Roman numerals are a that originated in and remained the usual way of writing numbers throughout Europe well into the . Numbers in this system are represented by combinations of letters from the . Modern style uses seven symbols, each with a fixed integer value:
The use of Roman numerals continued long after the decline of the . From the 14th century on, Roman numerals began to be replaced by ; 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 s. For instance, on the clock of (designed in 1852), the hours from 1 to 12 are written as:
The notations and 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 "" on Roman numeral clocks.
Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. , signifying "a thousand, and a hundred less than another thousand", means 1900, so 1912 is written . For the years of this century, indicates 2000. The current year is ().

The numerals for 4 () and 9 () are written using "subtractive notation",Stanislas Dehaene (1997): ''The Number Sense : How the Mind Creates Mathematics''. Oxford University Press; 288 pages. where the first symbol () is ''subtracted'' from the larger one (, or ), thus avoiding the clumsier (, and ). Subtractive notation is also used for 40 (), 90 (), 400 () and 900 ().Ûrij Vasilʹevič Prokhorov and Michiel Hazewinkel, editors (1990):

Encyclopaedia of Mathematics

', Volume 10, page 502. Springer; 546 pages. These are the only subtractive forms in standard use. A number containing several decimal digits is built by appending the Roman numeral equivalent for each, from highest to lowest, as in the following examples: * 39 = + = . * 246 = + + = . * 789 = + + = . *2,421 = + + + = . Any missing place (represented by a zero in the place-value equivalent) is omitted, as in Latin (and English) speech: * 160 = + = * 207 = + = *1,009 = + = *1,066 = + + = In practice, Roman numerals for large numbers are currently used mainly for year numbers, as in these examples: * 1776 = + + + = (the date written on the book held by the ). * 1918 = + + + = (the first year of the pandemic) * 1954 = + + + = (as in the for the movie ') * 2014 = + + = (the year of the games of the (22nd) (in )) The largest number that can be represented in this notation is 3,999 (), but since the largest Roman numeral likely to be required today is (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 below.

Commentarii de Bello Gallico

'. Book II, Section 4: "... XV milia Atrebates, Ambianos X milia, Morinos XXV milia, Menapios VII milia, Caletos X milia, Veliocasses et Viromanduos totidem, Atuatucos XVIIII milia; ..." Section 8: "... ab utroque latere eius collis transversam fossam obduxit circiter passuum CCCC et ad extremas fossas castella constituit..." Book IV, Section 15: "Nostri ad unum omnes incolumes, perpaucis vulneratis, ex tanti belli timore, cum hostium numerus capitum CCCCXXX milium fuisset, se in castra receperunt." Book VII, Section 4: "...in hiberna remissis ipse se recipit die XXXX Bibracte." continued to be used, including in compound numbers like ,Angelo Rocca (1612) ''De campanis commentarius''. Published by Guillelmo Faciotti, Rome. : "Campana a XXIIII hominibus pulsata" ("Bell to be sounded by 24 men") ,Gerard Ter Borch (1673): '. Date on painting: "Out. XXIIII Jaer. // M. DC. LXXIIII". and .Pliny the Elder (77–79 AD):

Naturalis Historia

', Book III: "Saturni vocatur, Caesaream Mauretaniae urbem CCLXXXXVII p ssum traiectus. reliqua in ora flumen Tader ... ortus in Cantabris haut procul oppido Iuliobrica, per CCCCL p. fluens ..." Book IV: "Epiri, Achaiae, Atticae, Thessalia in porrectum longitudo CCCCLXXXX traditur, latitudo CCLXXXXVII." Book VI: "tam vicinum Arsaniae fluere eum in regione Arrhene Claudius Caesar auctor est, ut, cum intumuere, confluant nec tamen misceantur leviorque Arsanias innatet MMMM ferme spatio, mox divisus in Euphraten mergatur." The additive forms for 9, 90, and 900 (, ,Thomas Bennet (1731): ''Grammatica Hebræa, cum uberrima praxi in usum tironum ... Editio tertia.'' Published by T. Astley, copy in the British Library; 149 pages. Page 24: "PRÆFIXA duo sunt ''viz.'' ''He'' emphaticum vel relativum (de quo Cap VI Reg. LXXXX.) & ''Shin'' cum ''Segal'' sequente ''Dagesh'', quod denotat pronomen relativum..." and Pico Della Mirandola (1486)

Conclusiones sive Theses DCCCC

' ("Conclusions, or 900 Theses").) 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 , is systematically used instead of , but subtractive notation is used for ; so that gate 44 is labelled . Modern s that use Roman numerals still very often use for four o'clock but for nine o'clock, a practice that goes back to very early clocks such as the of the late 14th century.. However, this is far from universal: for example, the clock on the tower, , uses a subtractive for 4 o'clock. once mentioned an "interesting theory" that Romans avoided using because it was the initial letters of , the Latin spelling of , and might have seemed . He did not say whose theory it was. Several monumental inscriptions created in the early 20th century use variant forms for "1900" (usually written ). These vary from for 1910 as seen on , London, to the more unusual, if not unique for 1903, on the north entrance to the . Especially on tombstones and other funerary inscriptions 5 and 50 have been occasionally written and instead of and , and there are instances such as and rather than or .

Acta publica inter invictissimos gloriosissimosque&c. ... et Ferdinandum II. Romanorum Imperatores...

'. Printed by Ian-Friderici Weissii. Page 123: "Sub Dato Pragæ IIIXX Decemb. A. C. M. DC. IIXX". Page 126, end of the same document: "Dabantur Pragæ 17 Decemb. M. DC. IIXX" for 18,Raphael Sulpicius à Munscrod (1621):

Vera Ac Germana Detecto Clandestinarvm Deliberationvm

'. Page 16, line 1: "repertum Originale Subdatum IIIXXX Aug. A. C. MDC.IIXX". Page 41, upper right corner: "Decemb. A. C. MDC.IIXX". Page 42, upper left corner: "Febr. A. C. MDC.XIX". Page 70: "IIXX. die Maij sequentia in consilio noua ex Bohemia allata....". Page 71: "XIX. Maij". for 97,Wilhelm Ernst Tentzel (1699):

Als Ihre Königl. Majestät in Pohlen und ...

'. Page 39: "... und der Umschrifft: LITHUANIA ASSERTA M. DC. IIIC " for 98,Joh. Caspar Posner (1698):

Mvndvs ante mvndvm sive De Chao Orbis Primordio

', title page: "Ad diem jvlii A. O. R. M DC IIC".Wilhelm Ernst Tentzel (1700):

Saxonia Nvmismatica: Das ist: Die Historie Des Durchlauchtigsten...

'. Page 26: "Die Revers hat eine feine Inscription: SERENISSIMO DN.DN... SENATUS.QVERNF. A. M DC IIC D. 18 OCT ear 1698 day 18 oct" and for 99. (1698):

Opera Geographica et Historica

'. Helmstadt, J. M. Sustermann. Title page of first edition: "Bibliopolæ ibid. M DC IC" A possible explanation is that the word for 18 in Latin is , literally "two from twenty", 98 is (two from hundred), and 99 is (one from hundred). However, the explanation does not seem to apply to and , since the Latin words for 17 and 97 were (seven ten) and (ninety seven), respectively. There are multiple examples of being used for 8. There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than . was used by officers of the to write their number. The notation appears prominently on the of their senior ( – AD 9). On the publicly displayed official Roman calendars known as , is used for the 18 days to the next , and for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the .

(2005) Legio XX Valeria Victrix...

'. PhD thesis. On page 396 it discusses many coins with "Leg. IIXX" and notes that it must be Legion 22. The footnote on that page says: "The form IIXX clearly reflecting the Latin duo et vicensima 'twenty-second': cf. X5398, legatus I g III et vicensim(ae) Pri; VI 1551, legatus leg] IIXX Prj; III 14207.7, miles leg IIXX; and III 10471-3, a vexillation drawn from four German legions including 'XVIII PR' – surely here the stonecutter's hypercorrection for IIXX PR. Apparently, at least one ancient mistakenly thought that the of "22nd Legion" stood for 18, and "corrected" it to . * There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as , corresponding to the common reading "sixteen thirteen" of such year numbers in English, or 1519 as as in ''quinze-cent-dix-neuf'' (fifteen-hundred and nineteen), and similar readings in other languages.M. Gachard (1862):

II. Analectes historiques, neuvième série (n^{os} CCLXI-CCLXXXIV)

. ''Bulletin de la Commission royale d'Historie'', volume 3, pages 345–554. Page 347: ''Lettre de Philippe le Beau aux échevins...'', quote: "Escript en nostre ville de Gand, le XXIIII^{me} de febvrier, l'an IIII^{XX}XIX uatre-vingt-dix-neuf = 99" Page 356: ''Lettre de l'achiduchesse Marguerite au conseil de Brabant...'', quote: "... Escript à Bruxelles, le dernier jour de juing anno XV^{c}XIX 519" Page 374: ''Letters patentes de la rémission ... de la ville de Bruxelles'', quote: "... Op heden, tweentwintich twenty-two'daegen in decembri, anno vyfthien hondert tweendertich fifteen hundred thirty-two'... Gegeven op ten vyfsten dach in deser jegewoirdige maent van decembri anno XV tweendertich ^{me} de juillet XV^{c} huytante-six 586"
* In some French texts from the 15th century and later one finds constructions like for 99, reflecting the French reading of that number as ''quatre-vingt-dix-neuf'' (four-score and nineteen). Similarly, in some English documents one finds, for example, 77 written as "" (which could be read "three-score and seventeen").Herbert Edward Salter (1923)

Registrum Annalium Collegii Mertonensis 1483–1521

' Oxford Historical Society, volume 76; 544 pages. Page 184 has the computation in pounds:shillings:pence (li:s:d) x:iii:iiii + xxi:viii:viii + xlv:xiiii:i = iii^{xx}xvii:vi:i, i.e. 10:3:4 + 21:8:8 + 45:14:1 = 77:6:1.
* Another medieval accounting text from 1301 renders numbers like 13,573 as "", that is, "13×1000 + 5×100 + 3×20 + 13".Johannis de Sancto Justo (1301): "E Duo Codicibus Ceratis" ("From Two Texts in Wax"). In de Wailly, Delisle (1865):

Contenant la deuxieme livraison des monumens des regnes de saint Louis,...

' Volume 22 of ''Recueil des historiens des Gaules et de la France''. Page 530: "SUMMA totalis, XIII. M. V. C. III. XX. XIII. l. III s. XI d. um total, 13 thousand 5 hundred 3 score 13 livres, 3 sous, 11 deniers * Other numerals that do not fit the usual patterns – such as for 45, instead of the usual — may be due to scribal errors, or the writer's lack of familiarity with the system, rather than being genuine variant usage.

Nombre, chiffre, lettre : Formes et réformes. Des notations chiffrées de l'étrusque

("Between Numbers and Letters: About Etruscan Notations of Numeral Sequences"). ''Revue de philologie, de littérature et d'histoire anciennes'', volume (83), issue 1, pages 103–130. 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 (or "𐌢𐌣" for 40), and wrote "𐌡𐌠𐌠", "𐌡𐌠𐌠𐌠" and "𐌡𐌠𐌠𐌠𐌠" for 7, 8, and 9, respectively.

Description

Roman numerals are essentially a decimal or "base ten" number system, but instead of (in which place-keeping zeros enable a digit to represent different powers of ten) the system uses a set of symbols with fixed values, including "built in" powers of ten. Tally-like combinations of these fixed symbols correspond to the (placed) digits of Arabic numerals. This structure allows for significant flexibility in notation, and many variant forms are attested. In fact, there has never been an officially binding, 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". On the other hand, especially where a Roman numeral is considered a legally binding expression of a number, as in (where an "incorrect" or ambiguous numeral may invalidate a copyright claim, or affect the termination date of the copyright period) it is desirable to strictly follow the usual style described below.Standard form

The following table displays how Roman Numerals are usually written:The numerals for 4 () and 9 () are written using "subtractive notation",Stanislas Dehaene (1997): ''The Number Sense : How the Mind Creates Mathematics''. Oxford University Press; 288 pages. where the first symbol () is ''subtracted'' from the larger one (, or ), thus avoiding the clumsier (, and ). Subtractive notation is also used for 40 (), 90 (), 400 () and 900 ().Ûrij Vasilʹevič Prokhorov and Michiel Hazewinkel, editors (1990):

Encyclopaedia of Mathematics

', Volume 10, page 502. Springer; 546 pages. These are the only subtractive forms in standard use. A number containing several decimal digits is built by appending the Roman numeral equivalent for each, from highest to lowest, as in the following examples: * 39 = + = . * 246 = + + = . * 789 = + + = . *2,421 = + + + = . Any missing place (represented by a zero in the place-value equivalent) is omitted, as in Latin (and English) speech: * 160 = + = * 207 = + = *1,009 = + = *1,066 = + + = In practice, Roman numerals for large numbers are currently used mainly for year numbers, as in these examples: * 1776 = + + + = (the date written on the book held by the ). * 1918 = + + + = (the first year of the pandemic) * 1954 = + + + = (as in the for the movie ') * 2014 = + + = (the year of the games of the (22nd) (in )) The largest number that can be represented in this notation is 3,999 (), but since the largest Roman numeral likely to be required today is (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 below.

Variant forms

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

While subtractive notation for 4, 40 and 400 (, and ) has been the usual form since Roman times, additive notation to represent these numbers (, and )Julius Caesar (52–49 BC):Commentarii de Bello Gallico

'. Book II, Section 4: "... XV milia Atrebates, Ambianos X milia, Morinos XXV milia, Menapios VII milia, Caletos X milia, Veliocasses et Viromanduos totidem, Atuatucos XVIIII milia; ..." Section 8: "... ab utroque latere eius collis transversam fossam obduxit circiter passuum CCCC et ad extremas fossas castella constituit..." Book IV, Section 15: "Nostri ad unum omnes incolumes, perpaucis vulneratis, ex tanti belli timore, cum hostium numerus capitum CCCCXXX milium fuisset, se in castra receperunt." Book VII, Section 4: "...in hiberna remissis ipse se recipit die XXXX Bibracte." continued to be used, including in compound numbers like ,Angelo Rocca (1612) ''De campanis commentarius''. Published by Guillelmo Faciotti, Rome. : "Campana a XXIIII hominibus pulsata" ("Bell to be sounded by 24 men") ,Gerard Ter Borch (1673): '. Date on painting: "Out. XXIIII Jaer. // M. DC. LXXIIII". and .Pliny the Elder (77–79 AD):

Naturalis Historia

', Book III: "Saturni vocatur, Caesaream Mauretaniae urbem CCLXXXXVII p ssum traiectus. reliqua in ora flumen Tader ... ortus in Cantabris haut procul oppido Iuliobrica, per CCCCL p. fluens ..." Book IV: "Epiri, Achaiae, Atticae, Thessalia in porrectum longitudo CCCCLXXXX traditur, latitudo CCLXXXXVII." Book VI: "tam vicinum Arsaniae fluere eum in regione Arrhene Claudius Caesar auctor est, ut, cum intumuere, confluant nec tamen misceantur leviorque Arsanias innatet MMMM ferme spatio, mox divisus in Euphraten mergatur." The additive forms for 9, 90, and 900 (, ,Thomas Bennet (1731): ''Grammatica Hebræa, cum uberrima praxi in usum tironum ... Editio tertia.'' Published by T. Astley, copy in the British Library; 149 pages. Page 24: "PRÆFIXA duo sunt ''viz.'' ''He'' emphaticum vel relativum (de quo Cap VI Reg. LXXXX.) & ''Shin'' cum ''Segal'' sequente ''Dagesh'', quod denotat pronomen relativum..." and Pico Della Mirandola (1486)

Conclusiones sive Theses DCCCC

' ("Conclusions, or 900 Theses").) 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 , is systematically used instead of , but subtractive notation is used for ; so that gate 44 is labelled . Modern s that use Roman numerals still very often use for four o'clock but for nine o'clock, a practice that goes back to very early clocks such as the of the late 14th century.. However, this is far from universal: for example, the clock on the tower, , uses a subtractive for 4 o'clock. once mentioned an "interesting theory" that Romans avoided using because it was the initial letters of , the Latin spelling of , and might have seemed . He did not say whose theory it was. Several monumental inscriptions created in the early 20th century use variant forms for "1900" (usually written ). These vary from for 1910 as seen on , London, to the more unusual, if not unique for 1903, on the north entrance to the . Especially on tombstones and other funerary inscriptions 5 and 50 have been occasionally written and instead of and , and there are instances such as and rather than or .

Irregular subtractive notation

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 function in , which can turn 499 into , , , , or depending on the "" setting. 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 for 17,Michaele Gasp. Lvndorphio (1621):Acta publica inter invictissimos gloriosissimosque&c. ... et Ferdinandum II. Romanorum Imperatores...

'. Printed by Ian-Friderici Weissii. Page 123: "Sub Dato Pragæ IIIXX Decemb. A. C. M. DC. IIXX". Page 126, end of the same document: "Dabantur Pragæ 17 Decemb. M. DC. IIXX" for 18,Raphael Sulpicius à Munscrod (1621):

Vera Ac Germana Detecto Clandestinarvm Deliberationvm

'. Page 16, line 1: "repertum Originale Subdatum IIIXXX Aug. A. C. MDC.IIXX". Page 41, upper right corner: "Decemb. A. C. MDC.IIXX". Page 42, upper left corner: "Febr. A. C. MDC.XIX". Page 70: "IIXX. die Maij sequentia in consilio noua ex Bohemia allata....". Page 71: "XIX. Maij". for 97,Wilhelm Ernst Tentzel (1699):

Als Ihre Königl. Majestät in Pohlen und ...

'. Page 39: "... und der Umschrifft: LITHUANIA ASSERTA M. DC. IIIC " for 98,Joh. Caspar Posner (1698):

Mvndvs ante mvndvm sive De Chao Orbis Primordio

', title page: "Ad diem jvlii A. O. R. M DC IIC".Wilhelm Ernst Tentzel (1700):

Saxonia Nvmismatica: Das ist: Die Historie Des Durchlauchtigsten...

'. Page 26: "Die Revers hat eine feine Inscription: SERENISSIMO DN.DN... SENATUS.QVERNF. A. M DC IIC D. 18 OCT ear 1698 day 18 oct" and for 99. (1698):

Opera Geographica et Historica

'. Helmstadt, J. M. Sustermann. Title page of first edition: "Bibliopolæ ibid. M DC IC" A possible explanation is that the word for 18 in Latin is , literally "two from twenty", 98 is (two from hundred), and 99 is (one from hundred). However, the explanation does not seem to apply to and , since the Latin words for 17 and 97 were (seven ten) and (ninety seven), respectively. There are multiple examples of being used for 8. There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than . was used by officers of the to write their number. The notation appears prominently on the of their senior ( – AD 9). On the publicly displayed official Roman calendars known as , is used for the 18 days to the next , and for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the .

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. * was how people associated with the 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).Stephen James Malone,(2005) Legio XX Valeria Victrix...

'. PhD thesis. On page 396 it discusses many coins with "Leg. IIXX" and notes that it must be Legion 22. The footnote on that page says: "The form IIXX clearly reflecting the Latin duo et vicensima 'twenty-second': cf. X5398, legatus I g III et vicensim(ae) Pri; VI 1551, legatus leg] IIXX Prj; III 14207.7, miles leg IIXX; and III 10471-3, a vexillation drawn from four German legions including 'XVIII PR' – surely here the stonecutter's hypercorrection for IIXX PR. Apparently, at least one ancient mistakenly thought that the of "22nd Legion" stood for 18, and "corrected" it to . * There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as , corresponding to the common reading "sixteen thirteen" of such year numbers in English, or 1519 as as in ''quinze-cent-dix-neuf'' (fifteen-hundred and nineteen), and similar readings in other languages.M. Gachard (1862):

II. Analectes historiques, neuvième série (n

. ''Bulletin de la Commission royale d'Historie'', volume 3, pages 345–554. Page 347: ''Lettre de Philippe le Beau aux échevins...'', quote: "Escript en nostre ville de Gand, le XXIIII

532
__NOTOC__
Year 532 ( DXXXII) was a leap year starting on ThursdayA leap year starting on Thursday is any year with 366 days (i.e. it includes 29 February) that begins on Thursday 1 January, and ends on Friday 31 December. Its dominical letter ...

vorschreven." Page 419: ''Acte du duc de Parme portant approbation...'', quote": "Faiet le XVRegistrum Annalium Collegii Mertonensis 1483–1521

' Oxford Historical Society, volume 76; 544 pages. Page 184 has the computation in pounds:shillings:pence (li:s:d) x:iii:iiii + xxi:viii:viii + xlv:xiiii:i = iii

Contenant la deuxieme livraison des monumens des regnes de saint Louis,...

' Volume 22 of ''Recueil des historiens des Gaules et de la France''. Page 530: "SUMMA totalis, XIII. M. V. C. III. XX. XIII. l. III s. XI d. um total, 13 thousand 5 hundred 3 score 13 livres, 3 sous, 11 deniers * Other numerals that do not fit the usual patterns – such as for 45, instead of the usual — 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, "" and "" have other connotations in addition to their values as Roman numerals, while "" more often than not is a of "I excel", and is in any case not an unambiguous Roman numeral.Zero

"Place-keeping" zeros are alien to the system of Roman numerals - however the actual number (what remains after 1 is subtracted from 1) was also missing from the classical Roman numeral system. The word (the word meaning "none") was used to represent 0, although the earliest attested instances are medieval. For instance used alongside Roman numerals in a manuscript from A.D.525. About 725, or one of his colleagues used the letter , the initial of or of (the Latin word for "nothing") for 0, in a table of , all written in Roman numerals.C. W. Jones, ed., ''Opera Didascalica'', vol. 123C in ''Corpus Christianorum, Series Latina''. The use of to indicate "none" long survived in the historic of measurement: used well into the 20th century to designate quantities in pharmaceutical prescriptions.Fractions

The base "Roman fraction" is , indicating . The use of (as in to indicate 7) is attested in some ancient inscriptions and also in the now rare apothecaries' system (usually in the form ): but while Roman numerals for are essentially does not correspond to , as one might expect, but . The Romans used a rather than a decimal system for , as the of twelve makes it easier to handle the common of and than does a system based on ten . Notation for fractions other than is mainly found on surviving s, many of which had values that were duodecimal fractions of the unit . Fractions less than are indicated by a dot (·) for each "twelfth", the source of the English words ''inch'' and ''ounce''; dots are repeated for fractions up to five twelfths. Six twelfths (one half), is for "half". ''Uncia'' dots were added to for fractions from seven to eleven twelfths, just as tallies were added to for whole numbers from six to nine. The arrangement of the dots was variable and not necessarily . Five dots arranged like (⁙) (as on the face of a ) are known as a , from the name of the Roman fraction/coin. The Latin words ' and ' are the source of the English words ' and '. Each fraction from to had a name in Roman times; these corresponded to the names of the related coins: Other Roman fractional notations included the following: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'', in which 500 was written as , while 1,000 was written as . This is a system of encasing numbers to denote thousands (imagine the s and s as parentheses), which has its origins in Etruscan numeral usage. The and used to represent 500 and 1,000 most likely preceded, and subsequently influenced, the adoption of "" and "" in conventional Roman numerals. Each additional set of and surrounding raises the value by a power of ten: represents 10,000 and represents 100,000. Similarly, each additional to the right of raises the value by a power of ten: represents 5,000 and represents 50,000. Numerals larger than do not occur. Sometimes was reduced to for 1,000. is often credited for introducing the symbol for (modern ∞), and one conjecture is that he based it on this usage, since 1,000 was used to represent very large numbers. Similarly, for 5,000 was reduced to ; for 10,000 to ; for 50,000 to (); and () for 100,000 to .Vinculum

Another system was the ', in which conventional Roman numerals were multiplied by 1,000 by adding a "bar" or "overline". 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). 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. 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, and the reader is required to decipher the intended meaning of the overline from the context. The ''vinculum'' for marking 1,000s continued in use in the Middle Ages, though it became known more commonly as ''titulus''. Some modern sources describe Vinculum as if it were a part of the current "standard". However, this is purely hypothetical, since no common modern usage requires numbers larger than the current year (). Nonetheless, here are some examples, to give an idea of how it ''might'' be used: * = 4,000 * = 4,627 * = 25,000 * = 25,459 Another inconsistent medieval usage was the addition of ''vertical'' lines (or brackets) before and after the numeral to multiply it by 10 (or 100): thus for 10,000 as an alternative form for . In combination with the overline the bracketed forms might be used to raise the multiplier to (say) ten (or one hundred) thousand, thus: * for 80,000 (or 800,000) * for 200,000 (or 2,000,000) 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.Origin

The system is closely associated with the ancient 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 : "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 was written from right to left.)Gilles Van Heems (2009)>Nombre, chiffre, lettre : Formes et réformes. Des notations chiffrées de l'étrusque

("Between Numbers and Letters: About Etruscan Notations of Numeral Sequences"). ''Revue de philologie, de littérature et d'histoire anciennes'', volume (83), issue 1, pages 103–130. 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 (or "𐌢𐌣" for 40), and wrote "𐌡𐌠𐌠", "𐌡𐌠𐌠𐌠" and "𐌡𐌠𐌠𐌠𐌠" for 7, 8, and 9, respectively.

Early Roman numerals

The early Roman numerals for 1, 10, and 100 were the Etruscan ones: "", "", and "". The symbols for 5 and 50 changed from and "𐌣" to and ↆ at some point. The latter had flattened to (an inverted T) by the time of , and soon afterwards became identified with the graphically similar letter . The symbol for 100 was written variously as or , was then abbreviated to or , with (which matched a Latin letter) finally winning out. It may have helped that is the initial of ''centum'', Latin for "hundred". The numbers 500 and 1000 were denoted by or overlaid with a box or circle. Thus 500 was like a superimposed on a . It became or by the time of Augustus, under the graphic influence of the letter . It was later identified as the letter ; an alternative symbol for "thousand" was a , and half of a thousand or "five hundred" is the right half of the symbol, , and this may have been converted into . The notation for 1000 was a circled or boxed : Ⓧ, , , and by Augustinian times was partially identified with the Greek letter '. Over time, the symbol changed to and . The latter symbol further evolved into , then , and eventually changed to under the influence of the Latin word ''mille'' "thousand". According to Paul Kayser, the basic numerical symbols were , , and (or ) and the intermediate ones were derived by taking half of those (half an is , half a is and half a is ).Classical Roman numerals

The was constructed in Rome in CE 72–80, and while the original perimeter wall has largely disappeared, the numbered entrances from (23) to (54) survive, to demonstrate that in Imperial times Roman numerals had already assumed their classical form: . The most obvious anomaly () is the inconsistent use of subtractive notation - while is used for 40, is avoided in favour of : in fact gate 44 is labelled .Use in the Middle Ages and Renaissance

, or ''minuscule'', letters were developed in the Middle Ages, well after the demise of the , and since that time lower-case versions of Roman numbers have also been commonly used: , , , , and so on. Since the Middle Ages, a "" has sometimes been substituted for the final "" of a "lower-case" Roman numeral, such as "" for 3 or "" for 7. This "" can be considered a variant of "". Into the early 20th century, the use of a final "" was still sometimes used in s to prevent tampering with or misinterpretation of a number after it was written. 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 "" for "", or "" for ""), while others serve as abbreviations for compound numerals ("" for "", or "" for ""). Although they are still listed today in some dictionaries, they are long out of use. s, messages with dates encoded into them, were popular during the era. The chronogram would be a phrase containing the letters , , , , , , and . 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 , by way of 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 ). 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. of the United Kingdom, . These are referred to as s and are usually read as ; e.g. is pronounced "the second". This tradition began in Europe sporadically in the , gaining widespread use in England during the reign of . Previously, the monarch was not known by numeral but by an such as . Some monarchs (e.g. and ) seem to have preferred the use of instead of on their coinage (see illustration). * , particularly in the U.S., for people sharing the same name across generations, for example . * In the , initiated during the , years were numbered by Roman numerals – from the year (1792) when this calendar was introduced to the year (1805) when it was abandoned. * The year of production of films, television shows and other works of art within the work itself. It has been suggested – by , perhaps facetiously – that this was originally done "in an attempt to disguise the age of films or television programmes." Outside reference to the work will use regular Arabic numerals. * Hour marks on s. In this context, 4 is often written . * The year of construction on s and s. * 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 , Scene 2). * s to some films, video games, and other works (as in ', '). * that use numbers to show hierarchical relationships. * Occurrences of a recurring grand event, for instance: ** The and (e.g. the ; the ) ** The , the annual championship game of the (e.g. ; was a one-time exception) ** , the annual event for the (e.g. ). This usage has also been inconsistent.Specific disciplines

In , the s or "moons" of the s are traditionally by capital Roman numerals appended to the planet's name. For example, 's designation is . In , Roman numerals are often used to denote the of the . They are also used in the , for the of s which can take on several different positive charges. They are also used for naming of s, such as . In , school grades (in the sense of year-groups rather than test scores) are sometimes referred to by a Roman numeral; for example, "grade " is sometimes seen for "grade 9". In , the broods of the thirteen and seventeen year are identified by Roman numerals. In stylised Roman numerals may represent numeric values. In , Roman numerals are commonly used to help organize legal codes as part of an . In advanced (including , , and ), when a graph includes negative numbers, its quadrants are named using , , , and . 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 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 , Roman numerals are used in several contexts: * are often numbered using Roman numerals. * In , is identified using Roman Numerals. * Individual strings of , such as the , are often denoted by Roman numerals, with higher numbers denoting lower strings. In , Roman numerals were used with the now largely obsolete of measurement: including to denote "one half" and to denote "zero". In , Roman numerals (with zero) are used to denote varying levels of brightness when using the . In , Roman numerals are used to designate degrees of the of earthquakes. In the team containing the "top" players and representing a nation or province, a or a school at the highest level in (say) is often called the "1st ", while a lower-ranking or team might be the "3rd ". In , Roman numerals (with zero) are used to denote the cards of the . In and , the is often referred to as , as this translation of the 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 and in other regions (e.g. ) that use a European language other than English. For instance: Capital or small capital Roman numerals are widely used in to denote , e.g. the French ' and the Spanish ' mean "18th century". Slavic languages in and adjacent to Russia similarly favor Roman numerals (). On the other hand, in Slavic languages in , like most , 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 is written in Roman numerals, while the day is in Arabic numerals: "4..1789" and ".4.1789" both refer unambiguously to 4 June 1789. Roman numerals are sometimes used to represent the in hours-of-operation signs displayed in windows or on doors of businesses, and also sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by . Sunday is represented by . 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 . Note that the listing uses 24-hour time. Roman numerals may also be used for . For instance, apartments in central are indicated as 138-, with both an Arabic numeral (number of the block or house) and a Roman numeral (floor number). The apartment on the ground floor is indicated as . In Italy, where roads outside built-up areas have , major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from to for the smaller intervals. The sign thus marks 17.9 km. Certain Spanish-speaking Latin American countries use Roman numerals to designate assemblies of their national legislatures. For instance, the composition of the from 2018 to 2021 (elected in the ) is called the (or more commonly the "LXIV Legislature"). A notable exception to the use of Roman numerals in Europe is in Greece, where (based on the Greek alphabet) are generally used in contexts where Roman numerals would be used elsewhere.Unicode

The "" block of the computer character set standard has a number of in the range of from U+2160 to U+2188. This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ or ). 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 " r most purposes, it is preferable to compose the Roman numerals from sequences of the appropriate Latin letters". The block also includes some ''apostrophus'' symbols for large numbers, an old variant of "L" (50) similar to the Etruscan character, the "reversed C", etc.See also

* * * * * * * * * *References

Notes

Citations

Sources

*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

* {{list of writing systems Latin alphabet