What is 1009 when expressed as Roman Numerals?
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Roman_numerals.txt
Roman numerals
The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Roman numerals, as used today, are based on seven symbols: 

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

Roman numeric system

The numbers 1 to 10 are usually expressed in Roman numerals as follows:

.

Numbers are formed by combining symbols and adding the values, so  is two (two ones) and  is thirteen (a ten and three ones). Because each numeral has a fixed value rather than representing multiples of ten, one hundred and so on, according to position, there is no need for "place keeping" zeros, as in numbers like 207 or 1066; those numbers are written as  (two hundreds, a five and two ones) and  (a thousand, a fifty, a 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  or ), subtractive notation is often used as follows:  
*  placed before  or  indicates one less, so four is  (one less than five) and nine is  (one less than ten)
*  placed before  or  indicates ten less, so forty is  (ten less than fifty) and ninety is  (ten less than a hundred)
*  placed before  or  indicates a hundred less, so four hundred is  (a hundred less than five hundred) and nine hundred is  (a hundred less than a thousand)Stroh, Michael. [http://articles.baltimoresun.com/1998-12-27/news/1998361013_1_roman-numerals-roman-numbers-information-on-roman/ Trick question: How to spell 1999? Numerals: Maybe the Roman Empire fell because their computers couldn't handle calculations in Latin.] The Baltimore Sun, December 27, 1998.

For example,  is one thousand nine hundred and four, 1904 ( is a thousand,  is nine hundred and  is four).

Some examples of the modern use of Roman numerals include:
* 1954 as , as in the trailer for the movie The Last Time I Saw Paris 
* 1990 as , used as the title of musical project Enigma's debut album MCMXC a.D., named after the year of its release.
* 2014 as , the year of the games of the  (22nd) Olympic Winter Games (in Sochi)

Alternative forms

The "standard" forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval and modern times.

Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as  and  instead of (or even as well as) subtractive forms such as  and . Both methods appear in documents from the Roman era, even within the same document. "Double subtractives" also occur, such as  or even  instead of . Sometimes  and  are not used, with instances such as  and  rather than  or .  

Such variation and inconsistency continued through the medieval period and into modern times, even becoming conventional. Clock faces that use Roman numerals normally show  for four o’clock but  for nine o’clock, a practice that goes back to very early clocks such as the Wells Cathedral clock.    However this is far from universal: for example, the clock on the Palace of Westminster in London (aka "Big Ben") uses . Similarly, at the beginning of the 20th century, different representations of 900 (commonly ) appeared in several inscribed dates. For instance, 1910 is shown on Admiralty Arch, London, as  rather than , while on the north entrance to the Saint Louis Art Museum, 1903 is inscribed as  rather than . 

History 

Pre-Roman times and ancient Rome

Although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used , , , , , and  for , , , , , and , of which only  and  happened to be letters in their alphabet.

Hypotheses about the origin of Roman numerals

Tally marks

One hypothesis is that the Etrusco-Roman numerals actually derive from notches on tally sticks, which continued to be used by Italian and Dalmatian shepherds into the 19th century. 

Thus,  descends not from the letter  but from a notch scored across the stick. Every fifth notch was double cut i.e. , , , , etc.), and every tenth was cross cut (), ), much like European tally marks today. This produced a positional system: Eight on a counting stick was eight tallies, , or the eighth of a longer series of tallies; either way, it could be abbreviated  (or ), as the existence of a  implies four prior notches. By extension, eighteen was the eighth tally after the first ten, which could be abbreviated , and so was . Likewise, number four on the stick was the I-notch that could be felt just before the cut of the  (), so it could be written as either  or  (). Thus the system was neither additive nor subtractive in its conception, but ordinal. When the tallies were transferred to writing, the marks were easily identified with the existing Roman letters ,  and .

The tenth  or  along the stick received an extra stroke. Thus 50 was written variously as , , , , , etc., but perhaps most often as a chicken-track shape like a superimposed  and : . This had flattened to  (an inverted T) by the time of Augustus, and soon thereafter became identified with the graphically similar letter . Likewise, 100 was variously , , , , or as any of the symbols for 50 above plus an extra stroke. The form  (that is, a superimposed  and  like: ) came to predominate. It was written variously as  or , was then abbreviated to  or , with  variant finally winning out because, as a letter, it stood for , Latin for "hundred".

The hundredth  or  was marked with a box or circle. Thus 500 was like a  superimposed on a  or , becoming  or  by the time of Augustus, under the graphic influence of the letter . It was later identified as the letter D; an alternative symbol for "thousand" was  (or  or ), and half of a thousand or "five hundred" is the right half of the symbol,  (or  or ), and this may have been converted into .  This at least was the etymology given to it later on.

Meanwhile, 1000 was a circled or boxed : , , , and by Augustinian times was partially identified with the Greek letter  phi. Over time, the symbol changed to  and . The latter symbol further evolved into , then , and eventually changed to  under the influence of the Latin word  "thousand".

Hand signals

Alfred Hooper has an alternative hypothesis for the origin of the Roman numeral system, for small numbers.  Hooper contends that the digits are related to hand gestures for counting. For example, the numbers , , ,  correspond to the number of fingers held up for another to see. , then represents that hand upright with fingers together and thumb apart. Numbers 6–10, are represented with two hands as follows (left hand, right hand) 6(,), 7
(,), 8(,), 9
(,), 10=(,) and  results from either crossing of the thumbs, or holding both hands up in a cross.

Intermediate symbols deriving from few original symbols

A third hypothesis about the origins states that the basic ciphers were , ,  and  (or ) and that the intermediary ones were derived from taking half of those (half a  is , half a  is  and half a  is ). 

Middle Ages and Renaissance

Minuscule (lower-case) letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and since that time lower-case versions of Roman numbers have also been commonly used: , , , , and so on.

Since the Middle Ages, a "" has sometimes been substituted for the final "" of a "lower-case" Roman numeral, such as "" for 3 or "" for 7. This "" can be considered a swash variant of "" (see example [http://www.marriagerecords.me.uk/roman-numerals/#.U764YkA1CSo]). The use of a final "" is still used in medical prescriptions to prevent tampering with or misinterpretation of a number after it is written.  

Numerals in documents and inscriptions from the Middle Ages sometimes include additional symbols, which today are called "medieval Roman numerals". Some simply substitute another letter for the standard one (such as "" for "", or "" for ""), while others serve as abbreviations for compound numerals ("" for "", or "" for ""). Although they are still listed today in some dictionaries, they are long out of use. 

Chronograms, messages with numbers encoded into them, were popular during the Renaissance era.  The chronogram would be a phrase containing the letters , , , , , , and .  By putting these letters together, the reader would obtain a number, usually indicating a particular year.

Modern use

By the 11th century, Hindu–Arabic numerals had been introduced into Europe from al-Andalus, by way of Arab traders and arithmetic treatises. 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). Their eventual, almost complete replacement by their more convenient "Arabic" equivalents happened quite gradually; in fact Roman numerals are still sometimes used today, especially in certain 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 regnal numbers; e.g.  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. Some monarchs (e.g. Charles IV of Spain and Louis XIV of France) seem to have preferred the use of  instead of  on their coinage (see illustration).
* Generational suffixes, particularly in the US, for people sharing the same name across generations, for example William Howard Taft IV.
*In the French Republican Calendar, initiated during the French Revolution, years were numbered by Roman numerals - from the year I (1792) when this calendar was introduced to the year XIV (1805) when it was abandoned. 
* The year of production of films, television shows and other works of art within the work itself. It has been suggested – by BBC News, perhaps facetiously – that this 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 .
* The year of construction on building faces and cornerstones.
* Page numbering of prefaces and introductions of books, and sometimes of annexes, too.
* Book volume and chapter numbers, as well as the several acts within a play (e.g. Act iii, Scene 2).
* Sequels of some movies, video games, and other works (as in Rocky II).
* Outlines that use numbers to show hierarchical relationships.
* Occurrences of a recurring grand event, for instance:
** The Summer and Winter Olympic Games (e.g. the  Olympic Winter Games; the Games of the  Olympiad)
** The Super Bowl, the annual championship game of the National Football League (e.g. Super Bowl ; Super Bowl 50 is a one-time exception )
** WrestleMania, the annual professional wrestling event for the WWE (e.g. WrestleMania ). This usage has also been inconsistent.
Specific disciplines

In astronomy, the natural satellites or "moons" of the planets are traditionally designated by capital Roman numerals appended to the planet’s name. For example, Titan's designation is Saturn .

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 computing, Roman numerals may be used in identifiers which are limited to alphabetic characters by syntactic constraints of the programming language. In LaTeX, for instance, \labelitemiii refers to the label of an item in the third level  of a nested list environment.

In military unit designation, Roman numerals are often used to distinguish between units at different levels. This reduces possible confusion, especially when viewing operational or strategic level maps. In particular, army corps are often numbered using Roman numerals (for example the American XVIII Airborne Corps or the WW2-era German III Panzerkorps) with Hindu-Arabic numerals being used for divisions and armies.

In music, Roman numerals are used in several contexts:
* Movements are often numbered using Roman numerals.
* In music theory, the diatonic functions are identified using Roman numerals. (See: Roman numeral analysis)
* Individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings.

In pharmacy, Roman numerals are used in some contexts, including  to denote "one half" and  to mean "nothing".  (See the sections below on "zero" and "fractions".)

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

In seismology, Roman numerals are used to designate degrees of the Mercalli intensity scale of earthquakes.

In tarot, Roman numerals (with zero) are used to denote the cards of the Major Arcana.

In theology and biblical scholarship, the Septuagint is often referred to as ', as this translation of the Old Testament into Greek is named for the legendary number of its translators (septuaginta being Latin for "seventy").

In entomology the broods of the thirteen and seventeen year periodical cicadas are identified by Roman numerals.

Modern non-English use

Capital or small capital Roman numerals are widely used in Romance languages to denote , e.g. the French '  and the Spanish ' mean "18th century". Slavic languages in and adjacent to Russia similarly favour Roman numerals (). On the other hand, in Slavic languages in Central Europe, like most Germanic languages, one writes "18." (with a period) before the local word for "century".

In many European countries, mixed Roman and Hindu-Arabic numerals are used to record dates (especially in formal letters and official documents, but also on tombstones). The  is written in Roman numerals, while the day is in Hindu-Arabic numerals: 14..1789 is 14 June 1789.

In parts of Europe it is conventional to employ Roman numerals to represent the  in hours-of-operation signs displayed in windows or on doors of businesses,  and also sometimes in railway and bus timetables. 
Monday, taken as the first day of the week, is represented by .  Sunday is represented by .
The hours of operation signs are tables composed of two columns where the left column is the day of the week in Roman numerals and the right column is a range of hours of operation from starting time to closing time. 
In the sample chart (left), the business opens from 9 AM to 5 PM on Mondays, Wednesdays, and Thursdays; 10 AM to 7 PM on Tuesdays and Fridays; and to 1 PM on Saturdays; and is closed on Sundays.

In several European countries Roman numerals are used for floor numbering.    For instance, apartments in central Amsterdam are indicated as 138-, with both a Hindu-Arabic numeral (number of the block or house) and a Roman numeral (floor number). The apartment on the ground floor is indicated as .

In Italy, where roads outside built-up areas have kilometre signs, major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from  to  for the smaller intervals.  The sign " | 17" thus marks kilometre 17.9.

A notable exception to the use of Roman numerals in Europe is in Greece, where Greek numerals (based on the Greek alphabet) are generally used in contexts where Roman numerals would be used elsewhere.

Special values

Zero 

The number zero does not have its own Roman numeral, but the word nulla (the Latin word meaning "none") was used by medieval scholars in lieu of 0. Dionysius Exiguus was known to use nulla alongside Roman numerals in 525.    About 725, Bede or one of his colleagues used the letter N, the initial of nulla, in a table of epacts, all written in Roman numerals.C. W. Jones, ed., Opera Didascalica, vol. 123C in Corpus Christianorum, Series Latina.

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  makes it easier to handle the common fractions of 1/3 and 1/4 than does a system based on ten  On coins, many of which had values that were duodecimal fractions of the unit , they used a tally-like notational system based on twelfths and halves. A dot (•) indicated an  "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  "half". Uncia dots were added to S for fractions from seven to eleven twelfths, just as tallies were added to  for whole numbers from six to nine. 

Each fraction from 1/12 to 12/12 had a name in Roman times; these corresponded to the names of the related coins:

The arrangement of the dots was variable and not necessarily linear. Five dots arranged like (⁙) (as on the face of a die) are known as a quincunx, from the name of the Roman fraction/coin. The Latin words ' and ' are the source of the English words sextant and quadrant.

Other Roman fractional notations included the following:
* 1/8  (from sesqui- + uncia, i.e. 1½ uncias), represented by a sequence of the symbols for the semuncia and the uncia.
* 1/24  (from semi- + uncia, i.e. ½ uncia), represented by several variant glyphs deriving from the shape of the Greek letter Sigma (Σ), one variant resembling the pound sign (£) without the horizontal line(s) (𐆒) and another resembling the Cyrillic letter Є.
* 1/36  ("two sextulas") or , represented by a sequence of two reversed Ss (ƧƧ).
* 1/48 , represented by a reversed C (Ɔ).
* 1/72  (1/6 of an uncia), represented by a reversed S (Ƨ).
* 1/144 = 12−2  ("half a sextula"), represented by a reversed S crossed by a horizontal line (𐆔).
* 1/288  (a scruple), represented by the symbol ℈.
* 1/1728 = 12−3 , represented by a symbol resembling closing guillemets (𐆕).

Large numbers 

A number of systems were developed for the expression of larger numbers that cannot be conveniently expressed using the normal seven letter symbols of conventional Roman numerals.

Apostrophus

One of these was the apostrophus, in which 500 (usually written as "") was written as |, while 1,000 was written as | instead of "". This is a system of encasing numbers to denote thousands (the s and s  functioned in this case as the Roman equivalent of parentheses), and has its origins in Etruscan numeral usage. The  and  used to represent 500 and 1,000 in conventional Roman numerals were probably derived from | and |, respectively.

In this system, an extra | denoted 500, | 5,000 and | 50,000. For example:

Sometimes | was reduced to ↀ for 1,000. John Wallis is often credited for introducing the symbol for infinity (modern ∞), and one conjecture is that he based it on this usage, since 1,000 was hyperbolically used to represent very large numbers. Similarly, | for 5,000 was reduced to ↁ; | for 10,000 to ↂ; | for 50,000 to ↇ; and | for 100,000 to ↈ.

Vinculum

Another system is the  vinculum, where a conventional Roman numeral is multiplied by 1,000  by adding an overline.
For instance: 
*  for 1,000
*  for 25,000
Adding further vertical lines before and after the numeral might also be used to raise the multiplier to (say) one hundred thousand, or a million.
thus:
* || for 800,000
* || for 2,000,000

This needs to be distinguished from the custom of adding both underline and overline to a Roman numeral, simply to make it clear that it IS a number, e.g. . Certain (serif) typefaces, for example Times New Roman, are designed with serifs that simulate the appearance of the under/over bar, e.g. .
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