Long and short scales

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The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten:

Long scale: Every new term greater than million is one million times larger than the previous term. Thus, billion means a million millions (1012), trillion means a million billions (1018), and so on.[1][2]
Short scale: Every new term greater than million is one thousand times larger than the previous term. Thus, 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.

Many countries, including most in continental Europe and Latin America, use the long scale whereas most English-speaking countries and Arabic-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 both the long and short scales.[1][2]

For most of the 19th century and into the early 20th century, the United Kingdom largely used the long scale,[3][4] 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. After several decades of increasing British usage of the short scale, in 1974, the government of the UK fully adopted it, which is reflected in its mass media and official usage.[5][6][7][8][9][10] With very few exceptions,[11] the British usage and American usage are now identical.

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

Comparison[edit]

At and above a thousand million (≥ 109), 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 
 Metric prefix   Value in
numerals 
 Short Scale   Long Scale 
Prefix Symbol Name Logic Name Logic
 100       one  one
 101  deca  D or da  10   ten  ten
 102  hecto  Lower 100   hundred  hundred
 103  kilo  Lower k  1,000   thousand  thousand
 104      10,000   ten thousand  ten thousand
 105      100,000   hundred thousand  hundred thousand
 106  mega  1,000,000   million 1,000×1,0001  million 1,000,0001
 109  giga  1,000,000,000   billion 1,000×1,0002  thousand million or milliard
 1012  tera  1,000,000,000,000   trillion 1,000×1,0003  billion 1,000,0002
 1015  peta  1,000,000,000,000,000   quadrillion 1,000×1,0004  thousand billion or billiard
 1018  exa  1,000,000,000,000,000,000   quintillion 1,000×1,0005  trillion 1,000,0003
 1021  zetta  1,000,000,000,000,000,000,000   sextillion 1,000×1,0006  thousand trillion or trilliard
 1024  yotta  1,000,000,000,000,000,000,000,000   septillion 1,000×1,0007  quadrillion 1,000,0004
  etc.         To go from one named order of magnitude to the next:
multiply by 1,000
To go from one named order of magnitude to the next:
multiply by 1,000,000

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 
 Metric prefix  Logic   Value in
Scientific notation 
 Metric prefix  Logic 
 Prefix  Symbol  Prefix  Symbol
million 106 mega M  1,000×1,0001  106 mega M  1,000,0001 
billion 109 giga G  1,000×1,0002  1012 tera T  1,000,0002 
trillion 1012 tera T  1,000×1,0003  1018 exa E  1,000,0003 
quadrillion 1015 peta P  1,000×1,0004  1024 yotta Y  1,000,0004 
etc. To go from one named order of magnitude to the next:
multiply by 1,000
To go 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". 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 1728.[12]

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, 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 a thousand long scale billions (i.e. 1015), and the word trilliard (or similar) for a thousand long scale trillions (i.e. 1021), etc.[13][14][15][16][17]

History[edit]

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; Polish bilion, Spanish billón; Slovenian bilijon 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]

  • In long scale countries, milliard was redefined down to its current value of 109, leaving billion at its original 1012 value and so on for the larger numbers.[12] Some of these countries, but not all, introduced new words billiard, trilliard, etc. as intermediate terms.[13][14][15][16][17]
  • In some short scale countries, milliard was redefined down to 109 and billion dropped altogether, with trillion redefined down to 1012 and so on for the larger numbers.[12]
  • 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
1200s The word million was not used in any language before the 13th century. Maximus Planudes (c. 1260–1305) was among the first recorded users.[12]
Late 1300s
Piers Plowman, a 17th century copy of the original 14th century allegorical narrative poem by William Langland
The word million entered the English language. One of the earliest references is William Langland's Piers Plowman (written c. 1360-1387 in Middle English),[12] with:

Coueyte not his goodes
For millions of moneye

Translation:

Covet not his goods
for millions of money

1475 French mathematician Jehan Adam, writing in Middle French, recorded the words bymillion and trimillion as meaning 1012 and 1018 respectively in a manuscript Traicté en arismetique pour la practique par gectouers, now held in the Bibliothèque Sainte-Geneviève in Paris.[18][19][20]

... item noctes que le premier greton dembas vault ung, le second vault ... dix, le trois vault ... [sic] 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 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,[21][22][23] 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.[21] Chuquet's original article was rediscovered in the 1870s and then published for the first time in 1880.

... 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 quinque.[24]

.. hoc est denas myriadum myriadas, quod vno verbo nostrates abaci studiosi Milliartum appellat, 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), attributing this meaning to the earlier usage by Guillaume Budé[24]
1600s 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. 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 the original long scale billion from Adam, Chuquet and Pelletier.
1676 The first published use of milliard as 109 occurred in the Netherlands.[12][25]

.. milliart/ofte duysent millioenen..

Translation:

..milliart / also thousand millions..

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.
1923
1000 Mark German banknote, over-stamped in red with "Eine Milliarde Mark" (109 mark)
1000 Mark German banknote, over-stamped in red with "Eine Milliarde Mark" (109 mark)
Using German banknotes as wallpaper following the 1923 hyperinflation
Using German banknotes as wallpaper following the 1923 hyperinflation

German hyperinflation in the 1920s Weimar 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:

1 Rentenmark = 1 billion (long scale) Papiermark = 1012 Papiermark = 1 trillion (short scale) Papiermark

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.

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.

1946
1020 Hungarian pengő banknote issued in 1946
1020 Hungarian pengő banknote issued in 1946
Sweeping up pengő banknotes in the street, following the 1946 introduction of the forint
Sweeping up pengő banknotes in the street, following the 1946 introduction of the forint

Hyperinflation in Hungary in 1946 led to the introduction of the 1020 pengő banknote.

100 million b-pengő (long scale) = 100 trillion (long scale) pengő = 1020 pengő = 100 quintillion (short scale) pengő.

On 1 August 1946, the forint was introduced at a rate of:

1 forint = 400 quadrilliard (long scale) pengő = 4 x 1029 pengő = 400 octillion (short scale) pengő.

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.[26] 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.[26][27]
1960 The 11th General Conference on Weights and Measures adopted the International System of Units (SI), with its own set of numeric prefixes.[28] 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 ambiguous terms such as billion, trillion, etc.[29]
1961 The French Government confirmed their official usage of the long scale in the Journal officiel (the official French Government gazette).[30]
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.[6] Hansard,[5] 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.

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 (the Republic of 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 échelle longue (long scale) and échelle courte (short scale) to refer to the two numbering systems.[1][2]
1993
5 x 1011 Yugoslav dinar banknotes from 1993

Hyperinflation in Yugoslavia led to the introduction of 5 x 1011 dinar banknotes.

500 thousand million (long scale) dinars = 5 x 1011 dinar banknotes = 500 billion (short scale) dinars.

The later introduction of the new dinar came at an exchange rate of:

1 novi dinar = 1 × 1027 dinars = ~1.3 × 1027 pre 1990 dinars.

1994 The Italian Government confirmed their official usage of the long scale.[17]
2009
1014 Zimbabwean dollars banknote from 2009

Hyperinflation in Zimbabwe led to banknotes of 1014 Zimbabwean dollars, marked "One Hundred Trillion Dollars" (short scale), being issued in 2009, shortly ahead of the currency being abandoned.[31][32][33] As of 2013, a new currency has yet to be announced – so foreign currencies are being used instead.

100 trillion (short scale) Zimbabwean dollars = 1014 Zimbabwean dollars = 100 billion (long scale) Zimbabwean dollars = 1027 pre-2006 Zimbabwean dollars.

2013 As of 24 October 2013, the combined total public debt of the United States stood at $17.078 trillion.[34][35]

17 trillion (short scale) US Dollars = 1.7 x 1013 US Dollars = 17 billion (long scale) US Dollars

Current usage[edit]

Short and long scale usage throughout the world
  Pink: Short scale
  Blue: Long scale
  Purple: Both scales
  Yellow: Other naming system
  Light gray: No data

Short scale users[edit]

English-speaking[edit]

106 = one million, 109 = one billion, 1012 = one trillion, etc.

Most English-language countries and regions use the short scale with 109 = billion. For example:[shortscale note 1]

 American Samoa
 Anguilla
 Antigua and Barbuda
 Australia [shortscale note 2] [36]
 Bahamas
 Barbados
 Belize   (English-speaking)
 Bermuda
 Botswana   (English-speaking)
 British Virgin Islands
 Cameroon   (English-speaking)
 Cayman Islands
 Cook Islands
 Dominica
 Eritrea
 Ethiopia
 Falkland Islands
 Fiji
 Gambia
 Ghana   (English-speaking)
 Gibraltar
 Grenada
 Guam
 Guernsey
 Guyana   (English-speaking)
 Hong Kong   (English-speaking)
 Ireland   (English-speaking, Irish: billiún, trilliún)
 Isle of Man
 Jamaica
 Jersey
 Kenya   (English-speaking)
 Kiribati
 Lesotho
 Liberia
 Malawi   (English-speaking)
 Malaysia   (English-speaking; Malay: bilion billion, trilion trillion)
 Malta   (English-speaking; Maltese: biljun, triljun)
 Marshall Islands
 Federated States of Micronesia
 Montserrat
 Nauru
 New Zealand   (English-speaking)
 Nigeria   (English-speaking)
 Niue
 Norfolk Island
 Northern Mariana Islands
 Palau
 Papua New Guinea   (English-speaking)
 Philippines   (English-speaking) [shortscale note 3]
 Pitcairn Islands
 Rwanda
 Saint Helena, Ascension and Tristan da Cunha
 Saint Kitts and Nevis
 Saint Lucia
 Saint Vincent and the Grenadines
 Samoa
 Sierra Leone
 Singapore   (English-speaking)
 Solomon Islands
 South Georgia and the South Sandwich Islands
 South Sudan   (English-speaking)
 Swaziland
 Tanzania   (English-speaking)
 Tokelau
 Tonga
 Trinidad and Tobago
 Turks and Caicos Islands
 Tuvalu
 Uganda   (English-speaking)
 United Kingdom   (see Wales below) [shortscale note 4] [5][6][7][8][9]
 United States [shortscale note 5] [37][38]
 United States Virgin Islands
 Zambia   (English-speaking)
 Zimbabwe   (English-speaking) [31][32][33]

Arabic-speaking[edit]

106 = میليون  million, 109 = میليار  milyar, 1012 = تريليون  trilyon, etc.

Most Arabic-language countries and regions use the short scale with 109 = میليار   milyar. For example:[shortscale note 6] [39][40]

 Algeria
 Bahrain
 Chad
 Comoros
 Djibouti
 Egypt
 Eritrea
 Iraq
 Jordan
 Kuwait
 Lebanon
 Libya
 Mauritania
 Morocco
 Oman
 Palestine
 Qatar
 Saudi Arabia
 Somalia
 Sudan
 Syria
 Tunisia
 United Arab Emirates
 Western Sahara
 Yemen

Other short scale[edit]

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 like English use a word similar to billion to mean 109, most like Arabic 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:

 Afghanistan   (Dari: میلیارد milyard or بیلیون billion, تریلیون trillion, Pashto: میلیارد milyard, بیلیون billion, تریلیون trillion)
 Albania   (miliard, trilion) [41]
 Armenia   (միլիարդ miliard, տրիլիոն trilion)
 Azerbaijan   (milyard, trilyon)
 Belarus   (мільярд milyard, трыльён trilyon)
 Brazil   (Brazilian Portuguese: bilhão, trilhão)
 Brunei   (Brunei Malay: ; Malay: bilion, trilion)
 Bulgaria   (милиард miliard, трилион trilion)
 Burma   (Burmese: ဘီလျံ, IPA: [bìljàɴ]; ထရီလျံ, [tʰəɹìljàɴ]) [42]
 Cyprus   (Greek: δισεκατομμύριο disekatommyrio, τρισεκατομμύριο trisekatommyrio, Turkish: milyar, trilyon)
 Estonia   (miljard, triljon) [43][44]
 Georgia   (მილიარდი miliardi, ტრილიონი trilioni)
 Indonesia   (miliar, triliun)  [shortscale note 7] [45]
 Israel   (Hebrew: מיליארד millyard, טריליון trillyon)
 Kazakhstan   (Kazakh: миллиард milliard, триллион trillion)
 Kyrgyzstan   (Kyrgyz: миллиард milliard, триллион trillion)
 Latvia   (miljards, triljons)
 Lithuania   (milijardas, trilijonas)
 Moldova   (Romanian / Moldovan: miliard, trilion; Russian: миллиард milliard, триллион trillion)
 Romania   (miliard, trilion)
 Russia   (миллиард milliard, триллион trillion)
 Tajikistan   (Tajik: миллиард milliard, триллион trillion)
 Turkey   (milyar, trilyon)
 Turkmenistan   (Turkmen: ; Russian: миллиард milliard, триллион trillion)
 Ukraine   (мільярд mil'yard, трильйон tryl'yon)
 Uzbekistan   (Uzbek: ; Russian: миллиард milliard, триллион trillion)
 Wales   (biliwn, triliwn)

With other terminology[edit]

 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.)[46]

Long scale users[edit]

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 Albania, Bulgaria, Greece, Romania, 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.

Spanish-speaking[edit]

106 = millón, 109 = mil millones or millardo, 1012 = billón, etc.

Most Spanish-language countries and regions use the long scale with 109 = mil millones, for example:[longscale note 1] [47][48]

 Argentina  
 Bolivia  
 Chile  
 Colombia  
 Costa Rica  
 Cuba  
 Dominican Republic  
 Ecuador  
 El Salvador  
 Equatorial Guinea  
 Guatemala   (millardo)
 Honduras   (millardo)
 Mexico   (mil millones or millardo)
 Nicaragua   (mil millones or millardo)
 Panama   (mil millones or millardo)
 Paraguay  
 Peru  
 Spain   (millardo or typ. mil millones)
 Uruguay  
 Venezuela  

French-speaking[edit]

106 = million, 109 = milliard, 1012 = billion, etc.

Most French-language countries and regions use the long scale, for example:[longscale note 2] [49][50]

 Benin
 Burkina Faso
 Central African Republic
 Democratic Republic of the Congo
 Republic of the Congo
 France
 French Polynesia
 French Southern and Antarctic Lands
 Gabon
 Guadeloupe
 Guinea
 Haiti
 Ivory Coast   (Côte d'Ivoire)
 Mali
 Monaco
 New Caledonia
 Niger
 Saint Barthélemy
 Senegal
 Togo
 Wallis and Futuna

Portuguese-speaking[edit]

106 = milhão, 109 = mil milhões or milhar de milhões, 1012 = bilião

With the notable exception of Brazil, a short scale country, most Portuguese-language countries and regions use the long scale, for example:

 Angola
 Cape Verde
 East Timor
 Guinea-Bissau
 Macau
 Mozambique
 Portugal
 São Tomé and Príncipe

Dutch-speaking[edit]

106 = miljoen, 109 = miljard, 1012 =biljoen

Most Dutch-language countries and regions use the long scale, for example:[51][52]

 Aruba
 Curaçao
 Netherlands
 Sint Maarten
 Suriname

Other long scale[edit]

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

Some examples of long scale use, and the words used for 109 and 1012, are:

 Andorra   (Catalan: miliard or typ. mil milions, bilió)
 Austria   (Austrian German: Milliarde, Billion)
 Belgium   (Belgian French: milliard, billion; Flemish: miljard, biljoen; German: Milliarde, Billion)
 Bosnia and Herzegovina   (Bosnian: milijarda, bilion; Croatian: milijarda, bilijun, Serbian: милијарда milijarda, Билион bilion)
 Croatia   (milijarda, bilijun)
 Czech Republic   (miliarda, bilion)
 Denmark   (milliard, billion)
 Faroe Islands   (Danish: milliard, billion)
 Finland   (Finnish: miljardi, biljoona; Swedish: miljard, biljon)
 Germany   (Milliarde, Billion) [13][14]
 Hungary   (milliárd, billió or ezer milliárd)
 Iceland   (milljarður, billjón)
 Iran   (Persian: میلیارد milyard, بیلیون billion, تریلیون trillion)[citation needed]
 Italy   (miliardo, bilione) [longscale note 3] [17][53]
 Liechtenstein   (German: Milliarde, Billion)
 Luxembourg   (French: milliard, billion; German: Milliarde, Billion; Luxembourgish: milliard, billioun)
 Macedonia   (милијарда milijarda, Билион bilion)
 Madagascar   (French: milliard, billion; Malagasy: )
 Montenegro   (Montenegrin: milijarda, bilion)
 Norway   (Bokmål: milliard, billion; Nynorsk: milliard, billion)
 Poland   (miliard, bilion)
 San Marino   (Italian: miliardo, bilione)
 Serbia   (милијарда milijarda, Билион bilion)
 Slovakia   (miliarda, bilión)
 Slovenia   (milijarda, bilijon)
 Sweden   (miljard, biljon)
  Switzerland   (French: milliard, billion; German: Milliarde, Billion; Italian: miliardo, bilione, Romansh: milliarda, billiun [54])
  Vatican City   (Italian: miliardo, bilione)
Other long scale languages
Flag of Esperanto.svg Esperanto language   (miliardo, duiliono) [longscale note 4] [55]

Using both[edit]

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   (109 = billion, 1012 = trillion) Canadian French   (109 = milliard, 1012 = billion).
 Mauritius
 Seychelles
 Vanuatu
English   (109 = billion, 1012 = trillion) French   (109 = milliard, 1012 = billion)
 Namibia
 South Africa [shortscale longscale note 2]
South African English   (109 = billion, 1012 = trillion) Afrikaans   (109 = miljard, 1012 = biljoen)
 Puerto Rico Economic & technical (109 = billón, 1012 = trillón) Latin American export publications (109 = millardo or mil millones, 1012 = billón)

Using neither[edit]

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

 Country   Main article   Notes 
 Bangladesh,    India,      Nepal,    Pakistan Indian Numbering System  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 of China – PRC)
  •  Taiwan (Republic of China – ROC)
Chinese numerals Traditional myriad system for the larger numbers; special words and symbols up to 1088
 Greenland Inuit numerals Traditional system
 Japan Japanese numerals Traditional myriad system for the larger numbers; special words and symbols up to 1088
Korean numerals Traditional myriad system for the larger numbers; special words and symbols up to 1088
 Laos Lao numerals Traditional system
 Maldives,    Sri Lanka Traditional systems
 Mongolia Mongolian numerals Traditional myriad system for the larger numbers; special words up to 1067
 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 most continents, with usage dependent on the language used. Examples include:

Continent Short scale usage Long scale usage
Africa Arabic (Egypt, Libya, Tunisia), English (South Sudan), South African English Afrikaans, French (Benin, Central African Republic, Gabon, Guinea), Portuguese (Mozambique)
North America American English, Canadian English U.S. Spanish, Canadian French, Mexican Spanish
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)

Notes on current usage[edit]

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 [11] and the official status of the short scale in anglophone countries other than the UK and US is sometimes obscure.[citation needed]
  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.[36] 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.[5][6][7][8]
    Before the widespread use of billion for 109, UK usage generally referred to thousand million rather than milliard.[9] 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.[37][38]
  6. ^ Arabic language countries: Most Arabic-language countries use: 106 = میليون  million, 109 = میليار  milyar, 1012 = تريليون  trilyon, etc. [39][40]
  7. ^ 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.[45]
Long scale
  1. ^ Spanish language countries: Spanish-speaking countries sometimes use millardo (milliard)[47] 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, but this is considered unacceptable.[48]
  2. ^ 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.[30][49][50]
  3. ^ 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.[17]
    In Italian, the word bilione officially means 1012, trilione means 1018, etc.. Colloquially, bilione [53] 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.[17]
  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.[55] 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.[56]
  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 [57] and has been disparaged by the "Taalkommissie" (The Afrikaans Language Commission of the South African Academy of Science and Art)[58] and has thus, to most appearances, been abandoned.
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.[59]

Alternative approaches[edit]

Unambiguous ways of identifying large numbers include:

  • 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, say, 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". This becomes rather unwieldy for numbers above 1012.
  • Combination of numbers of more than 3 digits with the unambiguous word million, for example 13,600 million[60]
  • 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.
  • SI prefixes in combination with SI units, for example, giga for 109 and tera for 1012 can give Gigawatt (=109 W) and Terawatt (=1012 W), respectively. The International System of Units (SI) is independent of whichever scale is being used.[28] Use with non-SI units (e.g. "giga-dollars", "giga-miles") is uncommon.


See also[edit]

References[edit]

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  2. ^ a b c d e Guitel, Geneviève (1975). Histoire comparée des numérations écrites (in French). 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 978-2-08-211104-1. 
  3. ^ a b c d Fowler, H. W. (1926). A Dictionary of Modern English Usage. Great Britain: Oxford University Press. pp. 52–53. ISBN 978-0-19-860506-5. 
  4. ^ "British-English usage of 'Billion vs Thousand million vs Milliard'". Google Books ngram viewer. Google Inc. Retrieved 26 April 2014. 
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External links[edit]