Roman Numerals

Sun DialRoman numerals, the numeric system in ancient Rome, uses combinations of letters from the Latin alphabet to signify values. The numbers 1 to 10 can be expressed in Roman numerals as follows:

I, II, III, IV, V, VI, VII, VIII, IX, and X.

The Roman numeral system was inspired by Etruscan numerals. The Etruscans used I, Λ, X, ⋔, 8, ⊕, for I, V, X, L, C, and M – of which only I and X happened to be letters in their alphabet. This system was adapted from the Greek Attic numerals.

Use of Roman numerals continued after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by more convenient Hindu-Arabic numerals; however this process was gradual, and the use of Roman numerals in some minor applications continues to this day.

Reading Roman numerals

Roman Numerals, as used today, are based on seven symbols:

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

Numbers are formed by combining symbols together and adding the values. So II is two ones, i.e. 2, and XIII is a ten and three ones, i.e. 13. There is no zero in this system, so 207, for example, is CCVII, using the symbols for two hundreds, a five and two ones. 1066 is MLXVI, one thousand, fifty and ten, a five and a one.

Symbols are placed from left to right in order of value, starting with the largest. However, in a few specific cases, to avoid four characters being repeated in succession (such as IIII or XXXX) these can be reduced using subtractive notation as follows:

  • the numeral I can be placed before V and X to make 4 units (IV) and 9 units (IX) respectively
  • X can be placed before L and C to make 40 (XL) and 90 (XC) respectively
  • C can be placed before D and M to make 400 and 900 according to the same pattern

An example using the above rules would be 1904: this is composed of 1 (one thousand), 9 (nine hundreds), 0 (zero tens), and 4 (four units). To write the Roman numeral, each of the non-zero digits should be treated separately. Thus 1,000 = M, 900 = CM, and 4 = IV. Therefore, 1904 is MCMIV. This reflects typical modern usage rather than a universally accepted convention: historically Roman numerals were often written less consistently.

A common exception to the practice of placing a smaller value before a larger in order to reduce the number of characters, is the use of IIII instead of IV for 4, especially, although by no means exclusively, on clock faces. Another example of the same kind of thing is the representation of 1910 in Roman Numerals on Admiralty Arch, London – where DCCCC is used instead of CM for 900 (see illustration). In general, the “rules” about subtractively applied symbols are the most frequently “broken”.

Minuscule (lower case) letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and lower-case versions of Roman numbers are now also commonly used: i, ii, iii, iv, etc. In the Middle Ages, a j was sometimes substituted for the final i of a number, such as iij for 3 or vij for 7. This j was considered a swash variant of i. The use of a final j is still used in medical prescriptions to prevent tampering with or misinterpretation of a number after it is written.

A unique, more comprehensive shorthand for writing Roman numerals was developed during the Middle Ages, which today are called “medieval Roman numerals.” This system used almost every other letter of the Roman alphabet to stand as abbreviations for more longhand numbers (usually those that consisted of repetitions of the same symbol). They are still listed today in most dictionaries, although through disfavor are primarily out of use.

Modern usage

Roman numerals are still used today in several niche contexts. A few examples of their current use are:
  • Names of monarchs and Popes, e.g. Elizabeth II of the United Kingdom, Pope Benedict XVI. These are referred to as monarchical ordinals; e.g. “II” is pronounced “the second”. This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England only during the reign of Henry VIII. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor.
  • Male generational titles.
  • The year of production of films, television shows and other works of art within the work itself, which according to BBC News was originally done “in an attempt to disguise the age of films or television programmes.” Outside reference to the work will use regular Hindu–Arabic numerals.
  • Hour marks on timepieces. In this context 4 is usually written IIII.
  • The year of construction on building faces and cornerstones.
  • Page numbering of prefaces and introductions of books.
  • Book volume and chapter numbers.
  • Sequels of movies, video games, and other works.
  • Outlines.
  • A recurring grand event, such as the Olympic Games.
  • In astronomy, the natural satellites or “moons” of the planets are traditionally designated by capital Roman numerals.
  • In chemistry, Roman numerals are often used to denote the groups of the periodic table. 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 earthquake seismology, Roman numerals are used to designate degrees of the Mercalli intensity scale.
  • In music theory, the diatonic functions are identified using roman numerals. See: Roman numeral analysis.
  • In performance practice, individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings.
  • In photography, Roman numerals (with zero) are used to denote varying levels of brightness when using the Zone System.

Capital Roman numerals are used to denote centuries (e.g., XVIII refers to the eighteenth century) in many European countries. This use has largely been replaced by Hindu-Arabic numerals (e.g. 18.) in Czech and Slovak languages.

In many European countres, mixed Roman and Hindu-Arabic numerals are used to record dates (usually on tombstones, but also elsewhere, such as in formal letters and official documents). The month is written in Roman numerals while the day is in Hindu-Arabic numerals: 14.  VI. 1789 is 14 June 1789. This use has largely been replaced by Hindu-Arabic numerals (e.g. 14.06.1789).
 
In the Baltic and Eastern Europe nations, Roman numerals are used to represent the days of the week in hours-of-operation signs displayed in windows or on doors of businesses, and also sometimes in railway and bus timetables. Monday is represented by I, which is the initial day of the week. Sunday is represented by VII.

In Rome, Greece, Romania, and other European countries to a lesser extent, Roman numerals are used for floor numbering. Likewise, apartments in central Amsterdam are indicated as 138-III, with both an Hindu-Arabic numeral (number of the block or house) and a Roman numeral (floor number). The apartment on the ground floor is indicated as ‘138-huis’.

Fractions

Though the Romans used a decimal system for whole numbers, reflecting how they counted in Latin, they used a duodecimal system for fractions, because the divisibility of twelve (12 = 3 × 2 × 2) makes it easier to handle the common fractions of 1/3 and 1/4 than does a system based on ten (10 = 2 × 5). On coins, many of which had values that were duodecimal fractions of the unit as, they used a tally-like notational system based on twelfths and halves. A dot (•) indicated an uncia “twelfth”, the source of the English words inch and ounce; dots were repeated for fractions up to five twelfths. Six twelfths (one half) was abbreviated as the letter S for semis “half”. Uncia dots were added to S for fractions from seven to eleven twelfths, just as tallies were added to V for whole numbers from six to nine.

Each of these fractions had a name, which was also the name of the corresponding coin:

Fraction Roman Numeral Name (nominative and genitive) Meaning
1/12 uncia, unciae “ounce”
2/12 = 1/6 •• or : sextans, sextantis “sixth”
3/12 = 1/4 ••• or quadrans, quadrantis “quarter”
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 S• 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
“less a quarter” (de-quadransdodrans)
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”
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