Long and short scales

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The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.[1][2]

Some languages, particularly in East Asia and South Asia, have large number naming systems that are different from both the long and short scales, such as Chinese, Japanese or Korean numerals, and the Indian numbering system.[1][2]

Much of the remainder of the world adopted either the short scale or the long scale for everyday counting powers of ten. Countries with usage of the long scale include most countries in continental Europe and most that are French-speaking, German-speaking, Spanish-speaking[3] and Portuguese-speaking countries (except Brazil). Usage of the short scale is found in most English-speaking countries and most 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, in the short scale, "one billion" means one thousand millions (1,000,000,000), whereas in the long scale, it means one million millions (1,000,000,000,000). For interleaved values, the long scale system employs additional terms, typically substituting the word ending -ion for -iard.

To avoid confusion resulting from the coexistence of the two terms, the International System of Units (SI) recommends using the metric prefix to indicate orders of magnitude, associated with physical quantities.

Scales

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. For certain multipliers, including those for all numbers smaller than 109, both systems use the same names. 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 (short scale) 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 (long scale) 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 (long scale) 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:

 Value in positional notation   Value in
scientific notation  		 Metric prefix   Short scale   Long scale 
Prefix Symbol Name Logic Name Alternative name Logic
1 100     one one
10 101 deca da ten ten
100 102 hecto h hundred hundred
1,000 103 kilo k thousand thousand
1,000,000 106 mega M million 1,000 × 1,0001 million 1,000,0001
1,000,000,000 109 giga G billion 1,000 × 1,0002 thousand million milliard 1,000 × 1,000,0001
1,000,000,000,000 1012 tera T trillion 1,000 × 1,0003 billion 1,000,0002
1,000,000,000,000,000 1015 peta P quadrillion 1,000 × 1,0004 thousand billion billiard 1,000 × 1,000,0002
1,000,000,000,000,000,000 1018 exa E quintillion 1,000 × 1,0005 trillion 1,000,0003
1,000,000,000,000,000,000,000 1021 zetta Z sextillion 1,000 × 1,0006 thousand trillion trilliard 1,000 × 1,000,0003
1,000,000,000,000,000,000,000,000 1024 yotta Y septillion 1,000 × 1,0007 quadrillion 1,000,0004
1,000,000,000,000,000,000,000,000,000 1027 ronna R octillion 1,000 × 1,0008 thousand quadrillion quadrilliard 1,000 × 1,000,0004
1,000,000,000,000,000,000,000,000,000,000 1030 quetta Q nonillion 1,000 × 1,0009 quintillion 1,000,0005

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
quintillion 1018 exa E 1,000 × 1,0005 1030 quetta Q 1,000,0005
etc. For the next order of magnitude, multiply by 1,000 For the next order of magnitude, multiply by 1,000,000

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 (Template:Lang-fr) and long scale (Template:Lang-fr) 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 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 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 (Template:Circa–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.
Late 14th century
File:Piers Plowman.jpg
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The word million entered the English language. One of the earliest references is William Langland's Piers Plowman (written Template:Circa–1387 in Middle English),[5] with

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Translation: Template:Blockquote

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.[19][20][21]

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Translation: Template:Blockquote

1484
File:Chuquet.gif
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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.

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Translation: Template:Blockquote

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 ...

1516
File:Guillaume Budé, by Jean Clouet.jpg
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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]

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Translation: Template:Blockquote

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]

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Translation: Template:Blockquote

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.
1926
File:FowlersModernEnglishUsageFrontispiece.jpg
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H. W. Fowler's A Dictionary of Modern English Usage[11] noted

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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]
1960 The 11th General Conference on Weights and Measures adopted the International System of Units (SI), with its own set of numeric prefixes.[34] 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.[35] The National Institute of Standards and Technology within the US also considers that it is best that they be avoided entirely.[36]
1961 The French Government confirmed their official usage of the long scale in the Journal officiel (the official French Government gazette).[37]
1974
File:Lord Harold Wilson Allan Warren.jpg
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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.[13] Hansard,[12] for 20 December 1974, reported it

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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 (Template:Lang-fr) and short scale (Template:Lang-fr) to refer to the two numbering systems.[1][2]
1994 The Italian Government confirmed their official usage of the long scale.[10]

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.

Timeline
 Date  Event
1923 Template:Multiple image

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

1946 Template:Multiple image

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 × 1029 pengő = 400 octillion (short scale) pengő.

1993
File:500000000000 dinars.jpg
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Hyperinflation in Yugoslavia led to the introduction of 5 × 1011 dinar banknotes.

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

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

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

2009
File:Zimbabwe $100 trillion 2009 Obverse.jpg
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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[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.

100 trillion (short scale) Zimbabwean dollars = 1014 Zimbabwean dollars = 100 billion (long scale) Zimbabwean dollars = 1027 pre-2006 Zimbabwean dollars = 1 quadrilliard (long scale) pre-2006 Zimbabwean dollars.

2022 Template:As of, the combined total public debt of the United States stood at $31.299 trillion.[41]

31 trillion (short scale) US Dollars = 3.1 × 1013 US Dollars = 31 billion (long scale) US Dollars

Current usage

File:EScalas corta y larga.svg
Short and long scale usage throughout the worldTemplate:Refbegin Template:Legend Template:Legend Template:Legend Template:Legend Template:Legend Template:Legend Template:Refend

Short scale users

English-speaking

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

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Arabic-speaking

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Most Arabic-language countries and regions use the short scale with 109 being Template:Lang Template:Lang, except for a few countries like Saudi Arabia and the UAE which use the word بليون Template:Lang for 109. For example:[shortscale note 6][46][47]

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Other short scale

Template:Block indent

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

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Long scale users

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,[53] 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.

Dutch-speaking

Template:Block indent Most Dutch-language countries and regions use the long scale with 109 = Template:Lang, for example:[55][56]

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French-speaking

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Most French-language countries and regions use the long scale with 109 = Template:Lang, for example:[longscale note 1][57][58]

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German-speaking

Template:Block indent German-language countries and regions use the long scale with 109 = Template:Lang, for example:

Portuguese-speaking

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With the notable exception of Brazil, a short scale country, most Portuguese-language countries and regions use the long scale with 109 = Template:Lang or Template:Lang, for example: Template:Div col

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Spanish-speaking

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Most Spanish-language countries and regions use the long scale, for example:[longscale note 2][60][61]

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Other long scale

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

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Using both

Some countries use either the short or long scales, depending on the internal language being used or the context.

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Country or territory Short scale usage Long scale usage
Template:CAN[shortscale longscale note 1] Canadian English (109 = billion, 1012 = trillion) Canadian French (109 = Template:Lang, 1012 = Template:Lang[69] or Template:Lang).
Template:Unbulleted list English (109 = billion, 1012 = trillion) French (109 = Template:Lang, 1012 = Template:Lang)
Template:Unbulleted list South African English (109 = billion, 1012 = trillion) Afrikaans (109 = Template:Lang, 1012 = Template:Lang)
Template:PRI Economic and technical (109 = Template:Lang, 1012 = Template:Lang) Latin American export publications (109 = Template:Lang or Template:Lang, 1012 = Template:Lang)

Using neither

The following countries use naming systems for large numbers that are not etymologically related to the short and long scales:

Country Number system Naming of large numbers
Template:BGD, Template:IND, Template:MDV, Template:NPL, Template:PAK Indian numbering system Traditional system for everyday use, but short or long scale may also be in use [other scale note 1]
Template:BTN Dzongkha numerals Traditional system
Template:KHM Khmer numerals Traditional system
Template:Unbulleted list East Asian numbering system: Template:Unbulleted list Traditional myriad system for the larger numbers; special words and symbols up to 1068
Template:GRE Calque of the short scale Names of the short scale have not been loaned but calqued into Greek, based on the native Greek word for million, Template:Lang Template:Lang ("hundred-myriad", i.e. 100 × 10,000):
Template:LAO Lao numerals Traditional system
Template:MNG Mongolian numerals Traditional myriad system for the larger numbers; special words up to 1067
Template:LKA Template:Unbulleted list Traditional systems
Template:THA Thai numerals Traditional system based on millions
Template:VNM Vietnamese numerals Traditional system(s) based on thousands

By continent

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 (Angola, Mozambique)
North America American English, Canadian English Canadian French, Mexican Spanish, U.S. Spanish
South America Brazilian Portuguese, English (Guyana) American Spanish, Dutch (Suriname), French (French Guiana)
Antarctica Australian English, British English, New Zealand English, Russian American Spanish (Argentina, Chile), French (France), Norwegian (Norway)
Asia Burmese (Myanmar), Hebrew (Israel), Indonesian, Kazakh, Kyrgyz, Malaysian English, Philippine English, Uzbek Persian (Iran), Portuguese (East Timor, Macau)
Europe British English, Estonian, Greek, Latvian, Lithuanian, Russian, Turkish, Ukrainian, Welsh Danish, Dutch, Finnish, French, German, Icelandic, Italian, Norwegian, Polish, Portuguese, Romanian, Spanish, Swedish and most other languages of continental Europe
Oceania Australian English, New Zealand English French (French Polynesia, New Caledonia)

Notes on current usage

Short scale

  1. ↑ 1.0 1.1 1.2 1.3 1.4 Histoire comparée des numérations écrites{{#if:Guitel|, Guitel}. Flammarion(1975). ISBN 978-2-08-211104-1
  2. ↑ 2.0 2.1 2.2 2.3 2.4 Histoire comparée des numérations écrites{{#if:Guitel|, Guitel}. Flammarion(1975). ISBN 978-2-08-211104-1
  3. ↑ Authoritative Real Academia Española (RAE) dictionary: billón. Retrieved 12 March 2015.
  4. ↑ 4.0 4.1 British-English usage of 'Billion vs Thousand million vs Milliard'{{#if:|, {{{last}}}}. Google Inc
  5. ↑ 5.00 5.01 5.02 5.03 5.04 5.05 5.06 5.07 5.08 5.09 5.10 History of Mathematics{{#if:Smith|, Smith}. Courier Dover Publications(1953). ISBN 978-0-486-20430-7
  6. ↑ 6.0 6.1 6.2 Wortschatz-Lexikon: Milliarde. Universität Leipzig: Wortschatz-Lexikon. Retrieved 19 August 2011.
  7. ↑ 7.0 7.1 7.2 Wortschatz-Lexikon: Billion. Universität Leipzig: Wortschatz-Lexikon. Retrieved 19 August 2011.
  8. ↑ 8.0 8.1 Wortschatz-Lexikon: Billiarde. Universität Leipzig: Wortschatz-Lexikon. Retrieved 28 July 2011.
  9. ↑ 9.0 9.1 Wortschatz-Lexikon: Trilliarde. Universität Leipzig: Wortschatz-Lexikon. Retrieved 28 July 2011.
  10. ↑ 10.0 10.1 10.2 10.3 10.4 10.5 Direttiva CEE / CEEA / CE 1994 n. 55, p.12. Italian Government(21 November 1994). Retrieved 24 July 2011.
  11. ↑ 11.0 11.1 11.2 11.3 A Dictionary of Modern English Usage{{#if:Fowler|, Fowler}. Oxford University Press(1926). ISBN 978-0-19-860506-5
  12. ↑ 12.0 12.1 12.2 12.3 "BILLION" (DEFINITION) — HC Deb 20 December 1974 vol 883 cc711W–712W. Hansard(20 December 1972). Retrieved 2 April 2009.
  13. ↑ 13.0 13.1 13.2 13.3 Britain's £1 trillion debt mountain – How many zeros is that?. The Scotsman(30 July 2004). Retrieved 31 January 2008.
  14. ↑ Who wants to be a trillionaire?. BBC News(7 May 2007). Retrieved 11 May 2010.
  15. ↑ 15.0 15.1 15.2 Template:Cite mailing list
  16. ↑ 16.0 16.1 16.2 Oxford Dictionaries: How many is a billion?. Oxford University Press. Retrieved 7 May 2018.
  17. ↑ Oxford Dictionaries: Billion. Oxford University Press. Retrieved 24 July 2011.
  18. ↑ 18.0 18.1 The Little Green Handbook{{#if:Nielsen|, Nielsen}. Macmillan Publishers(2006). ISBN 978-0-312-42581-4
  19. ↑ Traicté en arismetique pour la practique par gectouers... (MS 3143)({Template:Year).
  20. ↑ HOMMES DE SCIENCE, LIVRES DE SAVANTS A LA BIBLIOTHÈQUE SAINTE-GENEVIÈVE, Livres de savants II. Bibliothèque Sainte-Geneviève. Retrieved 25 October 2014.
  21. ↑ The Arithmetic of Jehan Adam, 1475 A.D. The American Mathematical Monthly({Template:Year).
  22. ↑ 22.0 22.1 Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien. Bulletino di Bibliographia e di Storia delle Scienze Matematische e Fisische({Template:Date).
  23. ↑ Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien, Chuquet, Nicolas. miakinen.net(1880). Retrieved 1 March 2008.
  24. ↑ Tracing the origins of One, Two, Three.. New Scientist({Template:Date).
  25. ↑ 25.0 25.1 De Asse et partibus eius Libri quinque{{#if:Budaeus|, Budaeus}(1516)
  26. ↑ Dictionnaire de la langue française{{#if:Littré|, Littré}. L. Hachette(1873–1874)
  27. ↑ Arithmetic({Template:Year).
  28. ↑ Dictionnaire de l'académie françoise{{#if:|, {{{last}}}}. Institut de France(1762)
  29. ↑ Dictionnaire de l'Académie française{{#if:|, {{{last}}}}(1835)
  30. ↑ Dictionnaire de l'Académie française{{#if:|, {{{last}}}}. Institut de France(1877)
  31. ↑ Dictionnaire de l'Académie française{{#if:|, {{{last}}}}. Institut de France(1932–1935)
  32. ↑ 32.0 32.1 Resolution 6 of the 9th meeting of the CGPM (1948). BIPM. Retrieved 7 August 2011.
  33. ↑ Resolution 6 of the 10th meeting of the CGPM (1954). BIPM. Retrieved 23 June 2012.
  34. ↑ Resolution 12 of the 11th meeting of the CGPM (1960). BIPM. Retrieved 28 July 2011.
  35. ↑ The International System of Units (SI){{#if:|, {{{last}}}}. BIPM(May 2006). ISBN 92-822-2213-6
  36. ↑ Guide for the Use of the International System of Units (SI), NIST SP – 811. NIST({Template:Date).
  37. ↑ 37.0 37.1 Décret 61-501. Journal Officiel({Template:Date).
  38. ↑ 38.0 38.1 BBC News: Zimbabweans play the zero game. BBC(23 July 2008). Retrieved 13 July 2012.
  39. ↑ 39.0 39.1 BBC News: Zimbabwe rolls out Z$100tr note. BBC(16 January 2009). Retrieved 24 July 2010.
  40. ↑ 40.0 40.1 BBC News: Zimbabwe abandons its currency. BBC(29 January 2009). Retrieved 13 July 2012.
  41. ↑ US National Debt Clock. Retrieved 24 Nov 2022.
  42. ↑ 42.0 42.1 RBA: Definition of billion. Reserve Bank of Australia. Retrieved 22 August 2011.
  43. ↑ 43.0 43.1 BBC News: Who wants to be a trillionaire?. BBC(7 May 2007). Retrieved 11 May 2010.
  44. ↑ 44.0 44.1 Template:Cite dictionary
  45. ↑ 45.0 45.1 trillion. Cambridge University Press. Retrieved 21 August 2011.
  46. ↑ 46.0 46.1 Al Jazem English-Arabic online dictionary: Billion. Encyclopædia Britannica. Retrieved 6 June 2012.
  47. ↑ 47.0 47.1 Al Jazem English-Arabic online dictionary:Trillion. Encyclopædia Britannica. Retrieved 6 June 2012.
  48. ↑ An English-Albanian Dictionary, Qeli, Albi. Albi Qeli, MD. Retrieved 6 June 2012.
  49. ↑ Eesti õigekeelsussõnaraamat ÕS 2006: miljard. Institute of the Estonian Language (Eesti Keele Instituut). Retrieved 13 August 2011.
  50. ↑ Eesti õigekeelsussõnaraamat ÕS 2013: biljon. Institute of the Estonian Language (Eesti Keele Instituut). Retrieved 25 June 2017.
  51. ↑ Eesti õigekeelsussõnaraamat ÕS 2006: triljon. Institute of the Estonian Language (Eesti Keele Instituut). Retrieved 13 August 2011.
  52. ↑ 52.0 52.1 Robson S. O. (Stuart O.), Singgih Wibisono, Yacinta Kurniasih. Javanese English dictionary Tuttle Publishing: 2002, Template:ISBN, 821 pages
  53. ↑ 53.0 53.1 [{{{url}}} May We Introduce the Romanian Language to You?]. Editura Fundatiei Culturale Române.
  54. ↑ Britain to Reduce $4 billion from Defence. Bi-Weekly Eleven({Template:Date).
  55. ↑ De Geïntegreerde Taal-Bank: miljard. Instituut voor Nederlandse Lexicologie. Retrieved 19 August 2011.
  56. ↑ De Geïntegreerde Taal-Bank: biljoen. Instituut voor Nederlandse Lexicologie. Retrieved 19 August 2011.
  57. ↑ 57.0 57.1 French Larousse: milliard. Éditions Larousse. Retrieved 19 August 2011.
  58. ↑ 58.0 58.1 French Larousse: billion. Éditions Larousse. Retrieved 19 August 2011.
  59. ↑ Template:Cite dictionaryTemplate:Dead link
  60. ↑ 60.0 60.1 Diccionario Panhispánico de Dudas: millardo. Real Academia Española. Retrieved 19 August 2011.
  61. ↑ 61.0 61.1 Diccionario Panhispánico de Dudas: billon. Real Academia Española. Retrieved 24 July 2010.
  62. ↑ Diccionario de la lengua española. Real Academia Española. Retrieved 2 July 2018.
  63. ↑ 63.0 63.1 Plena Manlibro de Esperanta Gramatiko, Wennergren, Bertilo(8 March 2008). Retrieved 15 September 2010.
  64. ↑ 64.0 64.1 Italian-English Larousse: bilione. Éditions Larousse. Retrieved 21 August 2011.
  65. ↑ [{{{url}}} Dicționarul explicativ al limbii române (ediția a II-a revăzută și adăugită)]. Editura Univers Enciclopedic Gold.
  66. ↑ Scara numerică(2016). Retrieved 3 May 2016.
  67. ↑ Switzerland: Words and Phrases. TRAMsoft Gmbh(29 August 2009). Retrieved 15 August 2011.
  68. ↑ Canadian government standards website. Canadian Government. Retrieved 15 September 2010.
  69. ↑ billion. Granddictionnaire.com(13 May 2013). Retrieved 24 April 2018.
  70. ↑ Units of measurement: past, present and future: international system of units{{#if:Gupta|, Gupta}. Springer(2010). ISBN 978-3642007385
  71. ↑ Greek Numbers and Numerals (Ancient and Modern), Foundalis, Harry. Retrieved 20 May 2007.

Long scale

Both long and short scale

Neither long nor short scale

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".[1]
  • Scientific notation (also known as standard form or exponential notation, for example 1Template:E, 1Template:E, 1Template:E, 1Template:E, etc.), or its engineering notation variant (for example 1Template:E, 10Template:E, 100Template:E, 1Template:E, 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). The International System of Units (SI) is independent of whichever scale is being used.[2] Use with non-SI units (e.g. "giga-dollars", "megabucks") is possible. k€ and M€ is frequently encountered.

See also

Template:Div col

Template:Div col end

References

  1. ↑ BBC: GCSE Bitesize – The origins of the universe. Retrieved 28 July 2011.
  2. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named si

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