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# Roman numerals

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Numeral systems

The system of Roman numerals is a numeral system originating in ancient Rome. It is based on certain letters which are given values:

The early Romans used the above letters. Later Romans used a horizontal line above a particular numeral to represent one thousand times that numeral, and additional vertical lines on either side of the numeral to denote one hundred times the number, as in these examples:

```  _
I for 1000
_
V for 5000
_
|I| for 100,000
_
|V| for 500,000
```

The same overline was also used with a different meaning, to clarify that the letters were numbers.

When describing members of a list, first A, B, C, D tended to be used, then 1, 2, 3 then i, ii, iii, iv.

In medieval times, well before the letter j was thought up as a distinct letter, a series of letters i in Roman numerals was ended with a flourish; hence they actually looked like: ij, iij, and iiij. This practice is now merely an antiquarian's note, it is never used. (It did, however, result in the Dutch diphtong IJ.)

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## Zero

In general, the number zero did not have its own Roman numeral, but the concept of zero as a number was well known by all medieval computists (calculators of Easter). They included zero (via the Latin word nullae meaning nothing) as one of nineteen epacts, or the age of the moon on March 22. The first three epacts were nullae, xi, and xxii (written in minuscule or lower case). The first known computist to use zero was Dionysius Exiguus in 525, but the concept of zero was no doubt well known earlier. Only one instance of a Roman numeral for zero is known. About 725, Bede or one of his colleagues used the letter N, the initial of nullae, in a table of epacts, all written in Roman numerals.

The presence of a notation for the number zero should not be confused with the role of the digit zero in a positional notation system. The lack of a character to represent zero prevented Roman numerals from developing into a positional notation, and led to their gradual replacement by Arabic numerals in the early second millennium.

## IIII or IV?

Throughout the centuries, there has been variation in some of its symbols — specifically, the subtractive notation (which uses, e.g., IV instead of IIII to denote the number represented by 4) has entered universal use only in modern times. For example, Forme of Cury, a manuscript from 1390, uses IX for 9, but IIII for 4. Another document in the same manuscript, from 1381, uses IV and IX. A third document in the same manuscript uses IIII, IV, and IX.

The Romans themselves didn't seem to bother that much about what the correct formation of a number was; constructions such as IIX for eight have been discovered. In many cases, there seems to have been a certain reluctance in the use of subtractive notation.

Some rules regarding Roman numerals state that a symbol representing 10x may not precede any symbol larger than 10x+1; use XCIX not IC for 99. However, these rules are not set in stone.

The use of subtractive notation with Roman numerals increased the complexity of performing Roman arithmetic without conveying the benefits of a full positional notation system.

## Calendars and clocks

Clock faces typically show IIII for 4 o'clock and IX for 9 o'clock — using the subtractive principle in one case and not in the other. There are several suggested reasons for this:

• The four-character form IIII creates a visual symmetry with the VIII on the other side, which IV would not.
• IV is the first two letters of IVPITER, the supreme god of the Romans, and therefore not appropriate to use.
• The total number of symbols on the clock totals twenty I's, four V's, and four X's; so clock makers need only a mould with five I's, a V, and an X in order to make the correct number of numerals for the clocks.
• IV is difficult to read upside down and on an angle, particularly at that location on the clock.
• A particular Roman ruler had a clock manufactured incorrectly (with IIII) and others started making their clocks that way in order not to offend him.
• Louis XIV, king of France, preferred IIII over IV, ordered his clockmakers to produce clocks with IIII and not IV, and thus it has remained.

## Year in Roman numerals

In the seventeenth century at least, using Roman numerals for the year of publication for books was standard; there were many other places it was used as well. They even attempted to make the number easier to figure out. On British title pages, there were often spaces between the groups of digits: M DCC LXI is one example. This may have come from the French, who instead of or in addition to this practice also separated the groups of digits with periods: M.DCC.LXV. and M. DCC. LXV. are examples. Notice the period at the end of the sequence; many foreign countries did this for roman numerals in general, but not necessarily Britain.

These practices faded from general use before the start of the twentieth century, though the cornerstones of major buildings still occasionally use them. Roman numerals are today still used on building faces for dates: 2005 can be represented as MMV.

The film industry has used them perhaps since its inception to denote the year a film was made, so that it could be redistributed later either locally or to a foreign country with many not knowing the wiser; this became more useful when films were broadcast on television to prevent people from reacting against an older film. From this came the policy of the broadcasting industry, including the BBC, to use them to denote the year in which a television program was made (the Australian Broadcasting Corporation has largely stopped this practice but still occasionally lapses).

## Other modern usage by English-speaking peoples

Roman numerals remained in common use until about the 14th century, when they were replaced by Arabic numerals (thought to have been introduced to Europe from al-Andalus, by way of Arab traders and arithmetic treatises, around the 11th century). The use of Roman numerals today is mostly restricted to ordinal numbers, such as volumes or chapters in a book or the numbers identifying monarchs (e.g. Elizabeth II).

Sometimes they are written using lower-case letters (thus: i, ii, iii, iv, etc.), particularly if numbering paragraphs or sections within chapters, or for the pagination of the front matter of a book.

Undergraduate degrees at British universities are generally graded using I, IIi, IIii, III for first, upper second, lower second and third class respectively.

Modern English usage also employs Roman numerals in many books (especially anthologies), movies (e.g., Star Wars), and sporting events (e.g., the Super Bowl). The common unifying theme seems to be stories or events that are episodic or annual in nature.

## Modern foreign usage

The above uses are customary for English-speaking countries. Although many of them are also maintained in other countries, those countries may have some additional uses for them which are unknown in English-speaking regions.

The French use capital roman numerals to denote centuries, e.g., 'XVIII' refers to the eighteenth century, so as to not confuse the first two digits of the century with the first two digits of most, if not all, of the years in the century. The Italians do not, for they refer to the digits in the years, e.g., quattrocento is their name for the fifteenth century. Some scholars in English-speaking countries prefer the French method, among them Lyon Sprague de Camp.

In Germany, Poland, and Russia, roman numerals were used in a method of recording the date. Just as an old clock recorded the hour by roman numerals while minutes were measured in arabic numerals, in this system, the month was in roman numerals while the day was in arabic numerals, e.g. 14-VI-1789 was June the fourteenth, 1789. It is by this method that dates are inscribed on the walls of the Kremlin, for example. This method has the advantage that days and months are not confused in rapid note-taking, and that any range of dates or months could be expressed in a mixture of arabic and roman numerals with no confusion, e.g., V-VIII is May to August, while 1-V-31-VIII is May first to August thirty-first.

But as the French use capital roman numerals to refer to the quarters of the year , e.g., 'III' is the third quarter , and which has apparently become standard in some European standards organization, (but which in American business is 'Q3'), the aforementioned method of recording the date has had to switch to minuscule roman numerals, e.g., 4-viii-1961. (Later still, the ISO specified that dates should be given in all arabic numerals, which can lead to confusion.)

Romanian uses Roman numerals for floor numbers.

## Table of Roman numerals

The "modern" Roman numerals, post-Victorian era, are shown below:

Roman Alternative Arabic Notes
none none 0 There was no need for a zero.
I 1
II ⅠⅠ (or Ⅱ) 2
III ⅠⅠⅠ (or Ⅲ) 3
IV ⅠⅤ (or Ⅳ) 4 IIII (ⅠⅠⅠⅠ) is still used on clock and card faces.
V 5
VI ⅤⅠ (or Ⅵ) 6
VII ⅤⅠⅠ (or Ⅶ) 7
VIII ⅤⅠⅠⅠ (or Ⅷ) 8
IX ⅠⅩ (or Ⅸ) 9
X 10
XI ⅩⅠ (or Ⅺ) 11
XII ⅩⅠⅠ (or Ⅻ) 12
XIII ⅩⅠⅠⅠ 13
XIV ⅩⅠⅤ 14
XV ⅩⅤ 15
XIX ⅩⅠⅩ 19
XX ⅩⅩ 20
XXX ⅩⅩⅩ 30
XL ⅩⅬ 40
L 50
LX ⅬⅩ 60
LXX ⅬⅩⅩ 70 The abbreviation for the Septuagint
LXXX ⅬⅩⅩⅩ 80
XC ⅩⅭ 90
C 100 This is the origin of using the slang term "C-bill" or "C-note" for "\$100 bill".
CC ⅭⅭ 200
CD ⅭⅮ 400
D 500
DCLXVI ⅮⅭⅬⅩⅤⅠ 666 Using every basic symbol but M once gives the beast number.
CM ⅭⅯ 900
M 1000
ⅭⅠↃ 1000 Conjoined C, I and reversed C, alternative to M.
none 1000 A glyph similar to the Infinity sign, alternative to M.
MCMXLV ⅯⅭⅯⅩⅬⅤ 1945
MCMXCIX ⅯⅭⅯⅩⅭⅠⅩ 1999 Note that officially there are no short cuts, and the I can only precede V or X. IMM (ⅠⅯⅯ) or MIM (ⅯⅠⅯ) is therefore invalid.
MM ⅯⅯ 2000
MMM ⅯⅯⅯ 3000
ⅠↃↃ 5000 I followed by two reversed C, an adapted Chalcidic sign
ⅭⅭⅠↃↃ 10000 CCI, then two reversed C
none Reversed 100 Reversed C, used in combination with C and I to form large numbers.

An accurate way to write large numbers in Roman numerals is to handle first the thousands, then hundreds, then tens, then units.
Example: the number 1988.
One thousand is M, nine hundred is CM, eighty is LXXX, eight is VIII.
Put it together: MCMLXXXVIII (ⅯⅭⅯⅬⅩⅩⅩⅤⅠⅠⅠ).

The "shortcut method" for large numbers such as 1998 is not recommended, but still used by some:
1998
Two thousand is MM (ⅯⅯ), so subtract two (II [ⅠⅠ]) and you have 1998
MIIM (ⅯⅠⅠⅯ) or alternatively IIMM (ⅠⅠⅯⅯ).

Unicode has a number of characters specifically designated as Roman numerals, as part of the Number Forms range from U+2160 to U+2183. For example, MCMLXXXVIII could alternatively be written as ⅯⅭⅯⅬⅩⅩⅩⅤⅠⅠⅠ. This range includes both upper- and lowercase numerals, as well as pre-combined glyphs for numbers up to 12 (Ⅻ or XII), mainly intended for the clock faces for compatibility with non–West-European languages. The pre-combined glyphs should only be used to represent the individual numbers where the use of individual glyphs is not wanted, and not to replace compounded numbers. Similarily precombined glyphs for 5000 and 10000 exist.

The Unicode characters are present only for compatibility with other character standards which provide these characters; for ordinary uses, the regular Latin letters are preferred. Displaying these characters requires a user agent that can handle Unicode and a font that contains appropriate glyphs for them.

## Games

After the Renaissance, the Roman system could also be used to write chronograms. It was common to put in the first page of a book some phrase, so that when adding the I, V, X, L, C, D, M present in the phrase, the reader would obtain a number, usually the year of publication. The phrase was often (but not always) in Latin, as chronograms can be rendered in any language that utilises the Roman alphabet.