Roman numerals

[1] Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of films and television programmes.

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".

While subtractive notation for 4, 40, and 400 (IV, XL, and CD) has been the usual form since Roman times [citation needed], additive notation to represent these numbers (IIII, XXXX, and CCCC)[9] very frequently continued to be used, including in compound numbers like 24 (XXIIII),[10] 74 (LXXIIII),[11] and 490 (CCCCLXXXX).

[15][16] 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.

[19][20][21] 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.

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.

[24][25] The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius (c. 45 BC – 9 AD).

[33] 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.

The ROMAN() function in Microsoft Excel supports multiple subtraction modes depending on the "Form" setting.

The relevant Microsoft help page offers no explanation for this function other than to describe its output as "more concise".

[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.

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.

[22] This system of encasing numbers to denote thousands (imagine the Cs and Ↄs as parentheses) had its origins in Etruscan numeral usage.

[48] Sometimes CIↃ (1000) is reduced to ↀ, IↃↃ (5,000) to ↁ; CCIↃↃ (10,000) to ↂ; IↃↃↃ (50,000) to ↇ; and CCCIↃↃↃ (100,000) to ↈ.

[49] It is likely IↃ (500) reduced to D and CIↃ (1000) influenced the later M. John Wallis is often credited with 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.

[51][52] It continued in use in the Middle Ages, though it became known more commonly as titulus,[53] and it appears in modern editions of classical and medieval Latin texts.

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 itself was located next to the southern edge of the Etruscan domain, which covered a large part of north-central Italy.

As in the basic Roman system, the Etruscans wrote the symbols that added to the desired number, from higher to lower value.

[60] The Colosseum was constructed in Rome in CE 72–80,[61] and while the original perimeter wall has largely disappeared, the numbered entrances from XXIII (23) to LIIII (54) survive,[62] 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.

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").

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).

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

[44][73] In photography, Roman numerals (with zero) are used to denote varying levels of brightness when using the Zone System.

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.

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,[76] and also sometimes in railway and bus timetables.

[79] This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ or XII).

[80] 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.