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# Roman numerals

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Roman numerals are a numeral system that was used by ancient Rome. Numbers in this system uses letters from the Latin alphabet. Currently, it uses seven symbols:[1]

 Symbol Value I V X L C D M 1 5 10 50 100 500 1,000

The Europeans still used Roman numerals even after the fall of the Roman Empire. From the 14th century, the Europeans replaced Roman numerals with Arabic numerals. However, people still uses the Roman numerals to this day.

One place they are sometimes seen is on clock faces. For example, on the clock of Big Ben, the hours from 1 to 12 are written as:

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII

The IV and IX can be read as "one less than 5" (4) and "one less than 10" (9). On most Roman numeral clock faces, however, 4 is written as IIII.[2]

## Subtraction rule

There is a simple rule, whenever the same symbol is written four times, it is replaced by subtracting it from the next higher number (5,50,50,500). That way, IV is written instead of IIII (4), XL instead of XXXX (40), etc. It is used since about the Middle Ages. Usually only one number is subtracted, not two. So 18 is usually XVIII instead of IIXX. Also, the subtraction rule is only valid for the symbol which comes right beforehand in the sequence. This means that 99 is written XCIX, and not IC.

## Special values

### Zero

The number zero does not have its own Roman numeral. About 725, Bede or one of his colleagues used the letter N, the abbreviation (short form) of nihil (the Latin word for "nothing").[3]

### Fractions

A semis (S) coin.

The Romans also used fractions. The most common base for fractions was 1/12, which in Latin is called uncia (ounce).

Fraction Numeral Name (nominative and genitive) Meaning
1/12 · Uncia, unciae "Ounce"
2/12 = 1/6 ·· or : Sextans, sextantis "Sixth"
4/12 = 1/3 ···· or Triens, trientis "Third"
5/12 ····· or Quincunx, quincuncis "Five-ounce" (quinque unciaequincunx)
6/12 = 1/2 S Semis, semissis "Half"
7/12 Septunx, septuncis "Seven-ounce" (septem unciaeseptunx)
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
or "ninth ounce" (nona uncianonuncium)
10/12 = 5/6 S···· or S∷ Dextans, dextantis
or decunx, decuncis
"Less a sixth" (de-sextansdextans)
or "ten ounces" (decem unciaedecunx)
11/12 S····· or S⁙ Deunx, deuncis "Less an ounce" (de-unciadeunx)
12/12 = 1 I As, assis "Unit"

### Large numbers

A number of numeral systems are developed for large numbers that cannot be shown with I, V, X, L, C, D and M.

#### Apostrophus

One of the systems is the apostrophus,[4] in which D is written as (500) and M is written as CIƆ (1,000).[5] In this system, an extra Ɔ means 500, and multiple extra Ɔs are used to mean 5,000, 50,000 etc.

 Numeral Value IƆ CIƆ CIƆƆ IƆƆ CCIƆƆ CCIƆƆƆ CCIƆƆƆƆ IƆƆƆ CCCIƆƆƆ CCCIƆƆƆƆ CCCIƆƆƆƆƆ CCCIƆƆƆƆƆƆ 500 1,000 1,500 5,000 10,000 10,500 15,000 50,000 100,000 100,500 105,000 150,000

#### Vinculum

Another system is the vinculum, in which V, X, L, C, D and M are multiplied by 1,000 by adding an overline.

 Numeral Value V X L C D M 5,000 10,000 50,000 100,000 500,000 1,000,000

## Usage

• In the Baltics and Russia, the days of the week, are often written as Roman numbers, I being Monday.
• When writing dates by hand, the month is sometimes written as a Roman numeral, especially for dates written in day-month-year sequence. For example: 26.XI.2014 or XI.26.2014 = 26 November 2014.
• When movies or books are published, the year of publication or year of copyright may be done as a Roman numeral.
• When people write about Monarchs or Popes, Patriarchs, or other leading figures, they are sometimes counted with Roman numbers, e.g. Queen Elizabeth II (of England), Pope John Paul II, Pope Benedict XVI, Patriarch Alexius II (of the Russian-Orthodox church)
• In France, the trimesters are sometimes counted with Roman numerals.
• In Poland, roman numerals are used to show the month in dates and as a short method of writing ordinals (i.e. VI to be 6th).
• Unicode has a code block called Number Forms, which also contains representations of Roman numerals, at the positions U+2160 to U+2188.

### Write years

It is very easy to write a number as a Roman numeral. Simply substract the largest possible Roman numeral, as many times as possible from the number. This system will result in a valid Roman numeral, but will not take the subtraction rule into account.

 1 × 1000 + 1 × 500 + 4 × 100 + 1 × 50 + 3 × 10 + 4 × 1 = 1984 M + D + CCCC + L + XXX + IIII = MDCCCCLXXXIIII

Getting the number from the numeral is equally simple, by adding the values of the symbols.

In general, the values for 5, 50, 500,.. are not subtracted. The same number, with using the subtraction rule:

 1 × 1000 + (−1 × 100 + 1 × 1000) + 1 × 50 + 3 × 10 + (−1 × 1 + 1 × 5) = 1984 M + CM + L + XXX + IV = MCMLXXXIV

## References

1. Gordon, Arthur E. (1982). Illustrated Introduction to Latin Epigraphy. Berkeley: University of California Press. . "Alphabetic symbols for larger numbers, such as Q for 500,000, have also been used to various degrees of standardization.".
2. "The Mathematical Tourist : IIII versus IV on Clocks". Ivars Peterson. Retrieved 31 May 2019. "Expressed as Roman numerals, the first twelve numbers are usually given as I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII. However, on many clock faces, when the numbers on the dial are in Roman numerals, IIII replaces IV."
3. C. W. Jones, ed., Opera Didascalica, vol. 123C in Corpus Christianorum, Series Latina.
4. Asimov, Isaac (1966). Asimov On Numbers. Pocket Books, a division of Simon & Schuster, Inc. p. 12.