words inch and ounce; dots are repeated for fractions up to five twelfths. Six twelfths (one half), is 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.^[46] 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.

Each fraction from 1⁄12 to 12⁄12 had a name in Roman times; these corresponded to the names of the related coins:

Fraction	Roman numeral	Name (nominative and genitive)	Meaning
1⁄12	·	Uncia, unciae	«Ounce»
2⁄12 = 1⁄6	·· or :	Sextans, sextantis	«Sixth»
3⁄12 = 1⁄4	··· or ∴	Quadrans, quadrantis	«Quarter»
4⁄12 = 1⁄3	···· or ∷	Triens, trientis	«Third»
5⁄12	····· or ⁙	Quincunx, quincuncis	«Five-ounce» (quinque unciae → quincunx)
6⁄12 = 1⁄2	S	Semis, semissis	«Half»
7⁄12	S·	Septunx, septuncis	«Seven-ounce» (septem unciae → septunx)
8⁄12 = 2⁄3	S·· or S:	Bes, bessis	«Twice» (as in «twice a third»)
9⁄12 = 3⁄4	S··· or S∴	Dodrans, dodrantis or nonuncium, nonuncii	«Less a quarter» (de-quadrans → dodrans) or «ninth ounce» (nona uncia → nonuncium)
10⁄12 = 5⁄6	S···· or S∷	Dextans, dextantis or decunx, decuncis	«Less a sixth» (de-sextans → dextans) or «ten ounces» (decem unciae → decunx)
11⁄12	S····· or S⁙	Deunx, deuncis	«Less an ounce» (de-uncia → deunx)
12⁄12 = 1	I	As, assis	«Unit»

Other Roman fractional notations included the following:

Fraction	Roman numeral	Name (nominative and genitive)	Meaning
1⁄1728=12−3	𐆕	Siliqua, siliquae
1⁄288	℈	Scripulum, scripuli	«scruple»
1⁄144=12−2	𐆔	Dimidia sextula, dimidiae sextulae	«half a sextula»
1⁄72	𐆓	Sextula, sextulae	«1⁄6 of an uncia»
1⁄48	Ↄ	Sicilicus, sicilici
1⁄36	𐆓𐆓	Binae sextulae, binarum sextularum	«two sextulas» (duella, duellae)
1⁄24	Σ or 𐆒 or Є	Semuncia, semunciae	«1⁄2 uncia» (semi- + uncia)
1⁄8	Σ· or 𐆒· or Є·	Sescuncia, sescunciae	«1+1⁄2 uncias» (sesqui- + uncia)

Large numbers

During the centuries that Roman numerals remained the standard way of writing numbers throughout Europe, there were various extensions to the system designed to indicate larger numbers, none of which were ever standardised.

Apostrophus

One of these was the apostrophus,^[47] in which 500 was written as IↃ, while 1,000 was written as CIↃ.^[20] This is a system of encasing numbers to denote thousands (imagine the Cs and Ↄs as parentheses), which has its origins in Etruscan numeral usage.

Each additional set of C and Ↄ surrounding CIↃ raises the value by a factor of ten: CCIↃↃ represents 10,000 and CCCIↃↃↃ represents 100,000. Similarly, each additional Ↄ to the right of IↃ raises the value by a factor of ten: IↃↃ represents 5,000 and IↃↃↃ represents 50,000. Numerals larger than CCCIↃↃↃ do not occur.^[48]

Sometimes CIↃ was reduced to ↀ for 1,000. Similarly, IↃↃ for 5,000 was reduced to ↁ; CCIↃↃ for 10,000 to ↂ; IↃↃↃ for 50,000 to ↇ (ↇ); and CCCIↃↃↃ (ↈ) for 100,000 to ↈ.
^[49]

IↃ and CIↃ most likely preceded, and subsequently influenced, the adoption of «D» and «M» in Roman numerals.

John Wallis is often credited for introducing the symbol for infinity ⟨∞⟩, and one conjecture is that he based it on ↀ, since 1,000 was hyperbolically used to represent very large numbers.

Vinculum

Another system was the vinculum, in which conventional Roman numerals were multiplied by 1,000 by adding a «bar» or «overline».^[49] It was a common alternative to the apostrophic ↀ during the Imperial era: both systems were in simultaneous use around the Roman world (M for ‘1000’ was not in use until the Medieval period).^[50]
[51]
The use of vinculum for multiples of 1,000 can be observed, for example, on the milestones erected by Roman soldiers along the Antonine Wall in the mid-2nd century AD.^[52] The vinculum for marking 1,000s continued in use in the Middle Ages, though it became known more commonly as titulus.^[53]

Some modern sources describe the vinculum as if it were a part of the current «standard».^[54] However, this is largely hypothetical, since no common modern usage requires numbers larger than the current year (MMXXIII). Nonetheless, here are some examples, to give an idea of how it might be used:

• IV = 4,000
• IVDCXXVII = 4,627
• XXV = 25,000
• XXVCDLIX = 25,459

This use of lines is distinct from the custom, once very common, of adding both underline and overline (or very large serifs) to a Roman numeral, simply to make it clear that it is a number, e.g.
for 1967. There is some scope for confusion when an overline is meant to denote multiples of 1,000, and when not. The Greeks and Romans often overlined letters acting as numerals to highlight them from the general body of the text, without any numerical significance. This stylistic convention was, for example, also in use in the inscriptions of the Antonine Wall,^[55] and the reader is required to decipher the intended meaning of the overline from the context.

Another medieval usage was the addition of vertical lines (or brackets) before and after the numeral to multiply it by 10:^{[citation needed]} thus M for 10,000 as an alternative form for X. In combination with the overline the bracketed forms might be used to raise the multiplier to ten thousand, thus:

• VIII for 80,000
• XX for 200,000

This same syntax may also have indicated multiplication by 100^{[citation needed]} so the above two examples are 800,000 and 2,000,000.

Origin

The system is closely associated with the ancient city-state of Rome and the Empire that it created. However, due to the scarcity of surviving examples, the origins of the system are obscure and there are several competing theories, all largely conjectural.

Etruscan numerals

Rome was founded sometime between 850 and 750 BC. At the time, the region was inhabited by diverse populations of which the Etruscans were the most advanced. The ancient Romans themselves admitted that the basis of much of their civilization was Etruscan. Rome itself was located next to the southern edge of the Etruscan domain, which covered a large part of north-central Italy.

The Roman numerals, in particular, are directly derived from the Etruscan number symbols: ⟨𐌠⟩, ⟨𐌡⟩, ⟨𐌢⟩, ⟨𐌣⟩, and ⟨𐌟⟩ for 1, 5, 10, 50, and 100 (They had more symbols for larger numbers, but it is unknown which symbol represents which number). As in the basic Roman system, the Etruscans wrote the symbols that added to the desired number, from higher to lower value. Thus the number 87, for example, would be written 50 + 10 + 10 + 10 + 5 + 1 + 1 = 𐌣𐌢𐌢𐌢𐌡𐌠𐌠 (this would appear as 𐌠𐌠𐌡𐌢𐌢𐌢𐌣 since Etruscan was written from right to left.)^[56]

The symbols ⟨𐌠⟩ and ⟨𐌡⟩ resembled letters of the Etruscan alphabet, but ⟨𐌢⟩, ⟨𐌣⟩, and ⟨𐌟⟩ did not. The Etruscans used the subtractive notation, too, but not like the Romans. They wrote 17, 18, and 19 as 𐌠𐌠𐌠𐌢𐌢, 𐌠𐌠𐌢𐌢, and 𐌠𐌢𐌢, mirroring the way they spoke those numbers («three from twenty», etc.); and similarly for 27, 28, 29, 37, 38, etc. However, they did not write 𐌠𐌡 for 4 (nor 𐌢𐌣 for 40), and wrote 𐌡𐌠𐌠, 𐌡𐌠𐌠𐌠 and 𐌡𐌠𐌠𐌠𐌠 for 7, 8, and 9, respectively.^[56]

Early Roman numerals

The early Roman numerals for 1, 10, and 100 were the Etruscan ones: ⟨𐌠⟩, ⟨𐌢⟩, and ⟨𐌟⟩. The symbols for 5 and 50 changed from ⟨𐌡⟩ and ⟨𐌣⟩ to ⟨V⟩ and ⟨ↆ⟩ at some point. The latter had flattened to ⟨⊥⟩ (an inverted T) by the time of Augustus, and soon afterwards became identified with the graphically similar letter ⟨L⟩.^[48]

The symbol for 100 was written variously as ⟨𐌟⟩ or ⟨ↃIC⟩, and was then abbreviated to ⟨Ↄ⟩ or ⟨C⟩, with ⟨C⟩ (which matched the Latin letter C) finally winning out. It might have helped that C was the initial letter of CENTUM, Latin for «hundred».

The numbers 500 and 1000 were denoted by V or X overlaid with a box or circle. Thus 500 was like a Ↄ superimposed on a Þ. It became 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» was a CIↃ, and half of a thousand or «five hundred» is the right half of the symbol, IↃ, and this may have been converted into D.^[20]

The notation for 1000 was a circled or boxed X: Ⓧ, ⊗, ⊕, and by Augustinian times was partially identified with the Greek letter Φ phi. Over time, the symbol changed to Ψ and ↀ. The latter symbol further evolved into ∞, then ⋈, and eventually changed to M under the influence of the Latin word mille «thousand».^[48]

According to Paul Kayser, the basic numerical symbols were I, X, C and Φ (or ⊕) and the intermediate ones were derived by taking half of those (half an X is V, half a C is L and half a Φ/⊕ is D).^[57]

Classical Roman numerals

The Colosseum was constructed in Rome in CE 72–80,^[58] and while the original perimeter wall has largely disappeared, the numbered entrances from XXIII (23) to LIIII (54) survive,^[59] to demonstrate that in Imperial times Roman numerals had already assumed their classical form: as largely standardised in current use. The most obvious anomaly (a common one that persisted for centuries) is the inconsistent use of subtractive notation — while XL is used for 40, IV is avoided in favour of IIII: in fact gate 44 is labelled XLIIII.

Use in the Middle Ages and Renaissance

Lower case, or minuscule, letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and since that time lower-case versions of Roman numbers have also been commonly used: i, ii, iii, iv, and so on.

Since the Middle Ages, a «j» has sometimes been substituted for the final «i» of a «lower-case» Roman numeral, such as «iij» for 3 or «vij» for 7. This «j» can be considered a swash variant of «i«. Into the early 20th century, the use of a final «j» was still sometimes used in medical prescriptions to prevent tampering with or misinterpretation of a number after it was written.^[60]

Numerals in documents and inscriptions from the Middle Ages sometimes include additional symbols, which today are called «medieval Roman numerals». Some simply substitute another letter for the standard one (such as «A» for «V«, or «Q» for «D«), while others serve as abbreviations for compound numerals («O» for «XI«, or «F» for «XL«). Although they are still listed today in some dictionaries, they are long out of use.^[61]

Number	Medieval abbreviation	Notes and etymology
5	A	Resembles an upside-down V. Also said to equal 500.
6	ↅ	Either from a ligature of VI, or from digamma (ϛ), the Greek numeral 6 (sometimes conflated with the στ ligature).[48]
7	S, Z	Presumed abbreviation of septem, Latin for 7.
9.5	X̷	Scribal abbreviation, an x with a slash through it. Likewise, IX̷ represented 8.5
11	O	Presumed abbreviation of onze, French for 11.
40	F	Presumed abbreviation of English forty.
70	S	Also could stand for 7, with the same derivation.
80	R
90	N	Presumed abbreviation of nonaginta, Latin for 90. (Ambiguous with N for «nothing» (nihil)).
150	Y	Possibly derived from the lowercase y’s shape.
151	K	Unusual, origin unknown; also said to stand for 250.[62]
160	T	Possibly derived from Greek tetra, as 4 × 40 = 160.
200	H	Could also stand for 2 (see also 𐆙, the symbol for the dupondius). From a barring of two I‘s.
250	E
300	B
400	P, G
500	Q	Redundant with D; abbreviates quingenti, Latin for 500. Also sometimes used for 500,000.[63]
800	Ω	Borrowed from Gothic.
900	ϡ	Borrowed from Gothic.
2000	Z

Chronograms, messages with dates encoded into them, were popular during the Renaissance era. The chronogram would be a phrase containing the letters I, V, X, L, C, D, and M. By putting these letters together, the reader would obtain a number, usually indicating a particular year.

Modern use

By the 11th century, Arabic numerals had been introduced into Europe from al-Andalus, by way of Arab traders and arithmetic treatises. Roman numerals, however, proved very persistent, remaining in common use in the West well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Replacement by their more convenient «Arabic» equivalents was quite gradual, and Roman numerals are still used today in certain contexts. A few examples of their current use are:

• Names of monarchs and popes, e.g. Elizabeth II of the United Kingdom, Pope Benedict XVI. These are referred to as regnal numbers and are usually read as ordinals; e.g. II is pronounced «the second». This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England during the reign of Henry VIII. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor. Some monarchs (e.g. Charles IV of Spain and Louis XIV of France) seem to have preferred the use of IIII instead of IV on their coinage (see illustration).
• Generational suffixes, particularly in the U.S., for people sharing the same name across generations, for example William Howard Taft IV. These are also usually read as ordinals.
• In the French Republican Calendar, initiated during the French Revolution, years were numbered by Roman numerals – from the year I (1792) when this calendar was introduced to the year XIV (1805) when it was abandoned.
• The year of production of films, television shows and other works of art within the work itself. Outside reference to the work will use regular Arabic numerals.

• Hour marks on timepieces. In this context, 4 is often written IIII.
• The year of construction on building façades and cornerstones.
• Page numbering of prefaces and introductions of books, and sometimes of appendices and annexes, too.
• Book volume and chapter numbers, as well as the several acts within a play (e.g. Act iii, Scene 2).
• Sequels to some films, video games, and other works (as in Rocky II, Grand Theft Auto V).
• Outlines that use numbers to show hierarchical relationships.
• Occurrences of a recurring grand event, for instance:
  • The Summer and Winter Olympic Games (e.g. the XXI Olympic Winter Games; the Games of the XXX Olympiad).
  • The Super Bowl, the annual championship game of the National Football League (e.g. Super Bowl XLII; Super Bowl 50 was a one-time exception^[64]).
  • WrestleMania, the annual professional wrestling event for the WWE (e.g. WrestleMania XXX). This usage has also been inconsistent.

Specific disciplines

In astronautics, United States rocket model variants are sometimes designated by Roman numerals, e.g. Titan I, Titan II, Titan III, Saturn I, Saturn V.

In astronomy, the natural satellites or «moons» of the planets are traditionally designated by capital Roman numerals appended to the planet’s name. For example, Titan’s designation is Saturn VI.

In chemistry, Roman numerals are often used to denote the groups of the periodic table. They are also used in the IUPAC nomenclature of inorganic chemistry, for the oxidation number of cations which can take on several different positive charges. They are also used for naming phases of polymorphic crystals, such as ice.

In education, school grades (in the sense of year-groups rather than test scores) are sometimes referred to by a Roman numeral; for example, «grade IX» is sometimes seen for «grade 9».

In entomology, the broods of the thirteen and seventeen year periodical cicadas are identified by Roman numerals.

In graphic design stylised Roman numerals may represent numeric values.

In law, Roman numerals are commonly used to help organize legal codes as part of an alphanumeric outline.

In advanced mathematics (including trigonometry, statistics, and calculus), when a graph includes negative numbers, its quadrants are named using I, II, III, and IV. These quadrant names signify positive numbers on both axes, negative numbers on the X axis, negative numbers on both axes, and negative numbers on the Y axis, respectively. The use of Roman numerals to designate quadrants avoids confusion, since Arabic numerals are used for the actual data represented in the graph.

In military unit designation, Roman numerals are often used to distinguish between units at different levels. This reduces possible confusion, especially when viewing operational or strategic level maps. In particular, army corps are often numbered using Roman numerals (for example the American XVIII Airborne Corps or the WW2-era German III Panzerkorps) with Arabic numerals being used for divisions and armies.

In music, Roman numerals are used in several contexts:

• Movements are often numbered using Roman numerals.
• In Roman Numeral Analysis, harmonic function is identified using Roman Numerals.
• Individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings.

In pharmacy, Roman numerals were used with the now largely obsolete apothecaries’ system of measurement: including SS to denote «one half» and N to denote «zero».^[44][65]

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

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

In sport the team containing the «top» players and representing a nation or province, a club or a school at the highest level in (say) rugby union is often called the «1st XV«, while a lower-ranking cricket or American football team might be the «3rd XI«.

In tarot, Roman numerals (with zero) are used to denote the cards of the Major Arcana.

In theology and biblical scholarship, the Septuagint is often referred to as LXX, as this translation of the Old Testament into Greek is named for the legendary number of its translators (septuaginta being Latin for «seventy»).

Modern use in European languages other than English

Some uses that are rare or never seen in English speaking countries may be relatively common in parts of continental Europe and in other regions (e.g. Latin America) that use a European language other than English. For instance:

Capital or small capital Roman numerals are widely used in Romance languages to denote centuries, e.g. the French XVIII^e siècle^[66] and the Spanish siglo XVIII mean «18th century». Slavic languages in and adjacent to Russia similarly favor Roman numerals (xviii век). On the other hand, in Slavic languages in Central Europe, like most Germanic languages, one writes «18.» (with a period) before the local word for «century».

Mixed Roman and Arabic numerals are sometimes used in numeric representations of dates (especially in formal letters and official documents, but also on tombstones). The month is written in Roman numerals, while the day is in Arabic numerals: «4.VI.1789″ and «VI.4.1789″ both refer unambiguously to 4 June 1789.

Roman numerals are sometimes used to represent the days of the week in hours-of-operation signs displayed in windows or on doors of businesses,^[67] and also sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by I. Sunday is represented by VII. 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. In the example case (left), the business opens from 10 AM to 7 PM on weekdays, 10 AM to 5 PM on Saturdays and is closed on Sundays. Note that the listing uses 24-hour time.

Roman numerals may also be used for floor numbering.^[68][69] For instance, 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 Italy, where roads outside built-up areas have kilometre signs, major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from I to IX for the smaller intervals. The sign IX/17 thus marks 17.9 km.

Certain romance-speaking countries use Roman numerals to designate assemblies of their national legislatures. For instance, the composition of the Italian Parliament from 2018 to 2022 (elected in the 2018 Italian general election) is called the XVIII Legislature of the Italian Republic (or more commonly the «XVIII Legislature»).

A notable exception to the use of Roman numerals in Europe is in Greece, where Greek numerals (based on the Greek alphabet) are generally used in contexts where Roman numerals would be used elsewhere.

Unicode

The «Number Forms» block of the Unicode computer character set standard has a number of Roman numeral symbols in the range of code points from U+2160 to U+2188.^[70] This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ or XII). One justification for the existence of pre-combined numbers is to facilitate the setting of multiple-letter numbers (such as VIII) on a single horizontal line in Asian vertical text. The Unicode standard, however, includes special Roman numeral code points for compatibility only, stating that «[f]or most purposes, it is preferable to compose the Roman numerals from sequences of the appropriate Latin letters».^[71]
The block also includes some apostrophus symbols for large numbers, an old variant of «L» (50) similar to the Etruscan character, the Claudian letter «reversed C», etc.

Symbol	ↀ	ↁ	ↂ	ↅ	ↆ	ↇ	ↈ
Value	1,000	5,000	10,000	6	50	50,000	100,000

See also

References

Notes

Citations

Sources

• Menninger, Karl (1992). Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications. ISBN 978-0-486-27096-8.

Further reading

• Aczel, Amir D. 2015. Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers. 1st edition. New York: Palgrave Macmillan.
• Goines, David Lance. A Constructed Roman Alphabet: A Geometric Analysis of the Greek and Roman Capitals and of the Arabic Numerals. Boston: D.R. Godine, 1982.
• Houston, Stephen D. 2012. The Shape of Script: How and Why Writing Systems Change. Santa Fe, NM: School for Advanced Research Press.
• Taisbak, Christian M. 1965. «Roman numerals and the abacus.» Classica et medievalia 26: 147–60.

External links

• «Roman Numerals (Totally Epic Guide)». Know The Romans.

Ответ на этот вопрос очень прост – в римской системе счисления не было нуля. Потому что римская система была не позиционная. Определенными знаками обозначались числа 1, 5, 10, 50, 100, 500 и 1000 (это были латинские буквы I, V, X, L, C, D и M соответственно). Все остальные числа составлялись из этих знаков с помощью операций сложения или вычитания по следующему алгоритму.

 1. Запись числа читается так же, как буквенные надписи, слева направо. Сначала идут римские цифры, соответствующие максимальным числам, потом меньшим и так по убыванию. Римские цифры I, X, C и M можно повторять до трех раз. Например, MDCCLIX – правильная запись, а записи CDM и CLLX – неправильные. В первом случае цифра M стоит на неправильном месте, во втором случае рядом стоят две цифры L.

 2. Перед любой цифрой кроме I может находиться одна цифра меньшего разряда (перед V и X может стоять I, перед L и C – X, перед D и M – C). В этом случае бóльшее число модифицируется, из него вычитается меньшее число. IV=5-1=4, XC=100-10=90.

 3. После того, как произведены все вычитания, модифицированные и не модифицированные цифры складываются. Например, XXXIX=3*10+(10-1)=39, XLVII=(50-10)+5+2*1=47.

 Нелегко, правда? Складывать и вычитать римские числа еще труднее. Попробуйте сложить XVII и XIX. Ответ: XXXVI.

 Такая сложная с нашей точки зрения система счисления была связана с тем, что римляне фактически записывали результаты счета на пальцах. Отсюда появление в качестве основания системы счисления чисел 5, 50 и 500.

 Небольшое отступление. Некоторые из Вас, дорогие читатели, вероятно, видели часы, на которых число 4, которое должно бы писаться так: IV, пишется в виде IIII. Совершенно не по правилам! В чем дело? Дело в культуре. Имя верховного бога древних римлян, Юпитера, писалось по-латински Ivupiter. Это – древнее написание, еще до того, как в латинском языке появились буквы U и J и имя громовержца стали писать Jupiter. Запрет на произнесение или написание имени божества без нужды («Не произноси имя божье всуе») был в ходу у многих народов тогдашнего мира. Римляне тоже уважительно относились к этому предрассудку. Поэтому две первые буквы имени Юпитера они предпочитали не писать. Отсюда IV=IIII.

 Как видим, ноль в такой системе записи чисел не нужен. Ноль ведь – отсутствие числа, а зачем записывать то, чего нет? Цифра ноль была придумана более 2 тысяч лет назад в Индии, тогда же, когда была придумана позиционная система счисления. Иногда еще ее называют поместной нумерацией. О том, что это такое, и чем позиционная система счисления лучше непозиционной, уже писалось в статье от 22.08.2013.

 Надо сказать, что древние римляне более всего проявили себя в положительных областях деятельности: в строительстве, в военном деле, в юриспруденции и в управлении. Философскими же вопросами они, в отличие от древних же греков, заниматься не любили. Римской философии, развитой и разветвленной, как у древних греков, не существует.
 Более того, римляне не страдали от этого комплексом неполноценности. Они совершенно чистосердечно считали, что поставлены богами для того, чтобы повелевать другими народами. Лучше всего этот взгляд на роль римлян выразил в эпической поэме «Энеида» великий поэт Вергилий.

 Герой поэмы, Эней, предок римлян, встречается в подземном царстве мёртвых, куда он попал в ходе своего путешествия из Трои в Италию, своего отца, Анхиза. Анхиз, поскольку он уже умер и приобщен к тайнам мира, через Энея обращается к своим далеким потомкам и провозглашает назначение будущего народа.

Смогут другие создать изваянья живые из бронзы
 Или обличье мужей повторить во мраморе лучше,
 Тяжбы лучше вести и движенья неба искусней
 Вычислят иль назовут восходящие звёзды, — не спорю:
 Римлянин! Ты научись народами править державно —
 В этом искусство твоё! — налагать условия мира,
 Милость покорным являть и смирять войною надменных

 Неплохо, правда? А вы говорите про какой-то там ноль!

Полезные ссылки:

1. Кто изобрел ноль?

• Главная
• Справочник
• Таблицы
• Большая таблица Римских цифр от 1 до 1000

Римские цифры — это натуральные числа, записанные при помощи повторения 7 латинских букв, в определённой прописанной правилами последовательности:

I (1), V (5), X (10), L (50), C (100), D (500), M (1000)

Арабские цифры	Римские цифры
1	I
2	II
3	III
4	IV
5	V
6	VI
7	VII
8	VIII
9	IX
10	X
11	XI
12	XII
13	XIII
14	XIV
15	XV
16	XVI
17	XVII
18	XVIII
19	XIX
20	XX
21	XXI
22	XXII
23	XXIII
24	XXIV
25	XXV
26	XXVI
27	XXVII
28	XXVIII
29	XXIX
30	XXX
31	XXXI
32	XXXII
33	XXXIII
34	XXXIV
35	XXXV
36	XXXVI
37	XXXVII
38	XXXVIII
39	XXXIX
40	XL
41	XLI
42	XLII
43	XLIII
44	XLIV
45	XLV
46	XLVI
47	XLVII
48	XLVIII
49	XLIX
50	L
51	LI
52	LII
53	LIII
54	LIV
55	LV
56	LVI
57	LVII
58	LVIII
59	LIX
60	LX
61	LXI
62	LXII
63	LXIII
64	LXIV
65	LXV
66	LXVI
67	LXVII
68	LXVIII
69	LXIX
70	LXX
71	LXXI
72	LXXII
73	LXXIII
74	LXXIV
75	LXXV
76	LXXVI
77	LXXVII
78	LXXVIII
79	LXXIX
80	LXXX
81	LXXXI
82	LXXXII
83	LXXXIII
84	LXXXIV
85	LXXXV
86	LXXXVI
87	LXXXVII
88	LXXXVIII
89	LXXXIX
90	XC
91	XCI
92	XCII
93	XCIII
94	XCIV
95	XCV
96	XCVI
97	XCVII
98	XCVIII
99	XCIX
100	C
101	CI
102	CII
103	CIII
104	CIV
105	CV
106	CVI
107	CVII
108	CVIII
109	CIX
110	CX
111	CXI
112	CXII
113	CXIII
114	CXIV
115	CXV
116	CXVI
117	CXVII
118	CXVIII
119	CXIX
120	CXX
121	CXXI
122	CXXII
123	CXXIII
124	CXXIV
125	CXXV
126	CXXVI
127	CXXVII
128	CXXVIII
129	CXXIX
130	CXXX
131	CXXXI
132	CXXXII
133	CXXXIII
134	CXXXIV
135	CXXXV
136	CXXXVI
137	CXXXVII
138	CXXXVIII
139	CXXXIX
140	CXL
141	CXLI
142	CXLII
143	CXLIII
144	CXLIV
145	CXLV
146	CXLVI
147	CXLVII
148	CXLVIII
149	CXLIX
150	CL
151	CLI
152	CLII
153	CLIII
154	CLIV
155	CLV
156	CLVI
157	CLVII
158	CLVIII
159	CLIX
160	CLX
161	CLXI
162	CLXII
163	CLXIII
164	CLXIV
165	CLXV
166	CLXVI
167	CLXVII
168	CLXVIII
169	CLXIX
170	CLXX
171	CLXXI
172	CLXXII
173	CLXXIII
174	CLXXIV
175	CLXXV
176	CLXXVI
177	CLXXVII
178	CLXXVIII
179	CLXXIX
180	CLXXX
181	CLXXXI
182	CLXXXII
183	CLXXXIII
184	CLXXXIV
185	CLXXXV
186	CLXXXVI
187	CLXXXVII
188	CLXXXVIII
189	CLXXXIX
190	CXC
191	CXCI
192	CXCII
193	CXCIII
194	CXCIV
195	CXCV
196	CXCVI
197	CXCVII
198	CXCVIII
199	CXCIX
200	CC
201	CCI
202	CCII
203	CCIII
204	CCIV
205	CCV
206	CCVI
207	CCVII
208	CCVIII
209	CCIX
210	CCX
211	CCXI
212	CCXII
213	CCXIII
214	CCXIV
215	CCXV
216	CCXVI
217	CCXVII
218	CCXVIII
219	CCXIX
220	CCXX
221	CCXXI
222	CCXXII
223	CCXXIII
224	CCXXIV
225	CCXXV
226	CCXXVI
227	CCXXVII
228	CCXXVIII
229	CCXXIX
230	CCXXX
231	CCXXXI
232	CCXXXII
233	CCXXXIII
234	CCXXXIV
235	CCXXXV
236	CCXXXVI
237	CCXXXVII
238	CCXXXVIII
239	CCXXXIX
240	CCXL
241	CCXLI
242	CCXLII
243	CCXLIII
244	CCXLIV
245	CCXLV
246	CCXLVI
247	CCXLVII
248	CCXLVIII
249	CCXLIX
250	CCL
251	CCLI
252	CCLII
253	CCLIII
254	CCLIV
255	CCLV
256	CCLVI
257	CCLVII
258	CCLVIII
259	CCLIX
260	CCLX
261	CCLXI
262	CCLXII
263	CCLXIII
264	CCLXIV
265	CCLXV
266	CCLXVI
267	CCLXVII
268	CCLXVIII
269	CCLXIX
270	CCLXX
271	CCLXXI
272	CCLXXII
273	CCLXXIII
274	CCLXXIV
275	CCLXXV
276	CCLXXVI
277	CCLXXVII
278	CCLXXVIII
279	CCLXXIX
280	CCLXXX
281	CCLXXXI
282	CCLXXXII
283	CCLXXXIII
284	CCLXXXIV
285	CCLXXXV
286	CCLXXXVI
287	CCLXXXVII
288	CCLXXXVIII
289	CCLXXXIX
290	CCXC
291	CCXCI
292	CCXCII
293	CCXCIII
294	CCXCIV
295	CCXCV
296	CCXCVI
297	CCXCVII
298	CCXCVIII
299	CCXCIX
300	CCC
301	CCCI
302	CCCII
303	CCCIII
304	CCCIV
305	CCCV
306	CCCVI
307	CCCVII
308	CCCVIII
309	CCCIX
310	CCCX
311	CCCXI
312	CCCXII
313	CCCXIII
314	CCCXIV
315	CCCXV
316	CCCXVI
317	CCCXVII
318	CCCXVIII
319	CCCXIX
320	CCCXX
321	CCCXXI
322	CCCXXII
323	CCCXXIII
324	CCCXXIV
325	CCCXXV
326	CCCXXVI
327	CCCXXVII
328	CCCXXVIII
329	CCCXXIX
330	CCCXXX
331	CCCXXXI
332	CCCXXXII
333	CCCXXXIII
334	CCCXXXIV
335	CCCXXXV
336	CCCXXXVI
337	CCCXXXVII
338	CCCXXXVIII
339	CCCXXXIX
340	CCCXL
341	CCCXLI
342	CCCXLII
343	CCCXLIII
344	CCCXLIV
345	CCCXLV
346	CCCXLVI
347	CCCXLVII
348	CCCXLVIII
349	CCCXLIX
350	CCCL
351	CCCLI
352	CCCLII
353	CCCLIII
354	CCCLIV
355	CCCLV
356	CCCLVI
357	CCCLVII
358	CCCLVIII
359	CCCLIX
360	CCCLX
361	CCCLXI
362	CCCLXII
363	CCCLXIII
364	CCCLXIV
365	CCCLXV
366	CCCLXVI
367	CCCLXVII
368	CCCLXVIII
369	CCCLXIX
370	CCCLXX
371	CCCLXXI
372	CCCLXXII
373	CCCLXXIII
374	CCCLXXIV
375	CCCLXXV
376	CCCLXXVI
377	CCCLXXVII
378	CCCLXXVIII
379	CCCLXXIX
380	CCCLXXX
381	CCCLXXXI
382	CCCLXXXII
383	CCCLXXXIII
384	CCCLXXXIV
385	CCCLXXXV
386	CCCLXXXVI
387	CCCLXXXVII
388	CCCLXXXVIII
389	CCCLXXXIX
390	CCCXC
391	CCCXCI
392	CCCXCII
393	CCCXCIII
394	CCCXCIV
395	CCCXCV
396	CCCXCVI
397	CCCXCVII
398	CCCXCVIII
399	CCCXCIX
400	CD
401	CDI
402	CDII
403	CDIII
404	CDIV
405	CDV
406	CDVI
407	CDVII
408	CDVIII
409	CDIX
410	CDX
411	CDXI
412	CDXII
413	CDXIII
414	CDXIV
415	CDXV
416	CDXVI
417	CDXVII
418	CDXVIII
419	CDXIX
420	CDXX
421	CDXXI
422	CDXXII
423	CDXXIII
424	CDXXIV
425	CDXXV
426	CDXXVI
427	CDXXVII
428	CDXXVIII
429	CDXXIX
430	CDXXX
431	CDXXXI
432	CDXXXII
433	CDXXXIII
434	CDXXXIV
435	CDXXXV
436	CDXXXVI
437	CDXXXVII
438	CDXXXVIII
439	CDXXXIX
440	CDXL
441	CDXLI
442	CDXLII
443	CDXLIII
444	CDXLIV
445	CDXLV
446	CDXLVI
447	CDXLVII
448	CDXLVIII
449	CDXLIX
450	CDL
451	CDLI
452	CDLII
453	CDLIII
454	CDLIV
455	CDLV
456	CDLVI
457	CDLVII
458	CDLVIII
459	CDLIX
460	CDLX
461	CDLXI
462	CDLXII
463	CDLXIII
464	CDLXIV
465	CDLXV
466	CDLXVI
467	CDLXVII
468	CDLXVIII
469	CDLXIX
470	CDLXX
471	CDLXXI
472	CDLXXII
473	CDLXXIII
474	CDLXXIV
475	CDLXXV
476	CDLXXVI
477	CDLXXVII
478	CDLXXVIII
479	CDLXXIX
480	CDLXXX
481	CDLXXXI
482	CDLXXXII
483	CDLXXXIII
484	CDLXXXIV
485	CDLXXXV
486	CDLXXXVI
487	CDLXXXVII
488	CDLXXXVIII
489	CDLXXXIX
490	CDXC
491	CDXCI
492	CDXCII
493	CDXCIII
494	CDXCIV
495	CDXCV
496	CDXCVI
497	CDXCVII
498	CDXCVIII
499	CDXCIX
500	D
501	DI
502	DII
503	DIII
504	DIV
505	DV
506	DVI
507	DVII
508	DVIII
509	DIX
510	DX
511	DXI
512	DXII
513	DXIII
514	DXIV
515	DXV
516	DXVI
517	DXVII
518	DXVIII
519	DXIX
520	DXX
521	DXXI
522	DXXII
523	DXXIII
524	DXXIV
525	DXXV
526	DXXVI
527	DXXVII
528	DXXVIII
529	DXXIX
530	DXXX
531	DXXXI
532	DXXXII
533	DXXXIII
534	DXXXIV
535	DXXXV
536	DXXXVI
537	DXXXVII
538	DXXXVIII
539	DXXXIX
540	DXL
541	DXLI
542	DXLII
543	DXLIII
544	DXLIV
545	DXLV
546	DXLVI
547	DXLVII
548	DXLVIII
549	DXLIX
550	DL
551	DLI
552	DLII
553	DLIII
554	DLIV
555	DLV
556	DLVI
557	DLVII
558	DLVIII
559	DLIX
560	DLX
561	DLXI
562	DLXII
563	DLXIII
564	DLXIV
565	DLXV
566	DLXVI
567	DLXVII
568	DLXVIII
569	DLXIX
570	DLXX
571	DLXXI
572	DLXXII
573	DLXXIII
574	DLXXIV
575	DLXXV
576	DLXXVI
577	DLXXVII
578	DLXXVIII
579	DLXXIX
580	DLXXX
581	DLXXXI
582	DLXXXII
583	DLXXXIII
584	DLXXXIV
585	DLXXXV
586	DLXXXVI
587	DLXXXVII
588	DLXXXVIII
589	DLXXXIX
590	DXC
591	DXCI
592	DXCII
593	DXCIII
594	DXCIV
595	DXCV
596	DXCVI
597	DXCVII
598	DXCVIII
599	DXCIX
600	DC
601	DCI
602	DCII
603	DCIII
604	DCIV
605	DCV
606	DCVI
607	DCVII
608	DCVIII
609	DCIX
610	DCX
611	DCXI
612	DCXII
613	DCXIII
614	DCXIV
615	DCXV
616	DCXVI
617	DCXVII
618	DCXVIII
619	DCXIX
620	DCXX
621	DCXXI
622	DCXXII
623	DCXXIII
624	DCXXIV
625	DCXXV
626	DCXXVI
627	DCXXVII
628	DCXXVIII
629	DCXXIX
630	DCXXX
631	DCXXXI
632	DCXXXII
633	DCXXXIII
634	DCXXXIV
635	DCXXXV
636	DCXXXVI
637	DCXXXVII
638	DCXXXVIII
639	DCXXXIX
640	DCXL
641	DCXLI
642	DCXLII
643	DCXLIII
644	DCXLIV
645	DCXLV
646	DCXLVI
647	DCXLVII
648	DCXLVIII
649	DCXLIX
650	DCL
651	DCLI
652	DCLII
653	DCLIII
654	DCLIV
655	DCLV
656	DCLVI
657	DCLVII
658	DCLVIII
659	DCLIX
660	DCLX
661	DCLXI
662	DCLXII
663	DCLXIII
664	DCLXIV
665	DCLXV
666	DCLXVI
667	DCLXVII
668	DCLXVIII
669	DCLXIX
670	DCLXX
671	DCLXXI
672	DCLXXII
673	DCLXXIII
674	DCLXXIV
675	DCLXXV
676	DCLXXVI
677	DCLXXVII
678	DCLXXVIII
679	DCLXXIX
680	DCLXXX
681	DCLXXXI
682	DCLXXXII
683	DCLXXXIII
684	DCLXXXIV
685	DCLXXXV
686	DCLXXXVI
687	DCLXXXVII
688	DCLXXXVIII
689	DCLXXXIX
690	DCXC
691	DCXCI
692	DCXCII
693	DCXCIII
694	DCXCIV
695	DCXCV
696	DCXCVI
697	DCXCVII
698	DCXCVIII
699	DCXCIX
700	DCC
701	DCCI
702	DCCII
703	DCCIII
704	DCCIV
705	DCCV
706	DCCVI
707	DCCVII
708	DCCVIII
709	DCCIX
710	DCCX
711	DCCXI
712	DCCXII
713	DCCXIII
714	DCCXIV
715	DCCXV
716	DCCXVI
717	DCCXVII
718	DCCXVIII
719	DCCXIX
720	DCCXX
721	DCCXXI
722	DCCXXII
723	DCCXXIII
724	DCCXXIV
725	DCCXXV
726	DCCXXVI
727	DCCXXVII
728	DCCXXVIII
729	DCCXXIX
730	DCCXXX
731	DCCXXXI
732	DCCXXXII
733	DCCXXXIII
734	DCCXXXIV
735	DCCXXXV
736	DCCXXXVI
737	DCCXXXVII
738	DCCXXXVIII
739	DCCXXXIX
740	DCCXL
741	DCCXLI
742	DCCXLII
743	DCCXLIII
744	DCCXLIV
745	DCCXLV
746	DCCXLVI
747	DCCXLVII
748	DCCXLVIII
749	DCCXLIX
750	DCCL
751	DCCLI
752	DCCLII
753	DCCLIII
754	DCCLIV
755	DCCLV
756	DCCLVI
757	DCCLVII
758	DCCLVIII
759	DCCLIX
760	DCCLX
761	DCCLXI
762	DCCLXII
763	DCCLXIII
764	DCCLXIV
765	DCCLXV
766	DCCLXVI
767	DCCLXVII
768	DCCLXVIII
769	DCCLXIX
770	DCCLXX
771	DCCLXXI
772	DCCLXXII
773	DCCLXXIII
774	DCCLXXIV
775	DCCLXXV
776	DCCLXXVI
777	DCCLXXVII
778	DCCLXXVIII
779	DCCLXXIX
780	DCCLXXX
781	DCCLXXXI
782	DCCLXXXII
783	DCCLXXXIII
784	DCCLXXXIV
785	DCCLXXXV
786	DCCLXXXVI
787	DCCLXXXVII
788	DCCLXXXVIII
789	DCCLXXXIX
790	DCCXC
791	DCCXCI
792	DCCXCII
793	DCCXCIII
794	DCCXCIV
795	DCCXCV
796	DCCXCVI
797	DCCXCVII
798	DCCXCVIII
799	DCCXCIX
800	DCCC
801	DCCCI
802	DCCCII
803	DCCCIII
804	DCCCIV
805	DCCCV
806	DCCCVI
807	DCCCVII
808	DCCCVIII
809	DCCCIX
810	DCCCX
811	DCCCXI
812	DCCCXII
813	DCCCXIII
814	DCCCXIV
815	DCCCXV
816	DCCCXVI
817	DCCCXVII
818	DCCCXVIII
819	DCCCXIX
820	DCCCXX
821	DCCCXXI
822	DCCCXXII
823	DCCCXXIII
824	DCCCXXIV
825	DCCCXXV
826	DCCCXXVI
827	DCCCXXVII
828	DCCCXXVIII
829	DCCCXXIX
830	DCCCXXX
831	DCCCXXXI
832	DCCCXXXII
833	DCCCXXXIII
834	DCCCXXXIV
835	DCCCXXXV
836	DCCCXXXVI
837	DCCCXXXVII
838	DCCCXXXVIII
839	DCCCXXXIX
840	DCCCXL
841	DCCCXLI
842	DCCCXLII
843	DCCCXLIII
844	DCCCXLIV
845	DCCCXLV
846	DCCCXLVI
847	DCCCXLVII
848	DCCCXLVIII
849	DCCCXLIX
850	DCCCL
851	DCCCLI
852	DCCCLII
853	DCCCLIII
854	DCCCLIV
855	DCCCLV
856	DCCCLVI
857	DCCCLVII
858	DCCCLVIII
859	DCCCLIX
860	DCCCLX
861	DCCCLXI
862	DCCCLXII
863	DCCCLXIII
864	DCCCLXIV
865	DCCCLXV
866	DCCCLXVI
867	DCCCLXVII
868	DCCCLXVIII
869	DCCCLXIX
870	DCCCLXX
871	DCCCLXXI
872	DCCCLXXII
873	DCCCLXXIII
874	DCCCLXXIV
875	DCCCLXXV
876	DCCCLXXVI
877	DCCCLXXVII
878	DCCCLXXVIII
879	DCCCLXXIX
880	DCCCLXXX
881	DCCCLXXXI
882	DCCCLXXXII
883	DCCCLXXXIII
884	DCCCLXXXIV
885	DCCCLXXXV
886	DCCCLXXXVI
887	DCCCLXXXVII
888	DCCCLXXXVIII
889	DCCCLXXXIX
890	DCCCXC
891	DCCCXCI
892	DCCCXCII
893	DCCCXCIII
894	DCCCXCIV
895	DCCCXCV
896	DCCCXCVI
897	DCCCXCVII
898	DCCCXCVIII
899	DCCCXCIX
900	CM
901	CMI
902	CMII
903	CMIII
904	CMIV
905	CMV
906	CMVI
907	CMVII
908	CMVIII
909	CMIX
910	CMX
911	CMXI
912	CMXII
913	CMXIII
914	CMXIV
915	CMXV
916	CMXVI
917	CMXVII
918	CMXVIII
919	CMXIX
920	CMXX
921	CMXXI
922	CMXXII
923	CMXXIII
924	CMXXIV
925	CMXXV
926	CMXXVI
927	CMXXVII
928	CMXXVIII
929	CMXXIX
930	CMXXX
931	CMXXXI
932	CMXXXII
933	CMXXXIII
934	CMXXXIV
935	CMXXXV
936	CMXXXVI
937	CMXXXVII
938	CMXXXVIII
939	CMXXXIX
940	CMXL
941	CMXLI
942	CMXLII
943	CMXLIII
944	CMXLIV
945	CMXLV
946	CMXLVI
947	CMXLVII
948	CMXLVIII
949	CMXLIX
950	CML
951	CMLI
952	CMLII
953	CMLIII
954	CMLIV
955	CMLV
956	CMLVI
957	CMLVII
958	CMLVIII
959	CMLIX
960	CMLX
961	CMLXI
962	CMLXII
963	CMLXIII
964	CMLXIV
965	CMLXV
966	CMLXVI
967	CMLXVII
968	CMLXVIII
969	CMLXIX
970	CMLXX
971	CMLXXI
972	CMLXXII
973	CMLXXIII
974	CMLXXIV
975	CMLXXV
976	CMLXXVI
977	CMLXXVII
978	CMLXXVIII
979	CMLXXIX
980	CMLXXX
981	CMLXXXI
982	CMLXXXII
983	CMLXXXIII
984	CMLXXXIV
985	CMLXXXV
986	CMLXXXVI
987	CMLXXXVII
988	CMLXXXVIII
989	CMLXXXIX
990	CMXC
991	CMXCI
992	CMXCII
993	CMXCIII
994	CMXCIV
995	CMXCV
996	CMXCVI
997	CMXCVII
998	CMXCVIII
999	CMXCIX
1000	M

На сегодняшний день в рамках общих правил число 15 правильно записывать в такой последовательности XV и не VVV или XIIIII.

Источник

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