Long and short scales

The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries use the short scale. In all such countries, the number names are translated into the local language, but retain a name similarity due to shared etymology. Some languages, particularly in East Asia and South Asia, have large number naming systems that are different from the long and short scales.[1][2]

Long scale is the English translation of the French term échelle longue. It refers to a system of large-number names in which every new term greater than million is 1,000,000 times the previous term: billion means a million millions (1012), trillion means a million billions (1018), and so on.[1][2]
Short scale is the English translation of the French term échelle courte. It refers to a system of large-number names in which every new term greater than million is 1,000 times the previous term: billion means a thousand millions (109), trillion means a thousand billions (1012), and so on.[1][2]

For integers less than a thousand million (< 109), the two scales are identical. At and above a thousand million (≥ 109), the two scales diverge by using the same words for different number values. These "false friends" can be a source of misunderstanding.

For most of the 19th and 20th centuries, the United Kingdom uniformly used the long scale,[3] while the United States of America used the short scale,[3] so that the two systems were often referred to as British and American in the English language. In 1974, the government of the UK switched to the short scale, a change that is reflected in its mass media and official usage.[4][5][6][7][8][9] Although some residual usage of the long scale continues in the UK,[10][11] the phrases British usage and American usage are no longer accurate characterisations. Usage of the two systems can be a subject of controversy. Differences in opinion as to which system should be used can evoke resentment between adherents, while national differences of any kind can acquire jingoistic overtones.[11]

The first recorded use of the terms échelle courte and échelle longue was by the French mathematician Geneviève Guitel in 1975.[1][2]

Contents

Comparison

The same numerical value has two different names, depending on whether the value is being expressed in the long or short scale. Equivalently, the same name has two different numerical values depending on whether it is being used in the long or short scale.

Each scale has a logical justification to explain the use of each such differing numerical name and value within that scale. The short scale logic is based on powers of one thousand, whereas the long scale logic is based on powers of one million. In both scales, the prefix bi- refers to "2" and tri- refers to "3", etc. However only in the long scale do the prefixes beyond one million indicate the actual power or exponent (of 1,000,000). In the short scale, the prefixes refer to one less than the exponent (of 1,000).

The relationship between the numeric values and the corresponding names in the two scales can be described as:

 Value in
Scientific notation 
 Value in
numerals 
 Short Scale   Long Scale 
Name Logic Name Logic
 10 0   one  one
 10 3  1,000   thousand  thousand
 10 6  1,000,000   million    million  
 10 9  1,000,000,000   billion or milliard 1,0002+1  thousand million or milliard
 1012  1,000,000,000,000   trillion 1,0003+1  billion 1,000,0002
 1015  1,000,000,000,000,000   quadrillion 1,0004+1  thousand billion or billiard
 1018  1,000,000,000,000,000,000   quintillion 1,0005+1  trillion 1,000,0003
 1021  1,000,000,000,000,000,000,000   sextillion 1,0006+1  thousand trillion or trilliard
 1024  1,000,000,000,000,000,000,000,000   septillion 1,0007+1  quadrillion 1,000,0004
  etc.   etc.   To get from one named order of magnitude to the next: multiply by 1,000 To get from one named order of magnitude to the next: multiply by 1,000,000

The root mil in "million" does not refer to the numeral "one". Rather, it refers to the Latin word for "thousand" (milia).

The relationship between the names and the corresponding numeric values in the two scales can be described as:

 Name   Short Scale   Long Scale 
 Value in
Scientific notation 
 Logic   Value in
Scientific notation 
 Logic 
million 106   106  
billion 109  1,0002+1  1012  1,000,0002 
trillion 1012  1,0003+1  1018  1,000,0003 
quadrillion 1015  1,0004+1  1024  1,000,0004 
etc. To get from one named order of magnitude to the next: multiply by 1,000 To get from one named order of magnitude to the next: multiply by 1,000,000

The word milliard, or its translation, is found in many European languages and is used in those languages for 109. However, it is unknown 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 it is unambiguous, unlike billion. Likewise, many long scale countries use the word billiard (or similar) for a thousand long scale billions (i.e. 1015), and the word trilliard (or similar) for a thousand long scale trillions (i.e. 1021), etc.

History

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, German Billion; Dutch biljoen; Swedish biljon; Finnish biljoona; Danish billion; Spanish billón and the European Portuguese word bilião (with an alternate spelling to the Brazilian Portuguese variant) all refer to 1012, being long-scale terms. Therefore, each of these words translates to the American English or post-1974 modern British English word: trillion (1012 in the short scale), and not billion (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 the Welsh word biliwn all refer to 109, being short scale terms. Each of these words translates to the American English or post-1974 modern British English word billion (109 in the short scale).

The terms billion and milliard both originally meant 1012 when introduced.[12]

The word million derives from the Old French Milion from the earlier Old Italian milione, an intensification of mille, a thousand. That is, a million is a "big thousand", much as a "great gross" is a dozen gross or 1728.[12]

Timeline
 Date  Event
1200s The word million was not used before the 13th century. Maximus Planudes (cir 1260–1305) was among the first recorded users.[12]
late 1300s The word million entered the English language. One of the earliest references is William Langland's Piers Plowman (written c. 1360-1387),[12] with:
Coueyte not his goodes
For millions of moneye
1475 French mathematician Jehan Adam recorded the words bymillion and trimillion as meaning 1012 and 1018 respectively.[16]
... item noctes que le premier greton dembas vault ung, le second vault ... cent, le quart vult 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 Mill Millions, Le XIe vault dix mill Millions, Le XIIe vault Cent mil Millions, Le XIIIe vault bymillion, Le XIIIIe vault dix bymillions, Le XVe vault 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:

... Item 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 billion, the 14th is worth ten billions, the 15th is worth one [hundred] billions, the 16th is worth one thousand billions, the 17th is worth ten thousand billions, the 18th is worth hundred thousand billions, the 19th is worth a trimillion, the 20th is worth ten trimillions ...
1484 French mathematician Nicolas Chuquet, in his article "Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien",[17][18][19] used the words byllion, tryllion, quadrillion, quyllion, sixlion, septyllion, ottyllion, and nonyllion to refer to 1012, 1018, etc. Chuquet's work was not published until the 1870s, but most of it was copied without attribution by Estienne de La Roche and published in his 1520 book, L'arismetique.[17]
... Item lon 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:

...Item: 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 ..."

1514 French mathematician Budaeus (Guillaume Budé), writing in Latin, used the term milliart to mean "Millions of millions" or 1012 in his book "De Asse et partibus eius Libri quinqz".[20]
.. hoc est denas myriadu myriadas, quod vno verbo nostrates abaci studiosi Milliartu appellat, quasi millionu millione

Translation:

.. this is ten myriad myriads, which in one word our students of numbers call Milliart, as if a million millions

Unfortunately, since 10 myriad myriads (10 * 104 * 104 = 109) is not equal to a million millions (106 * 106 = 1012), this is confusing.

1549 The influential French mathematician Jacques Pelletier du Mans used the name milliard (or milliart), attributing this meaning to the earlier usage by Guillaume Budé[20]
1600s The traditional six-digit groups were split into three-digit groups. In France and Italy, some scientists then began using billion to mean 109, trillion to mean 1012, etc. 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".[12] This meaning of milliard has been occasionally used in England,[3] but was widely adopted in France, Germany, Italy and the rest of Europe, for those keeping Chuquet's original long scale billion.
1676 The first published use of milliard as 109 occurred in 1676 in Houck's Arithmetic, published in the Netherlands.[12]
Early 1700s The short-scale meaning of the term billion was brought to the British American colonies
1729 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[12]
Early 1800s 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 had converted back to the long scale.
1926 H. W. Fowler's A Dictionary of Modern English Usage[3] noted:
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.
1948 The 9th General Conference on Weights and Measures received a proposal recommending the universal use of the long scale, inviting the short-scale countries to return or convert. The proposal was considered but not adopted.[21]
1960 The 11th General Conference on Weights and Measures adopted the International System of Units (SI), with its own set of numeric prefixes.[22] SI is therefore independent of the number scale being used. SI also notes the language-dependence of some larger-number names and advises against using such ambiguous terms as billion, trillion, etc.[23]
1961 The French Government confirmed their official usage of the long scale in the Journal Officiel (the official French Government gazette).[24]
1974 British prime minister Harold Wilson explained in a written answer to the House of Commons that UK government statistics would from then on use the short scale.[5] Hansard,[4] for the 20 December 1974, reported it:
Mr. Maxwell-Hyslop asked the Prime Minister whether he will 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.

During the last quarter of the 20th century, most other English-speaking countries (Ireland, Australia, New Zealand, South Africa, Zimbabwe, etc.) either 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 échelle longue (long scale) and échelle courte (short scale) to refer to the two numbering systems.[1][2]
1994 The Italian Government confirmed their official usage of the long scale.[15]

Current usage

Short scale countries and regions

English language-speaking countries and regions [shortscale note 1]
106 = one million, 109 = one billion, 1012 = one trillion, etc.

Most English-language countries use the short scale with 109 = billion. For example:

 Antigua and Barbuda
 Australia [shortscale note 2]
 Bahamas
 Barbados
 Belize   (English-speaking)
 Botswana   (English-speaking)
 Cameroon   (English-speaking)
 Dominica
 Eritrea
 Ethiopia
 Fiji
 Gambia
 Ghana   (English-speaking)
 Gibraltar
 Grenada
 Guernsey
 Guyana   (English-speaking)
 Hong Kong   (English-speaking)
 Isle of Man  
 Ireland   (English-speaking, Irish: billiún trilliún)
 Jamaica
 Jersey
 Kenya   (English-speaking)
 Lesotho
 Liberia
 Malawi   (English-speaking)
 Malta   (English-speaking, Maltese: biljun, triljun)
 Malaysia   (English-speaking)
 Nigeria   (English-speaking)
 New Zealand   (English-speaking)
 Papua New Guinea   (English-speaking)
 Philippines   (English-speaking) [shortscale note 3]
 Rwanda
 Sierra Leone
 Singapore   (English-speaking)
 South Sudan   (English-speaking)
 Sudan   (English-speaking)
 Swaziland
 Tanzania   (English-speaking)
 Tonga
 Trinidad and Tobago
 Tuvalu
 Uganda   (English-speaking)
 United Kingdom   (see Wales below) [shortscale note 4]
 United States [shortscale note 5]
 Zambia   (English-speaking)
 Zimbabwe   (English-speaking)[28]
Other short scale countries and regions
106 = one million, 109 = one milliard / billion, 1012 = one trillion, etc.

Other countries also use a word similar to trillion to mean 1012, etc. While a few of these countries use a word similar to billion to mean 109, most have kept a traditional long scale word similar to "milliard" for 109. Some examples of short scale use, and the words used for 109 and 1012, are:

 Albania   (miliard, trilion)
 Armenia   ( միլիարդ , տրիլիոն )
 Azerbaijan   (milyard, trilyon)
 Belarus   ( мільярд milyard, трыльён trilyon)
 Brazil   (Brazilian Portuguese: bilhão, trilhão)
 Bulgaria   (милиард miliard, трилион trilion)
 Cyprus   (Greek: δισεκατομμύριο disekatommyrio, τρισεκατομμύριο trisekatommyrio, Turkish: milyar, trilyon)
 Egypt   (Arabic: مليار billion, تريليون trillion)
 Estonia   (miljard, triljon)[29][30]
 Georgia   ( მილიარდი , ტრილიონი )
 Indonesia   (miliar, triliun)  [shortscale note 6]
 Iran   (Persian: میلیارد milyard or بیلیون billion, تریلیون trillion)[32][33][34]
 Israel   (Hebrew: מיליארד millyard, טריליון trillyon)
 Latvia   (miljards, triljons)
 Lithuania   (milijardas, trilijonas)
 Myanmar   (Burmese: ဘီလျံ, IPA: [bìljàɴ]; ထရီလျံ, [tʰəɹìljàɴ])[35]
 Russia   (миллиард milliard, триллион trillion)
 Saudi Arabia   (Arabic: مليار billion, تريليون trillion)
 Turkey   (milyar, trilyon)
 Ukraine   (мільярд milliard, трильйон trillion)
 Wales   (biliwn, triliwn)
Short scale use but with other terminology
 Greece (εκατομμύριο ekatommyrio "hundred-myriad" = 106; δισεκατομμύριο disekatommyrio "bi+hundred-myriad" = 109; τρισεκατομμύριο trisekatommyrio "tri+hundred-myriad" = 1012; τετράκις εκατομμύριο tetrakis ekatommyrio "quadri+hundred-myriad" = 1015, and so on.)[36]

Long scale countries and languages

106 = one million, 109 = one milliard / thousand million, 1012 = one billion, 1015 = one billiard / thousand billion, 1018 = one trillion, etc.

The traditional 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 Greece, Romania, Bulgaria 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 something equivalent to thousand millions. Some examples of long scale use, and the words used for 109 and 1012, are:

 Andorra   (Catalan: miliard or typ. mil milions, bilió)
 Argentina   (Spanish: mil millones, billón)
 Austria   (Austrian German: Milliarde, Billion)
 Belgium   (Belgian French: milliard, billion; Flemish: miljard, biljoen; German: Milliarde, Billion)
 Bolivia   (Spanish: mil millones, billón)
 Bosnia and Herzegovina   (Bosnian: milijarda, bilion; Croatian: milijarda, bilijun, Serbian: милијарда milijarda, Билион bilion)
 Chile   (Spanish: mil millones, billón)
 Colombia   (Spanish: mil millones, billón)
 Democratic Republic of the Congo   (French: milliard, billion)
 Costa Rica   (Spanish: mil millones, billón)
 Croatia   (milijarda, bilijun)
 Cuba   (Spanish: mil millones, billón)
 Czech Republic   (miliarda, bilion)
 Denmark   (milliard, billion)
 Dominican Republic   (Spanish: mil millones, billón)
 Ecuador   (Spanish: mil millones, billón)
 El Salvador   (Spanish: mil millones, billón)
 Finland   (Finnish: miljardi, biljoona; Swedish: miljard, biljon)
 France   (milliard, billion) [longscale note 1]
 Germany   (Milliarde, Billion)[39][40]
 Guatemala   (Spanish: millardo, billón)
 Honduras   (Spanish: millardo, billón)
 Hungary   (milliárd, billió or ezer milliárd)
 Iceland   (milljarður, billjón)
 Italy   (miliardo, bilione) [longscale note 2]
 Liechtenstein   (German: Milliarde, Billion)
 Luxembourg   (Luxembourgish: milliard, billioun; French: milliard, billion; German: Milliarde, Billion)
 Macau   (Portuguese: mil milhões or milhar de milhões, bilião)
 Macedonia   (милијарда milijarda, Билион bilion)
 Mexico   (Spanish: mil millones or millardo, billón)
 Monaco   (French: milliard, billion)
 Netherlands   (miljard, biljoen)[42][43]
 Nicaragua   (Spanish: mil millones or milliardo, billón)
 Norway   (milliard, billion)
 Panama   (Spanish: mil millones or millardo, billón)
 Paraguay   (Spanish: mil millones, billón)
 Peru   (Spanish: mil millones, billón)
 Poland   (miliard, bilion)
 Portugal   (mil milhões or milhar de milhões, bilião)
 Serbia   (милијарда milijarda, Билион bilion)
 Slovakia   (miliarda, bilión)
 Slovenia   (milijarda, bilijon)
 Spain   (millardo or typ. mil millones, billón) [longscale note 3]
 Suriname   (Dutch: miljard, biljoen)
 Sweden   (miljard, biljon)
 Switzerland   (French: milliard, billion; German: Milliarde, Billion; Italian: miliardo, bilione, Romansh: milliarda, billiun[46])
 Uruguay   (Spanish: mil millones or millardo, billón)
 Venezuela   (Spanish: mil millones or millardo, billón)
Esperanto language   (miliardo, duiliono) [longscale note 4]

Both long and short scale countries

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.
 Country or Territory   Short scale usage   Long scale usage 
 Canada [shortscale longscale note 1] Canadian English   (billion = 109, trillion = 1012) Canadian French   (milliard = 109, billion = 1012).
 Puerto Rico economic & technical (billón = 109, trillón = 1012) Latin American export publications (millardo or mil millones = 109, billón = 1012)
 Namibia
 South Africa [shortscale longscale note 2]
South African English   (billion = 109, trillion = 1012) Afrikaans   (miljard = 109, biljoen = 1012)
 Romania [shortscale longscale note 3] For numbers > 109, the short scale is used (trilion = 1012) For numbers ≤ 109, the long scale is used (miliard = 109)

Neither short nor long scale countries

The following Asian countries have their own numbering systems and use neither short nor long scales:

 Country   Main article   Notes 
 Bangladesh,    India,    Nepal,    Pakistan Indian numerals  For everyday use, but short or long scale may also be in use [other scale note 1]
 Bhutan Dzongkha numerals Traditional system
 Cambodia Khmer numerals Traditional system
 China (People's Republic),    Taiwan (Republic of China) Chinese numerals Traditional myriad system for the larger numbers; special words and symbols up to 1088.
 Japan Japanese numerals Traditional myriad system for the larger numbers; special words and symbols up to 1088.
 North Korea,    South Korea Korean numerals Traditional myriad system for the larger numbers; special words and symbols up to 1088.
 Mongolia Mongolian numerals Traditional myriad system for the larger numbers; special words up to 1067.
 Sri Lanka Sinhala numerals
Tamil numerals
Traditional systems
 Thailand Thai numerals Traditional system based on millions
 Vietnam Vietnamese numerals Traditional system(s) based on thousands
Presence on most continents

The long and short scales are both present on all continents, with usage dependent on the language used. Examples include:

Continent Short scale usage Long scale usage
Africa South African English Afrikaans
North America American English, Canadian English American Spanish, Canadian French
South America Brazilian Portuguese, English (Guyana) American Spanish, Dutch (Suriname), French (French Guiana)
Antarctica Australian English, British English, New Zealand English American Spanish (Argentina, Chile), French (France), Norwegian (Norway)
Asia Burmese (Myanmar), Hebrew (Israel), Indonesian, Malaysian English, Persian (Iran), Philippine English, Portuguese (Macau)
Europe British English, Hiberno-English, Scottish English, Welsh English, Welsh, Bulgarian, Estonian, Greek, Latvian, Lithuanian, Turkish, Ukrainian Danish, Dutch, Finnish, French, German, Icelandic, Italian, Norwegian, Polish, Portuguese, Spanish, Swedish and most other languages of continental Europe
Oceania Australian English, New Zealand English French (French Polynesia)
Alternative approaches

Unambiguous ways of identifying large numbers include:

Notes on current usage

Short scale
  1. ^ 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 and the official status of the short scale in anglophone countries other than the UK and US is sometimes obscure.
  2. ^ 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.[25] 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'.
  3. ^ Filipino usage: Some short-scale words have been adopted into Filipino.
  4. ^ 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.[4][5][6][7]
    Before the widespread use of billion for 109, UK usage generally referred to thousand million rather than milliard.[8] 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.
  5. ^ American usage: In the United States of America, the short scale has been taught in school since the early 19th century. It is therefore used exclusively.[26][27]
  6. ^ 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) are also used for 1012 less often. Terms greater than triliun are not very familiar to Indonesians.[31]
Long scale
  1. ^ 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.[24][37][38]
  2. ^ 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.[15]
    In Italian, the word bilione officially means 1012, trilione means 1018, etc.. Colloquially, bilione[41] can mean both 109 and 1012; trilione 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.[15]
  3. ^ Spanish usage: Spanish-speaking countries sometimes use millardo (milliard)[44] for 109, but mil millones (thousand millions) is used more frequently. The word billón is sometimes incorrectly used in the short scale sense in those countries more influenced by the United States, but this is considered unacceptable.[45]
  4. ^ Esperanto language usage: The Esperanto language words biliono, triliono etc. used to be ambiguous, and both long or short scale were used and presented in dictionaries. The current edition of the main Esperanto dictionary PIV however recommends the long scale meanings, as does the grammar PMEG.[47] Ambiguity may be avoided by the use of the unofficial but generally-recognised suffix -iliono, whose function is analogous to the long scale, i.e. it is appended to a (single) numeral indicating the power of a million, e.g. duiliono (from du meaning "two") = biliono = 1012, triiliono = triliono = 1018, etc. following the 1×106X long scale convention. Miliardo is an unambiguous term for 109, and generally the suffix -iliardo, for values 1×106X+3, for example triliardo = 1021 and so forth.
Both long and short scale
  1. ^ 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.[48]
  2. ^ 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 with most English publications now (2011) using the short scale. Some Afrikaans publications briefly attempted usage of the "American System" but that has led to comment in the papers and has been disparaged by the "Taalkommissie" (The Afrikaans Language Commission of the South African Academy of Science and Art) and has thus, to most appearances, been abandoned.
  3. ^ Romanian usage: Up to and including 109, Romania uses a standard long scale: milion = 106; miliard = 109; Above 109, the short scale is used: trilion = 1012. The official status of either scale is far from clear.
Neither long nor short scale
  1. ^ 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.[49]

See also

External links

References

  1. ^ a b c d e Guitel, Geneviève (1975) (in French). Histoire comparée des numérations écrites. Paris: Flammarion. pp. 51–52. ISBN 978-2082111041. 
  2. ^ a b c d e Guitel, Geneviève (1975) (in French). Histoire comparée des numérations écrites. Paris: Flammarion. pp. 566–574 Chapter: "Les grands nombres en numération parlée (État actuel de la question)", i.e. "The large numbers in oral numeration (Present state of the question)" . ISBN 978-2082111041. 
  3. ^ a b c d Fowler, H. W. (1926). A Dictionary of Modern English Usage. Great Britain: Oxford University Press. pp. 52–53. ISBN 978-0198605065. http://books.google.com/books?id=Vr7muDFR6j4C&q=billion#v=snippet&q=billion&f=false. 
  4. ^ a b c ""BILLION" (DEFINITION) – HC Deb 20 December 1974 vol 883 cc711W-712W". Hansard Written Answers. Hansard. 1974-12-20. http://hansard.millbanksystems.com/written_answers/1974/dec/20/billion-definition#S5CV0883P0_19741220_CWA_439. Retrieved 2009-04-02. 
  5. ^ a b c O'Donnell, Frank (30 July 2004). "Britain's £1 trillion debt mountain – How many zeros is that?". The Scotsman. http://news.scotsman.com/latestnews/Britains-1-trillion-debt-mountain.2550147.jp. Retrieved 2008-01-31. 
  6. ^ a b "BBC News: Who wants to be a trillionaire?". BBC. 7 May 2007. http://news.bbc.co.uk/1/hi/programmes/more_or_less/6625545.stm. Retrieved 2010-05-11. 
  7. ^ a b Comrie, Bernard (24 March 1996). "billion:summary". Linguist List mailing list. http://www.linguistlist.org/issues/7/7-451.html. Retrieved 2011-07-24. 
  8. ^ a b "Oxford Dictionaries: How many is a billion?". Oxford University Press. http://oxforddictionaries.com/page/howmanybillion?view=uk. Retrieved 2011-07-24. 
  9. ^ "Oxford Dictionaries: Billion". Oxford University Press. http://oxforddictionaries.com/definition/billion. Retrieved 2011-07-24. 
  10. ^ "Ask Jeeves: How Many Zeros In A Billion?". www.ask.com. 24 July 2011. http://uk.ask.com/question/how-many-zeros-in-a-billion. Retrieved 2011-07-24. 
  11. ^ a b Nielsen, Ron (2006). The Little Green Handbook. Macmillan Publishers. p. 290. ISBN 978-0312425814. 
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  14. ^ "Wortschatz-Lexikon: Trilliarde" (in German). Universität Leipzig: Wortschatz-Lexikon. http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Trilliarde. Retrieved 2011-07-28. 
  15. ^ a b c d "Direttiva CEE / CEEA / CE 1994 n. 55, p.12" (in Italian). Italian Government. 21 November 1994. http://www.frareg.com/news/legislazione/ambiente/direttiva_1994_55_CE.pdf. Retrieved 2011-07-24. 
  16. ^ Thorndike, Lynn. "The Arithmetic of Jehan Adam, 1475 A.D.". The American Mathematical Monthly (Mathematical Association of America) 1926 (January): 24. JSTOR 2298533. 
  17. ^ a b Chuquet, Nicolas (written 1484, published 1880). "Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien" (in French). Bulletino di Bibliographia e di Storia delle Scienze matematische e fisische (Bologna: Aristide Marre) XIII (1880): 593–594. ISSN 1123-5209. http://www.miakinen.net/vrac/nombres#lettres_zillions. Retrieved 2011-07-17. 
  18. ^ Chuquet, Nicolas (written 1484, published 1880). "Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien" (in French). www.miakinen.net. http://www.miakinen.net/vrac/nombres#lettres_zillions. Retrieved 2008-03-01. 
  19. ^ Flegg, Graham (23–30 December 1976). "Tracing the origins of One, Two, Three..". New Scientist (Reed Business Information) 72 (1032): 747. ISSN 0262-4079. http://books.google.co.uk/books?id=obHSBCxiJ1YC&lpg=PA746&ots=CQ41sD8q8A&dq=%2Bissn%20%22nicolas%20chuquet%22%20triparty%20%22new%20scientist%22&pg=PA747#v=onepage&q&f=false. Retrieved 2011-07-17. 
  20. ^ a b Budaeus (1514) (in Latin). De Asse et partibus eius Libri quinqz (Paris (1532) ed.). pp. folio 95, v. 
  21. ^ "Resolution 6 of the 9th meeting of the CGPM (1948)". BIPM. http://www.bipm.org/en/CGPM/db/9/6/. Retrieved 2011-08-07. 
  22. ^ a b "Resolution 12 of the 11th meeting of the CGPM (1960)". BIPM. http://www.bipm.org/jsp/en/ViewCGPMResolution.jsp?CGPM=11&RES=12. Retrieved 2011-07-28. 
  23. ^ (PDF) The International System of Units (SI) (8 ed.). BIPM. May 2006. pp. 134 / 5.3.7 Stating values of dimensionless quantities, or quantities of dimension one. ISBN 92-822-2213-6. http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf. 
  24. ^ a b "Décret 61-501" (in French) (PDF). Journal Officiel (French Government): page 4587 note 3a, and erratum on page 7572. commissioned 1961-05-03 published 1961-05-20 modified 1961-08-11. http://www.ensmp.net/pdf/1961/decr-61-0501.pdf. Retrieved 2008-01-31. 
  25. ^ "RBA: Definition of billion". Reserve Bank of Australia. http://www.rba.gov.au/glossary/index.html?search=billion. Retrieved 2011-08-22. 
  26. ^ "Cambridge Dictionaries Online: billion". American Dictionary. Cambridge University Press. http://dictionaries.cambridge.org/define.asp?key=billion*1+0&dict=A. Retrieved 2011-08-21. 
  27. ^ "Cambridge Dictionaries Online: trillion". American Dictionary. Cambridge University Press. http://dictionaries.cambridge.org/define.asp?key=trillion*1+0&dict=A. Retrieved 2011-08-21. 
  28. ^ "BBC News: Zimbabwe rolls out Z$100tr note". BBC. 16 January 2009. http://news.bbc.co.uk/1/hi/7832601.stm. Retrieved 2011-07-24. 
  29. ^ "Eesti õigekeelsussõnaraamat ÕS 2006: miljard" (in Estonian). Institute of the Estonian Language (Eesti Keele Instituut). 2006. http://www.eki.ee/dict/qs/index.cgi?Q=miljard&F=M. Retrieved 2011-08-13. 
  30. ^ "Eesti õigekeelsussõnaraamat ÕS 2006: triljon" (in Estonian). Institute of the Estonian Language (Eesti Keele Instituut). 2006. http://www.eki.ee/dict/qs/index.cgi?Q=triljon&F=M. Retrieved 2011-08-13. 
  31. ^ Robson S. O. (Stuart O.), Singgih Wibisono, Yacinta Kurniasih. Javanese English dictionary Tuttle Publishing: 2002, ISBN 079460000X: 821 pages
  32. ^ "Farsi-English Dictionary: milliard". Farsi Dictionary. http://www.farsidictionary.net/milliard.htm. Retrieved 2011-08-20. 
  33. ^ "Farsi-English Dictionary: billion". Farsi Dictionary. http://www.farsidictionary.net/index.php?q=%D8%A8%DB%8C%D9%84%DB%8C%D9%88%D9%86+%09. Retrieved 2011-08-20. 
  34. ^ "Farsi-English Dictionary: trillion". Farsi Dictionary. http://www.farsidictionary.net/index.php?q=%D8%AA%D8%B1%DB%8C%D9%84%DB%8C%D9%88%D9%86. Retrieved 2011-08-20. 
  35. ^ "Britain to Reduce $4 billion from Defence" (in Burmese). Bi-Weekly Eleven (Yangon) 3 (30). 15 October 2010. 
  36. ^ Foundalis, Harry. "Greek Numbers and Numerals (Ancient and Modern)". http://www.foundalis.com/lan/grknum.htm. Retrieved 2007-05-20. 
  37. ^ "Larousse: milliard" (in French). Éditions Larousse. http://www.larousse.com/en/dictionaries/french/milliard. Retrieved 2011-08-19. 
  38. ^ "Larousse: billion" (in French). Éditions Larousse. http://www.larousse.com/en/dictionaries/french/billion. Retrieved 2011-08-19. 
  39. ^ "Wortschatz-Lexikon: Milliarde" (in German). Universität Leipzig: Wortschatz-Lexikon. http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Milliarde. Retrieved 2011-08-19. 
  40. ^ "Wortschatz-Lexikon: Billion" (in German). Universität Leipzig: Wortschatz-Lexikon. http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Billion. Retrieved 2011-08-19. 
  41. ^ "Larousse: bilione". Éditions Larousse. http://www.larousse.com/en/dictionaries/italian-english/bilione/5726. Retrieved 2011-08-21. 
  42. ^ "De Geïntegreerde Taal-Bank: miljard" (in Dutch). Instituut voor Nederlandse Lexicologie. http://www.wnt.inl.nl/iWDB/search?actie=article&wdb=WFT&id=63043&lemmodern=miljard. Retrieved 2011-08-19. 
  43. ^ "De Geïntegreerde Taal-Bank: biljoen" (in Dutch). Instituut voor Nederlandse Lexicologie. http://gtb.inl.nl/iWDB/search?actie=article&wdb=WFT&id=8253&lemmodern=biljoen. Retrieved 2011-08-19. 
  44. ^ "Diccionario Panhispánico de Dudas: millardo" (in Spanish). Real Academia Española. http://buscon.rae.es/dpdI/SrvltConsulta?lema=millardo. Retrieved 2011-08-19. 
  45. ^ "Diccionario Panhispánico de Dudas: billon" (in Spanish). Real Academia Española. http://buscon.rae.es/dpdI/SrvltConsulta?lema=billon. Retrieved 2011-07-24. 
  46. ^ "Switzerland: Words and Phrases". TRAMsoft Gmbh. 2009-08-29. http://www.about.ch/culture/languages/words_n_phrases.html#numbers. Retrieved 2011-08-15. 
  47. ^ Wennergren, Bertilo (8 March 2008). "Plena Manlibro de Esperanta Gramatiko" (in Esperanto). http://bertilow.com/pmeg/. Retrieved 2010-09-15. 
  48. ^ "Canadian government standards website". Canadian Government. 2010. http://btb.termiumplus.gc.ca/tpv2alpha/alpha-eng.html?lang=eng&i=&index=frt&__index=frt&srchtxt=billion&comencsrch.x=12&comencsrch.y=10. Retrieved 2010-09-15. 
  49. ^ Gupta, S.V. (2010). Units of measurement: past, present and future : international system of units. Springer. pp. 12 (Section 1.2.8 Numeration). http://books.google.co.uk/books?id=pHiKycrLmEQC&lpg=PA12&dq=%2Bcrore%20%2Blakh%20%2Barab&pg=PA12#v=onepage&q=+crore%20+lakh%20+arab&f=false. Retrieved 2011-08-22. 
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