Roman numerals
Roman numerals are a numeral system that was used by ancient Rome. Numbers in this system use letters from the Latin alphabet. Currently, it uses seven symbols:[1]
| Numeral systems by culture | |
|---|---|
| Hindu–Arabic numerals | |
| Western Arabic Eastern Arabic Khmer |
Indian family Brahmi Thai |
| East Asian numerals | |
| Chinese Suzhou Counting rods |
Japanese Korean |
| Alphabetic numerals | |
| Abjad Armenian Cyrillic Ge'ez |
Hebrew Greek (Ionian) Āryabhaṭa |
| Other systems | |
| Attic Babylonian Egyptian Etruscan |
Mayan Roman Urnfield |
| List of numeral system topics | |
| Positional systems by base | |
| Decimal (10) | |
| 2, 4, 8, 16, 32, 64 | |
| 1, 3, 9, 12, 20, 24, 30, 36, 60, more… | |
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 use Roman numerals to this day.
One place in which they are sometimes seen is on clock faces (the front of a clock). 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 many clocks that use Roman numerals, however, 4 is written as IIII.[2]
Subtraction rule
Instead of writing the same letter four times, a rule for subtraction is used. The letter is written once, then the next largest Roman numeral is written. When a lower number (such as I) appears before a higher one (such as V), the lower number is subtracted from the higher one. For example, 4 is not written as IIII, but instead as IV, because IV is V (5) minus I (1). The same is done for 9 - it is not written as VIIII, but instead as IX, because IX is X (10) minus I (1).
Example
It is very easy to write a number as a Roman numeral. Simply subtract 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, and 500 are not subtracted. Here is the same number using the subtraction rule:
| 1 × 1000 | + | (1 × 1000) - (1 × 100) | + | 1 × 50 | + | 3 × 10 | + | (1 × 5) - (1 × 1) | = | 1984 |
| M | + | CM | + | L | + | XXX | + | IV | = | MCMLXXXIV |
Special values
Zero
The number zero has its own Roman numeral, which is O. At about 727, Bede or one of his colleagues used the letter N, the abbreviation (short form) of nihil (the Latin word for "nothing").[3]
Fractions
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 = 0.083 | · | Uncia, unciae | "Ounce" |
| 2/12 = 0.166 | ·· or : | Sextans, sextantis | "Sixth" |
| 3/12 = 0.25 | ··· or ∴ | Quadrans, quadrantis | "Quarter" |
| 4/12 = 0.333 | ···· or ∷ | Triens, trientis | "Third" |
| 5/12 = 0.416 | ····· or ⁙ | Quincunx, quincuncis | "Five-ounce" (quinque unciae → quincunx) |
| 6/12 = 0.5 | S | Semis, semissis | "Half" |
| 7/12 = 0.583 | S· | Septunx, septuncis | "Seven-ounce" (septem unciae → septunx) |
| 8/12 = 0.666 | S·· or S: | Bes, bessis | "Twice" (as in "twice a third") |
| 9/12 = 0.75 | S··· or S∴ | Dodrans, dodrantis or nonuncium, nonuncii |
"Less a quarter" (de-quadrans → dodrans) or "ninth ounce" (nona uncia → nonuncium) |
| 10/12 = 0.833 | S···· or S∷ | Dextans, dextantis or decunx, decuncis |
"Less a sixth" (de-sextans → dextans) or "ten ounces" (decem unciae → decunx) |
| 11/12 = 0.916 | S····· or S⁙ | Deunx, deuncis | "Less an ounce" (de-uncia → deunx) |
| 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 IƆ (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 | IƆ | CIƆ | CIƆƆ | IƆƆ | CCIƆƆ | CCIƆƆƆ | CCIƆƆƆƆ | IƆƆƆ | CCCIƆƆƆ | CCCIƆƆƆƆ | CCCIƆƆƆƆƆ | CCCIƆƆƆƆƆƆ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Value | 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 | V | X | L | C | D | M |
|---|---|---|---|---|---|---|
| Value | 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 numerals, with 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.
- Some video games use Roman numerals to indicate the game position in a series. The most famous examples are Final Fantasy games (Final Fantasy VII, Final Fantasy VIII, Final Fantasy X, etc...).
- When movies or books are published, the year of publication or year of copyright may be written 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 centuries are sometimes written with Roman numerals (example : "XXe siècle" meaning "20th century", XVIIIe siècle = "18th century", etc...).
- In Poland, roman numerals are used to show the month in dates and as a short method of writing ordinals (i.e. VI instead of 6th).
- Unicode has a code block called Number Forms, which also contains representations of Roman numerals, at the positions U+2160 to U+2188.
Roman Numerals Media
Roman numerals on stern of the ship Cutty Sark showing draught in feet. The numbers range from 13 to 22, from bottom to top.
A clock face with the Roman numerals typical for clocks, in Bad Salzdetfurth, Germany
The year number on Admiralty Arch, London. The year 1910 is rendered as MDCCCCX, rather than the more usual MCMX
Epitaph of centurion Marcus Caelius, showing "XIIX"
Excerpt from Bibliothèque nationale de France. The Roman numeral for 500 is rendered as Template:Overset, instead of D.
A triens coin (1⁄3 or 4⁄12 of an as). Note the four dots (····) indicating its value.
"1630" on the Westerkerk in Amsterdam. "M" and "D" are given archaic apostrophus form.
Page from a 16th-century manual, showing a mixture of apostrophus and vinculum numbers (see in particular the ways of writing 10,000).
Related pages
References
- ↑ Gordon, Arthur E. (1982). Illustrated Introduction to Latin Epigraphy. Berkeley: University of California Press. ISBN 0-520-05079-7.
Alphabetic symbols for larger numbers, such as Q for 500,000, have also been used to various degrees of standardization.
- ↑ "The Mathematical Tourist : IIII versus IV on Clocks". Ivars Peterson. 4 August 2010. 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.
- ↑ C. W. Jones, ed., Opera Didascalica, vol. 123C in Corpus Christianorum, Series Latina.
- ↑ "Merriam-Webster Unabridged Dictionary".
- ↑ Asimov, Isaac (1966). Asimov On Numbers (PDF). Pocket Books, a division of Simon & Schuster, Inc. p. 12.