Much of the remainder of the world adopted either the short scale or the long scale for everyday counting powers of ten. Countries with the usage of the long scale include most countries in continental Europe and most that are French-speaking, German-speaking and Spanish-speaking.[3] Usage of the short scale is found in Brazil and in most English-speaking and Arabic-speaking countries.
For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two scales are identical. For larger numbers, starting with 109, the two systems differ. For identical names, the long scale proceeds by powers of one million, whereas the short scale proceeds by powers of one thousand. For example, on the short scale, "one billion" means one thousand million (1,000,000,000), whereas in the long scale, it means one million million (1,000,000,000,000). The long scale system employs additional terms for interleaved values, typically replacing the word ending -ion by -iard.
In both short and long scale naming, names are given each multiplication step for increments of the base-10 exponent of three, i.e. for each integer n in the sequence of multipliers 103n. Both systems use the same names for certain multipliers, including those for all numbers smaller than 10. Both systems use the same names for certain multipliers, including those for all numbers smaller than 109. The differences arise from the assignment of identical names to specific values of n, for numbers starting with 109, for which n=3. In the short scale system, the identical names are for n=3, 4, 5, ..., while the long scale places them at n=4, 6, 8, etc.
Short scale
In the short scale, a billion means a thousand millions (1,000,000,000 which is 109), a trillion means one thousand billions (1012), and so on. Thus, a short scale n-illion equals 103n+3.[4]
Long scale
In the long scale, a billion means one million millions (1012) and a trillion means one million billions (1018), and so on. Therefore, a long scale n-illion equals 106n.[1][2]
In some languages, the long scale uses additional names for the intermediate multipliers, replacing the ending -ion with -iard; for example, the next multiplier after million is milliard (109); after a billion it is billiard (1015). Hence, a long scale n-iard equals 106n+3.
Comparison
The relationship between the numeric values and the corresponding names in the two scales can be described as:
The root mil in million does not refer to the numeral, 1. The word, million, derives from the Old French, milion, from the earlier Old Italian, milione, an intensification of the Latin word, mille, a thousand. That is, a million is a big thousand, much as a great gross is a dozen gross or 12 × 144 = 1728.[5]
The word milliard, or its translation, is found in many European languages and is used in those languages for 109. However, it is not found in American English, which uses billion, and not used in British English, which preferred to use thousand million before the current usage of billion. The financial term yard, which derives from milliard, is used on financial markets, as, unlike the term billion, it is internationally unambiguous and phonetically distinct from million. Likewise, many long scale countries use the word billiard (or similar) for one thousand long scale billions (i.e., 1015), and the word trilliard (or similar) for one thousand long scale trillions (i.e., 1021), etc.[6][7][8][9][10]
History
Although this situation has been developing since the 1200s, the first recorded use of the terms short scale (French: échelle courte) and long scale (French: échelle longue) was by the French mathematician Geneviève Guitel in 1975.[1][2]
The short scale was never widespread before its universal adoption in the United States. It has been taught in American schools since the early 1800s.[5] It has since become common in other English-speaking nations and several other countries. For most of the 19th and 20th centuries, the United Kingdom largely used the long scale,[4][11] whereas the United States used the short scale,[11] so that the two systems were often referred to as British and American in the English language. After several decades of increasing informal British usage of the short scale, in 1974 the government of the UK adopted it,[12] and it is used for all official purposes.[13][14][15][16][17][18] The British usage and American usage are now identical.
The existence of the different scales means that care must be taken when comparing large numbers between languages or countries, or when interpreting old documents in countries where the dominant scale has changed over time. For example, British English, French, and Italian historical documents can refer to either the short or long scale, depending on the date of the document, since each of the three countries has used both systems at various times in its history. Today, the United Kingdom officially uses the short scale, but France and Italy use the long scale.
The pre-1974 former British English word billion, post-1961 current French word billion, post-1994 current Italian word bilione, Spanish billón, German Billion, Dutch biljoen, Danish billion, Swedish biljon, Finnish biljoona, Slovenian bilijon, Polish bilion, and European Portuguese word bilião (with a different spelling to the Brazilian Portuguese variant, but in Brazil referring to short scale) all refer to 1012, being long-scale terms. Therefore, each of these words translates to the American English or post-1974 British English word: trillion (1012 in the short scale), and notbillion (109 in the short scale).
On the other hand, the pre-1961 former French word billion, pre-1994 former Italian word bilione, Brazilian Portuguese word bilhão, and Welsh word biliwn all refer to 109, being short scale terms. Each of these words translates to the American English or post-1974 British English word billion (109 in the short scale).
The term billion originally meant 1012 when introduced.[5]
In long scale countries, milliard was defined to its current value of 109, leaving billion at its original 1012 value and so on for the larger numbers.[5] Some of these countries, but not all, introduced new words billiard, trilliard, etc. as intermediate terms.[6][7][8][9][10]
In some short scale countries, milliard was defined to 109 and billion dropped altogether, with trillion redefined down to 1012 and so on for the larger numbers.[5]
In many short scale countries, milliard was dropped altogether and billion was redefined down to 109, adjusting downwards the value of trillion and all the larger numbers.
Timeline
Date
Event
13th century
The word million was not used in any language before the 13th century. The monk and polymath Maximus Planudes (c. 1260–1305) was among the first recorded users of the word to document Mediterranean trade between Constantinople and Italian states.[5] Over the next two centuries, the term became widely accepted and was adopted by other Italian states, France and other European countries.
... item noctes que le premier greton dembas vault ung, le second vault dix, le trois vault cent, le quart vult [sic] mille, le Ve vault dix M, le VIe vault cent M, le VIIe vault Milion, Le VIIIe vault dix Million, Le IXe vault cent Millions, Le Xe vault Mil Millions, Le XIe vault dix mil Millions, Le XIIe vault Cent mil Millions, Le XIIIe vault bymillion, Le XIIIIe vault dix bymillions, Le XVe vault cent mil [sic] bymillions, Le XVIe vault mil bymillions, Le XVIIe vault dix Mil bymillions, Le XVIIIe vault cent mil bymillions, Le XIXe vault trimillion, Le XXe vault dix trimillions ...
Translation:
... Likewise, note that the first counter from the bottom is worth one, the 2nd is worth ten, the 3rd is worth one hundred, the 4th is worth one thousand, the 5th is worth ten thousand, the 6th is worth one hundred thousand, the 7th is worth a million, the 8th is worth ten millions, the 9th is worth one hundred millions, the 10th is worth one thousand millions, the 11th is worth ten thousand millions, the 12th is worth one hundred thousand million, the 13th is worth a bymillion, the 14th is worth ten bymillions, the 15th is worth one [hundred] bymillions, the 16th is worth one thousand bymillions, the 17th is worth ten thousand bymillions, the 18th is worth hundred thousand bymillions, the 19th is worth a trimillion, the 20th is worth ten trimillions ...
1484
Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien an extract from Chuquet's original 1484 manuscript
French mathematician Nicolas Chuquet, in his article Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien,[22][23][24] used the words byllion,tryllion,quadrillion,quyllion,sixlion,septyllion,ottyllion, and nonyllion to refer to 1012, 1018, ... 1054. Most of the work was copied without attribution by Estienne de La Roche and published in his 1520 book, L'arismetique.[22] Chuquet's original article was rediscovered in the 1870s and then published for the first time in 1880.
...[preder s'] Item l'on doit savoir que ung million vault mille milliers de unitez, et ung byllion vault mille milliers de millions, et [ung] tryllion vault mille milliers de byllions, et ung quadrillion vault mille milliers de tryllions et ainsi des aultres : Et de ce en est pose ung exemple nombre divise et punctoye ainsi que devant est dit, tout lequel nombre monte 745324 tryllions 804300 byllions 700023 millions 654321. Exemple : 745324'8043000'700023'654321 ... [sic]
Translation:
...likewise, one should know that a million is worth a thousand thousand units, and a byllion is worth a thousand thousand millions, and tryllion is worth a thousand thousand byllions, and a quadrillion is worth a thousand thousand tryllions, and so on for the others. And an example of this follows, a number divided up and punctuated as previously described, the whole number being 745324 tryllions, 804300 byllions 700023 millions 654321. Example: 745324'8043000'700023'654321 ... [sic]
The extract from Chuquet's manuscript, the transcription and translation provided here all contain an original mistake: one too many zeros in the 804300 portion of the fully written out example: 745324'8043000 '700023'654321 ...
French mathematician Budaeus (Guillaume Budé), writing in Latin, used the term milliart to mean "ten myriad myriad" or 109 in his book De Asse et partibus eius Libri quinque.[25]
.. hoc est decem myriadum myriadas:quod vno verbo nostrates abaci studiosi Milliartum appellant:quasi millionum millionem
Translation:
.. this is ten myriad myriads, which in one word our students of numbers call Milliart, as if a million millions
1549
The influential French mathematician Jacques Pelletier du Mans used the name milliard (or milliart) to mean 1012, attributing the term to the earlier usage by Guillaume Budé[25]
17th century
With the increased usage of large numbers, the traditional punctuation of large numbers into six-digit groups evolved into three-digit group punctuation. In some places, the large number names were then applied to the smaller numbers, following the new punctuation scheme. Thus, in France and Italy, some scientists then began using billion to mean 109, trillion to mean 1012, etc.[26] This usage formed the origins of the later short scale. The majority of scientists either continued to say thousand million or changed the meaning of the Pelletier term, milliard, from "million of millions" down to "thousand million".[5] This meaning of milliard has been occasionally used in England,[11] but was widely adopted in France, Germany, Italy and the rest of Europe, for those keeping the original long scale billion from Adam, Chuquet and Pelletier.
1676
The first published use of milliard as 109 occurred in the Netherlands.[5][27]
.. milliart/ofte duysent millioenen..
Translation:
..milliart / also thousand millions..
1729
The short-scale meaning of the term billion had already been brought to the British American colonies. The first American appearance of the short scale value of billion as 109 was published in the Greenwood Book of 1729, written anonymously by Prof. Isaac Greenwood of Harvard College.[5]
Late 18th century
As early as 1762 (and through at least the early 20th century), the dictionary of the Académie française defined billion as a term of arithmetic meaning a thousand millions.[28][29][30][31]
Early 19th century
France widely converted to the short scale, and was followed by the U.S., which began teaching it in schools. Many French encyclopedias of the 19th century either omitted the long scale system or called it "désormais obsolète", a now obsolete system. Nevertheless, by the mid 20th century France would officially convert back to the long scale.
It should be remembered that "billion" does not mean in American use (which follows the French) what it means in British. For to us it means the second power of a million, i.e. a million millions (1,000,000,000,000); for Americans it means a thousand multiplied by itself twice, or a thousand millions (1,000,000,000), what we call a milliard. Since billion in our sense is useless except to astronomers, it is a pity that we do not conform.
Although American English usage did not change, within the next 50 years French usage changed from short scale to long and British English usage changed from long scale to short.
1948
The 9th General Conference on Weights and Measures received requests to establish an International System of Units. One such request was accompanied by a draft French Government discussion paper, which included a suggestion of universal use of the long scale, inviting the short-scale countries to return or convert.[32] This paper was widely distributed as the basis for further discussion. The matter of the International System of Units was eventually resolved at the 11th General Conference in 1960. The question of long scale versus short scale was not resolved and does not appear in the list of any conference resolutions.[32][33]
Mr. Maxwell-Hyslop asked the Prime Minister whether he would make it the practice of his administration that when Ministers employ the word 'billion' in any official speeches, documents, or answers to Parliamentary Questions, they will, to avoid confusion, only do so in its British meaning of 1 million million and not in the sense in which it is used in the United States of America, which uses the term 'billion' to mean 1,000 million.
The Prime Minister: No. The word 'billion' is now used internationally to mean 1,000 million and it would be confusing if British Ministers were to use it in any other sense. I accept that it could still be interpreted in this country as 1 million million and I shall ask my colleagues to ensure that, if they do use it, there should be no ambiguity as to its meaning.
The BBC and other UK mass media quickly followed the government's lead within the UK.
During the last quarter of the 20th century, most other English-speaking countries (Ireland, Australia, New Zealand, South Africa, Zimbabwe, etc.) either also followed this lead or independently switched to the short scale use. However, in most of these countries, some limited long scale use persists and the official status of the short scale use is not clear.
1975
French mathematician Geneviève Guitel introduced the terms long scale (French: échelle longue) and short scale (French: échelle courte) to refer to the two numbering systems.[1][2]
As large numbers in natural sciences are usually represented by metric prefixes, scientific notation or otherwise, the most commonplace occurrence of large numbers represented by long or short scale terms is in finance. The following table includes some historic examples related to hyper-inflation and other financial incidents.
1000 Mark German banknote, over-stamped in red with "Eine Milliarde Mark" (109 mark)
Using German banknotes as wallpaper following the 1923 hyperinflation
German hyperinflation in the 1920sWeimar Republic caused 'Eintausend Mark' (1000 Mark = 103 Mark) German banknotes to be over-stamped as 'Eine Milliarde Mark' (109 Mark). This introduced large-number names to the German populace.
The Mark or Papiermark was replaced at the end of 1923 by the Rentenmark at an exchange rate of
Hyperinflation in Zimbabwe led to banknotes of 1014Zimbabwean dollars, marked "One Hundred Trillion Dollars" (short scale), being issued in 2009, shortly ahead of the currency being abandoned[38][39][40] after a final redenomination to the 'fourth dollar'. From 2013 to 2019 when the RTGS Dollar entered use, no new currency was announced, and so foreign currencies were used instead.
Most Arabic-language countries and regions use the short scale with 109 being مليارmilyar, except for a few countries like Saudi Arabia and the UAE which use the word بليون billion for 109. For example:[shortscale note 5][46][47]
106, one million; 109, one milliard or one billion; 1012, one trillion; etc.
Other countries also use a word similar to trillion to mean 1012, etc. Whilst a few of these countries like English use a word similar to billion to mean 109, most like Arabic have kept a traditionally long scale word similar to milliard for 109. Some examples of short scale use, and the words used for 109 and 1012, are
The long scale is used by most Continental European countries and by most other countries whose languages derive from Continental Europe (with the notable exceptions of Albania, Greece, Romania,[49] and Brazil). These countries use a word similar to billion to mean 1012. Some use a word similar to milliard to mean 109, while others use a word or phrase equivalent to thousand millions.
With the notable exception of Brazil, a short scale country, most Portuguese-language countries and regions use the long scale with 109 = mil milhõesormilhar de milhões.
Some countries use either the short or long scales, depending on the internal language being used or the context.
106, one million; 109, either one billion (short scale) or one milliard / thousand million (long scale); 1012, either one trillion (short scale) or one billion (long scale), etc.
Names of the short scale have not been loaned but calqued into Greek, based on the native Greek word for million, εκατομμύριοekatommyrio ("hundred-myriad", i.e. 100 × 10,000):
^English language countries: Apart from the United States, the long scale was used for centuries in many English language countries before being superseded in recent times by short scale usage. Because of this history, some long scale use persists[18] and the official status of the short scale in anglophone countries other than the UK and US is sometimes obscure.[5]
^Australian usage: In Australia, education, media outlets, and literature all use the short scale in line with other English-speaking countries. The current recommendation by the Australian Government Department of Finance and Deregulation (formerly known as AusInfo), and the legal definition, is the short scale.[42] As recently as 1999, the same department did not consider short scale to be standard, but only used it occasionally. Some documents use the term thousand million for 109 in cases where two amounts are being compared using a common unit of one 'million'.
^British usage: Billion has meant 109 in most sectors of official published writing for many years now. The UK government, the BBC, and most other broadcast or published mass media, have used the short scale in all contexts since the mid-1970s.[12][13][43][15] Before the widespread use of billion for 109, UK usage generally referred to thousand million rather than milliard.[16] The long scale term milliard, for 109, is obsolete in British English, though its derivative, yard, is still used as slang in the London money, foreign exchange, and bond markets.
^American usage: In the United States, the short scale has been taught in school since the early 19th century. It is therefore used exclusively.[44][45]
^Arabic language countries: Most Arabic-language countries use: 106, مليونmillion; 109, مليارmilyar; 1012, ترليونtrilyon; etc.[46][47]
^Indonesian usage: Large numbers are common in Indonesia, in part because its currency (rupiah) is generally expressed in large numbers (the lowest common circulating denomination is Rp100 with Rp1000 is considered as base unit). The term juta, equivalent to million (106), is generally common in daily life. Indonesia officially employs the term miliar (derived from the long scale Dutch word miljard) for the number 109, with no exception. For 1012 and greater, Indonesia follows the short scale, thus 1012 is named triliun. The term seribu miliar (a thousand milliards) or more rarely sejuta juta (a million millions) or sejuta berkali-kali (a millions after a million or a millions over a million) are also used for 1012 less often. Terms greater than triliun are not very familiar to Indonesians.[48]
Long scale
^French usage: France, with Italy, was one of two European countries which converted from the long scale to the short scale during the 19th century, but returned to the original long scale during the 20th century. In 1961, the French Government confirmed their long scale status.[37][52][53] However the 9th edition of the dictionary of the Académie française describes billion as an outdated synonym of milliard, and says that the new meaning of 1012 was decreed in 1961, but never caught on.[54]
^Spanish language countries: Spanish-speaking countries sometimes use millardo (milliard)[55] for 109, but mil millones (thousand millions) is used more frequently. The word billón is sometimes used in the short scale sense in those countries more influenced by the United States, where "billion" means "one thousand millions". The usage of billón to mean "one thousand millions", controversial from the start, was denounced by the Royal Spanish Academy as recently as 2010,[56] but was finally accepted in a later version of the official dictionary as standard usage among educated Spanish speakers in the United States (including Puerto Rico).[57]
^Italian usage: Italy, with France, was one of the two European countries which partially converted from the long scale to the short scale during the 19th century, but returned to the original long scale in the 20th century. In 1994, the Italian Government confirmed its long scale status.[10] In Italian, the word bilione officially means 1012, trilione means 1018, etc.. Colloquially, bilione[58] can mean both 109 and 1012; trilione[citation needed] can mean both 1012 and (rarer) 1018 and so on. Therefore, in order to avoid ambiguity, they are seldom used. Forms such as miliardo (milliard) for 109, mille miliardi (a thousand milliards) for 1012, un milione di miliardi (a million milliards) for 1015, un miliardo di miliardi (a milliard of milliards) for 1018, mille miliardi di miliardi (a thousand milliard of milliards) for 1021 are more common.[10]
Both long and short scale
^Canadian usage: Both scales are in use currently in Canada. English-speaking regions use the short scale exclusively, while French-speaking regions use the long scale, though the Canadian government standards website recommends that in French billion and trillion be avoided, recommending milliard for 109, and mille milliards (a thousand milliards) for 1012.[60]
^South African usage: South Africa uses both the long scale (in Afrikaans and sometimes English) and the short scale (in English). Unlike the 1974 UK switch, the switch from long scale to short scale took time. As of 2011[update] most English language publications use the short scale. Some Afrikaans publications briefly attempted usage of the "American System" but that has led to comment in the papers[62] and has been disparaged by the "Taalkommissie" (The Afrikaans Language Commission of the South African Academy of Science and Art)[63] and has thus, to most appearances, been abandoned.
Neither long nor short scale
^Indian, Pakistani and Bangladeshi usage: Outside of financial media, the use of billion by Bangladeshi, Indian and Pakistani English speakers highly depends on their educational background. Some may continue to use the traditional British long scale. In everyday life, Bangladeshis, Indians and Pakistanis largely use their own common number system, commonly referred to as the Indian numbering system – for instance, Bangladeshi, Pakistani, and Indian English commonly use the words lakh to denote 100 thousand, crore to denote ten million (i.e. 100 lakhs) and arab to denote thousand million.[64]
Alternative approaches
In written communications, the simplest solution for moderately large numbers is to write the full amount, for example 1,000,000,000,000 rather than 1 trillion (short scale) or 1 billion (long scale).
Combinations of the unambiguous word million, for example: 109 = "one thousand million"; 1012 = "one million million".[66]
Scientific notation (also known as standard form or exponential notation, for example 1×109, 1×1010, 1×1011, 1×1012, etc.), or its engineering notation variant (for example 1×109, 10×109, 100×109, 1×1012, etc.), or the computing variant E notation (for example 1e9, 1e10, 1e11, 1e12, etc.). This is the most common practice among scientists and mathematicians, and is both unambiguous and convenient.
^ abcdeGuitel, Geneviève (1975). ""Les grands nombres en numération parlée (État actuel de la question)", i.e. "The large numbers in oral numeration (Present state of the question)"". Histoire comparée des numérations écrites (in French). Paris: Flammarion. pp. 566–574. ISBN978-2-08-211104-1.
^ abBudaeus, Guilielmus (1516). De Asse et partibus eius Libri quinque (in Latin). pp. folio 93.
^Littré, Émile (1873–1874). Dictionnaire de la langue française. Paris, France: L. Hachette. p. 347. Ce n'est qu'au milieu du XVIIe siècle qu'il fut réglé que les tranches, au lieu d'être de six en six chiffres, seraient de trois en trois chiffres; ce qui revint à diviser par 1000 l'ancien billion, l'ancien trillion, etc. [It was only in the middle of the 17th century that it was settled that the slices, instead of being from six to six digits, would be from three to three digits; which resulted in dividing by 1000 the old billion, the old trillion, and so on.]
^ ab"Décret 61-501"(PDF). Journal Officiel (in French). French Government: 4587 note 3a, and erratum on page 7572. 11 August 1961 [commissioned 3 May 1961 published 20 May 1961]. Archived from the original(PDF) on 20 January 2010. Retrieved 31 January 2008.
^ abRobson S. O. (Stuart O.), Singgih Wibisono, Yacinta Kurniasih. Javanese English dictionary Tuttle Publishing: 2002, ISBN0-7946-0000-X, 821 pages
^Avram, Mioara; Sala, Marius (2000), May We Introduce the Romanian Language to You?, Editura Fundatiei Culturale Române, p. 151, ISBN9789735772246, the numeral miliard "billion"
^billion (in French) (9th ed.). Académie française. 1992. Retrieved 17 January 2016. BILLION (les deux l se prononcent sans mouillure) n. m. XVe siècle, byllion, « un million de millions »; XVIe siècle, « mille millions ». Altération arbitraire de l'initiale de million, d'après la particule latine bi-, « deux fois ». Rare. Mille millions. Syn. vieilli de Milliard. Selon un décret de 1961, le mot Billion a reçu une nouvelle valeur, à savoir un million de millions (1012), qui n'est pas entrée dans l'usage. [BILLION (the two Ls are pronounced without palatalisation) masculine noun. Spelled byllion in the 15th century when it meant a million millions; in the 16th century it meant a thousand millions. It is an arbitrary alteration of the start of million by inserting the Latin prefix bi-, meaning twice. Now rarely used. It means a thousand millions. It is an outdated synonym of Milliard. According to a decree of 1961, the word Billion received a new value, to wit a million millions (1012), which has not come into common usage.] ((cite encyclopedia)): |work= ignored (help)[permanent dead link]
