20 In Roman Numerals

[Ilario Grijalva]

Romannumerals 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:

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. 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:

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 the current (21st) century, MM indicates 2000; this year is MMXXIV (2024).

Roman numerals use different symbols for each power of ten and there is 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 varied greatly in ancient Rome and became thoroughly chaotic in medieval times. The more recent restoration of a largely "classical" notation has gained popularity among some, while variant forms are used by some modern writers as seeking more "flexibility".[2] Roman numerals may be considered legally binding expressions 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]

The numerals for 4 (IV) and 9 (IX) are written using subtractive notation,[5] where the smaller 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.

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 24 (XXIIII),[10] 74 (LXXIIII),[11] and 490 (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][c]

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]

The ROMAN() function in Microsoft Excel supports multiple subtraction modes depending on the ".mw-parser-output .monospacedfont-family:monospace,monospaceForm" setting. For example, the number "499" (usually CDXCIX) can be rendered as LDVLIV, XDIX, VDIV or ID. The relevant Microsoft help page offers no explanation for this function other than to describe its output as "more concise".[34]

There are also historical examples of other additive and multiplicative forms, and forms which seem to reflect spoken phrases. Some of these variants may have been regarded as errors even by contemporaries.

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]

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]

Vinculum notation is distinct from the custom of adding an overline to a numeral simply to indicate that it is a number. Both usages can be seen on Roman inscriptions of the same period and general location, such as on the Antonine Wall.[57][58]

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.

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.

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.[63]

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.[64]

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.

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:

In chemistry, Roman numerals are sometimes used to denote the groups of the periodic table, but this has officially been deprecated in favour of Arabic numerals.[70] 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 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 Nazi III Panzerkorps) with Arabic numerals being used for divisions and armies.

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 Ireland, Roman numerals were used until the late 1980s to indicate the month on postage Franking. In documents, Roman numerals are sometimes still used to indicate the month to avoid confusion over day/month/year or month/day/year formats.

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