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Long and short scales

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(Redirected from Numerical scale)
For the concept related to musical instruments, see Scale length (string instruments).

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 the Indian numbering system and the Chinese, Japanese, or Korean numerals.[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 the usage of the long scale include most countries in continental Europe and most that are French-speaking, German-speaking and Spanish-speaking.[3] Usage of the short scale is found in Brazil and in most English-speaking and Arabic-speaking countries.

For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the two scales are identical. For larger numbers, starting with 109, the two systems differ. For identical names, the long scale proceeds by powers of one million, whereas the short scale proceeds by powers of one thousand. For example, the short scale "one billion" (in many languages other than English called "one milliard", even on the short scale) means one thousand million (1,000,000,000), whereas in the long scale, "one billion" always means one million million (1,000,000,000,000). The long scale system employs additional terms for interleaved values, typically replacing the word ending "-ion" by "-iard". For numbers from 1012 and up, all the names in the short scale have different meanings than they have in the long scale.

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

Scales

[edit]

In both short and long scale naming, names are given each multiplication step for increments of the base-10 exponent of three, i.e. for each integer n in the sequence of multipliers 103n. Both systems use the same names for certain multipliers, including those for all numbers smaller than 109. The differences arise from the assignment of identical names to specific values of n, for numbers starting with 109, for which n=3. In the short scale system, the identical names are for n=3, 4, 5, ..., while the long scale places them at n=4, 6, 8, etc.

Short scale

[edit]

In the short scale, a billion (in many countries called a "milliard") means a thousand millions (1,000,000,000, which is 109), a trillion means one thousand billions (1012), and so on. Thus, a short scale n-illion equals 103n+3.[4]

Long scale

[edit]

In the long scale, a billion means one million millions (1012) and a trillion means one million billions (1018), and so on. Therefore, a long scale n-illion equals 106n.[1][2]

In some languages, the long scale uses additional names for the intermediate multipliers, replacing the ending -ion with -iard; for example, the next multiplier after million is milliard (109); after a billion it is billiard (1015). Hence, a long scale n-iard equals 106n+3.

Comparison

[edit]

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 or milliard 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

[edit]

Although this situation has been developing since the 1200s, the first recorded use of the terms short scale (French: échelle courte) and long scale (French: échelle longue) was by the French mathematician Geneviève Guitel in 1975.[1][2]

The short scale was never widespread before its universal adoption in the United States. It has been taught in American schools since the early 1800s.[5] It has since become common in other English-speaking nations and several other countries. For most of the 19th and 20th centuries, the United Kingdom largely used the long scale,[4][11] whereas the United States used the short scale,[11] so that the two systems were often referred to as British and American in the English language. After several decades of increasing informal British usage of the short scale, in 1974 the government of the UK adopted it,[12] and it is used for all official purposes.[13][14][15][16][17][18] The British usage and American usage are now identical.

The existence of the different scales means that care must be taken when comparing large numbers between languages or countries, or when interpreting old documents in countries where the dominant scale has changed over time. For example, British English, French, and Italian historical documents can refer to either the short or long scale, depending on the date of the document, since each of the three countries has used both systems at various times in its history. Today, the United Kingdom officially uses the short scale, but France and Italy use the long scale.

The pre-1974 former British English word billion, post-1961 current French word billion, post-1994 current Italian word bilione, Spanish billón, German Billion, Dutch biljoen, Danish billion, Swedish biljon, Finnish biljoona, Slovenian bilijon, Polish bilion, and European Portuguese word bilião (with a different spelling to the Brazilian Portuguese variant, but in Brazil referring to short scale) all refer to 1012, being long-scale terms. Therefore, each of these words translates to the American English or post-1974 British English word: trillion (1012 in the short scale), and 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 (c. 1260–1305) was among the first recorded users of the word to document Mediterranean trade between Constantinople and Italian states.[5] Over the next two centuries, the term became widely accepted and was adopted by other Italian states, France and other European countries.
Late 14th century
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),[5] 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.[19][20][21]

... item noctes que le premier greton dembas vault ung, le second vault dix, le trois vault cent, le quart vult [sic] mille, le Ve vault dix M, le VIe vault cent M, le VIIe vault Milion, Le VIIIe vault dix Million, Le IXe vault cent Millions, Le Xe vault Mil Millions, Le XIe vault dix mil Millions, Le XIIe vault Cent mil Millions, Le XIIIe vault bymillion, Le XIIIIe vault dix bymillions, Le XVe vault cent mil [sic] bymillions, Le XVIe vault mil bymillions, Le XVIIe vault dix Mil bymillions, Le XVIIIe vault cent mil bymillions, Le XIXe vault trimillion, Le XXe vault dix trimillions ...

Translation:

... Likewise, note that the first counter from the bottom is worth one, the 2nd is worth ten, the 3rd is worth one hundred, the 4th is worth one thousand, the 5th is worth ten thousand, the 6th is worth one hundred thousand, the 7th is worth a million, the 8th is worth ten millions, the 9th is worth one hundred millions, the 10th is worth one thousand millions, the 11th is worth ten thousand millions, the 12th is worth one hundred thousand million, the 13th is worth a bymillion, the 14th is worth ten bymillions, the 15th is worth one [hundred] bymillions, the 16th is worth one thousand bymillions, the 17th is worth ten thousand bymillions, the 18th is worth hundred thousand bymillions, the 19th is worth a trimillion, the 20th is worth ten trimillions ...

1484
Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien
an extract from Chuquet's original 1484 manuscript
French mathematician Nicolas Chuquet, in his article Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien,[22][23][24] used the words byllion, tryllion, quadrillion, quyllion, sixlion, septyllion, ottyllion, and nonyllion to refer to 1012, 1018, ... 1054. Most of the work was copied without attribution by Estienne de La Roche and published in his 1520 book, L'arismetique.[22] Chuquet's original article was rediscovered in the 1870s and then published for the first time in 1880.

...[preder s'] Item l'on doit savoir que ung million vault
mille milliers de unitez, et ung byllion vault mille
milliers de millions, et [ung] tryllion vault mille milliers
de byllions, et ung quadrillion vault mille milliers de
tryllions et ainsi des aultres : Et de ce en est pose ung
exemple nombre divise et punctoye ainsi que devant est
dit, tout lequel nombre monte 745324 tryllions
804300 byllions 700023 millions 654321.
Exemple : 745324'8043000'700023'654321 ... [sic]

Translation:

...likewise, one should know that a million is worth
a thousand thousand units, and a byllion is worth a thousand
thousand millions, and tryllion is worth a thousand thousand
byllions, and a quadrillion is worth a thousand thousand
tryllions, and so on for the others. And an example of this follows,
a number divided up and punctuated as previously
described, the whole number being 745324 tryllions,
804300 byllions 700023 millions 654321.
Example: 745324'8043000'700023'654321 ... [sic]

The extract from Chuquet's manuscript, the transcription and translation provided here all contain an original mistake: one too many zeros in the 804300 portion of the fully written out example: 745324'8043000 '700023'654321 ...

1516
Guilielmus Budaeus or Guillaume Budé (1467–1540)
French mathematician Budaeus (Guillaume Budé), writing in Latin, used the term milliart to mean "ten myriad myriad" or 109 in his book De Asse et partibus eius Libri quinque.[25]

.. hoc est decem myriadum myriadas:quod vno verbo nostrates abaci studiosi Milliartum appellant:quasi millionum millionem

Translation:

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

1549 The influential French mathematician Jacques Pelletier du Mans used the name milliard (or milliart) to mean 1012, attributing the term to the earlier usage by Guillaume Budé[25]
17th century With the increased usage of large numbers, the traditional punctuation of large numbers into six-digit groups evolved into three-digit group punctuation. In some places, the large number names were then applied to the smaller numbers, following the new punctuation scheme. Thus, in France and Italy, some scientists then began using billion to mean 109, trillion to mean 1012, etc.[26] This usage formed the origins of the later short scale. The majority of scientists either continued to say thousand million or changed the meaning of the Pelletier term, milliard, from "million of millions" down to "thousand million".[5] This meaning of milliard has been occasionally used in England,[11] but was widely adopted in France, Germany, Italy and the rest of Europe, for those keeping the original long scale billion from Adam, Chuquet and Pelletier.
1676 The first published use of milliard as 109 occurred in the Netherlands.[5][27]

.. milliart/ofte duysent millioenen..

Translation:

..milliart / also thousand millions..

1729 The short-scale meaning of the term billion had already been brought to the British American colonies. The first American appearance of the short scale value of billion as 109 was published in the Greenwood Book of 1729, written anonymously by Prof. Isaac Greenwood of Harvard College.[5]
Late 18th century As early as 1762 (and through at least the early 20th century), the dictionary of the Académie française defined billion as a term of arithmetic meaning a thousand millions.[28][29][30][31]
Early 19th century France widely converted to the short scale, and was followed by the U.S., which began teaching it in schools. Many French encyclopedias of the 19th century either omitted the long scale system or called it "désormais obsolète", a now obsolete system. Nevertheless, by the mid 20th century France would officially convert back to the long scale.
1926
A Dictionary of Modern English Usage
by H. W. Fowler
H. W. Fowler's A Dictionary of Modern English Usage[11] 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.

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
British prime minister Harold Wilson
(1916–1995)
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] reported in Hansard for 20 December 1974:[12]

Mr. Maxwell-Hyslop asked the Prime Minister whether he would make it the practice of his administration that when Ministers employ the word 'billion' in any official speeches, documents, or answers to Parliamentary Questions, they will, to avoid confusion, only do so in its British meaning of 1 million million and not in the sense in which it is used in the United States of America, which uses the term 'billion' to mean 1,000 million.
The Prime Minister: No. The word 'billion' is now used internationally to mean 1,000 million and it would be confusing if British Ministers were to use it in any other sense. I accept that it could still be interpreted in this country as 1 million million and I shall ask my colleagues to ensure that, if they do use it, there should be no ambiguity as to its meaning.

The BBC and other UK mass media quickly followed the government's lead within the UK.

During the last quarter of the 20th century, most other English-speaking countries (Ireland, Australia, New Zealand, South Africa, Zimbabwe, etc.) either also followed this lead or independently switched to the short scale use. However, in most of these countries, some limited long scale use persists and the official status of the short scale use is not clear.

1975 French mathematician Geneviève Guitel introduced the terms long scale (French: échelle longue) and short scale (French: échelle courte) to refer to the two numbering systems.[1][2]
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
10 Milliarden Mark (1010 mark) stamp
10 Milliarden Mark (1010 mark) stamp
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

1946
1020 Hungarian pengő banknote issued in 1946
1020 Hungarian pengő banknote issued in 1946

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
5 × 1011 Yugoslav dinar banknotes from 1993

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
1014 (100 trillion) Zimbabwean dollar 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[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 As of 24 November 2022, 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

[edit]
Short and long scale usage throughout the world
  Long scale
  Short scale
  Short scale with milliard instead of billion
  Both scales
  Other naming system
  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 being billion. For example:[shortscale note 1]

Arabic-speaking

[edit]
106, مَلْيُوْن malyoon; 109, مِلْيَار milyar; 1012, تِرِلْيُوْن tirilyoon; etc.

Most Arabic-language countries and regions use the short scale with 109 being مليار milyar, except for a few countries like Saudi Arabia and the UAE which use the word بليون billion for 109. For example:[shortscale note 5][46][47]

Other short scale

[edit]
106, one million; 109, one milliard or one billion; 1012, one trillion; etc.

Other countries also use a word similar to trillion to mean 1012, etc. Whilst a few of these countries like English use a word similar to billion to mean 109, most like Arabic have kept a traditionally long scale word similar to milliard for 109. Some examples of short scale use, and the words used for 109 and 1012, are

Long scale users

[edit]

The long scale is used by most Continental European countries and by most other countries whose languages derive from Continental Europe (with the notable exceptions of Albania, Greece, Romania,[49] and Brazil). These countries use a word similar to billion to mean 1012. Some use a word similar to milliard to mean 109, while others use a word or phrase equivalent to thousand millions.

Dutch-speaking

[edit]
106, miljoen; 109, miljard; 1012, biljoen; etc.

Most Dutch-language countries and regions use the long scale with 109 = miljard.[50][51]

French-speaking

[edit]
106, million; 109, milliard; 1012, billion; etc.

Most French-language countries and regions use the long scale with 109 = milliard, for example:[longscale note 1][52][53]

German-speaking

[edit]
106, Million; 109, Milliarde; 1012, Billion; etc.

German-language countries and regions use the long scale with 109 = Milliarde.

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 with 109 = mil milhões or milhar de milhões.

Spanish-speaking

[edit]
106, millón; 109, mil millones or millardo; 1012, billón; etc.

Most Spanish-language countries and regions use the long scale, for example:[longscale note 2][55][56]

Other long scale

[edit]
106, one million; 109, one milliard or one thousand million; 1012, one billion; etc.

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

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[61] or mille milliards).
English (109 = billion, 1012 = trillion) French (109 = milliard, 1012 = billion)
South African English (109 = billion, 1012 = trillion) Afrikaans (109 = miljard, 1012 = biljoen)
 Puerto Rico Economic and technical (109 = billón, 1012 = trillón) Latin American export publications (109 = millardo or mil millones, 1012 = billón)

Using neither

[edit]

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
 Bangladesh,  India,  Maldives,  Nepal,  Pakistan Indian numbering system Traditional 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
East Asian numbering system:
Traditional myriad system for the larger numbers; special words and symbols up to 1068
 Greece 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, εκατομμύριο ekatommyrio ("hundred-myriad", i.e. 100 × 10,000):
  • δισεκατομμύριο disekatommyrio "bi+hundred-myriad" = 109 (short scale billion)
  • τρισεκατομμύριο trisekatommyrio "tri+hundred-myriad" = 1012 (short scale trillion)
  • τετράκις εκατομμύριο tetrakis ekatommyrio "quadri+hundred-myriad" = 1015 (short scale quadrillion), and so on.[65]
 Laos Lao numerals Traditional system
 Mongolia Mongolian numerals Traditional myriad system for the larger numbers; special words up to 1067
 Sri Lanka
Traditional systems
 Thailand Thai numerals Traditional system based on millions
 Vietnam Vietnamese numerals Traditional system(s) based on thousands

By continent

[edit]

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), South African English French (Benin, Guinea), Portuguese (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 Hebrew (Israel), Indonesian, Philippine English Persian (Iran), Portuguese (East Timor, Macau)
Europe British English, Russian, Turkish Dutch, French, German, Italian, Portuguese, Spanish
Oceania Australian English, New Zealand English French (French Polynesia, New Caledonia)

Notes on current usage

[edit]

Short scale

[edit]
  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[18] and the official status of the short scale in anglophone countries other than the UK and US is sometimes obscure.[5]
  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.[42] As recently as 1999, the same department did not consider short scale to be standard, but only used it occasionally. Some documents use the term thousand million for 109 in cases where two amounts are being compared using a common unit of one 'million'.
  3. ^ British usage: Billion has meant 109 in most sectors of official published writing for many years now. The UK government, the BBC, and most other broadcast or published mass media, have used the short scale in all contexts since the mid-1970s.[12][13][43][15]
    Before the widespread use of billion for 109, UK usage generally referred to thousand million rather than milliard.[16] The long scale term milliard, for 109, is obsolete in British English, though its derivative, yard, is still used as slang in the London money, foreign exchange, and bond markets.
  4. ^ American usage: In the United States, the short scale has been taught in school since the early 19th century. It is therefore used exclusively.[44][45]
  5. ^ Arabic language countries: Most Arabic-language countries use: 106, مليون million; 109, مليار milyar; 1012, ترليون trilyon; etc.[46][47]
  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) or sejuta berkali-kali (a millions after a million or a millions over a million) are also used for 1012 less often. Terms greater than triliun are not very familiar to Indonesians.[48]

Long scale

[edit]
  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.[37][52][53] However the 9th edition of the dictionary of the Académie française describes billion as an outdated synonym of milliard, and says that the new meaning of 1012 was decreed in 1961, but never caught on.[54]
  2. ^ Spanish language countries: Spanish-speaking countries sometimes use millardo (milliard)[55] for 109, but mil millones (thousand millions) is used more frequently. The word billón is sometimes used in the short scale sense in those countries more influenced by the United States, where "billion" means "one thousand millions". The usage of billón to mean "one thousand millions", controversial from the start, was denounced by the Royal Spanish Academy as recently as 2010,[56] but was finally accepted in a later version of the official dictionary as standard usage among educated Spanish speakers in the United States (including Puerto Rico).[57]
  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.[10] In Italian, the word bilione officially means 1012, trilione means 1018, etc.. Colloquially, bilione[58] can mean both 109 and 1012; trilione [citation needed] can mean both 1012 and (rarer) 1018 and so on. Therefore, in order to avoid ambiguity, they are seldom used. Forms such as miliardo (milliard) for 109, mille miliardi (a thousand milliards) for 1012, un milione di miliardi (a million milliards) for 1015, un miliardo di miliardi (a milliard of milliards) for 1018, mille miliardi di miliardi (a thousand milliard of milliards) for 1021 are more common.[10]

Both long and short scale

[edit]
  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, though the Canadian government standards website recommends that in French billion and trillion be avoided, recommending milliard for 109, and mille milliards (a thousand milliards) for 1012.[60]
  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. As of 2011 most English language publications use the short scale. Some Afrikaans publications briefly attempted usage of the "American System" but that has led to comment in the papers[62] and has been disparaged by the "Taalkommissie" (The Afrikaans Language Commission of the South African Academy of Science and Art)[63] and has thus, to most appearances, been abandoned.

Neither long nor short scale

[edit]
  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.[64]

Alternative approaches

[edit]
  • In written communications, the simplest solution for moderately large numbers is to write the full amount, for example 1,000,000,000,000 rather than 1 trillion (short scale) or 1 billion (long scale).
  • Combinations of the unambiguous word million, for example: 109 = "one thousand million"; 1012 = "one million million".[66]
  • Scientific notation (also known as standard form or exponential notation, for example 1×109, 1×1010, 1×1011, 1×1012, etc.), or its engineering notation variant (for example 1×109, 10×109, 100×109, 1×1012, etc.), or the computing variant E notation (for example 1e9, 1e10, 1e11, 1e12, etc.). This is the most common practice among scientists and mathematicians, and is both unambiguous and convenient.
  • 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.[34] Use with non-SI units (e.g. "giga-dollars", "megabucks") is possible. k€ and M€ is frequently encountered.

See also

[edit]

References

[edit]
  1. ^ a b c d e Guitel, Geneviève (1975). Histoire comparée des numérations écrites (in French). Paris: Flammarion. pp. 51–52. ISBN 978-2-08-211104-1.
  2. ^ a b c d e Guitel, Geneviève (1975). ""Les grands nombres en numération parlée (État actuel de la question)", i.e. "The large numbers in oral numeration (Present state of the question)"". Histoire comparée des numérations écrites (in French). Paris: Flammarion. pp. 566–574. ISBN 978-2-08-211104-1.
  3. ^ "Authoritative Real Academia Española (RAE) dictionary: billón". Archived from the original on 4 November 2015. Retrieved 12 March 2015.
  4. ^ a b British-English usage of 'Billion vs Thousand million vs Milliard'. Google Inc. Retrieved 26 April 2014 – via Google Books ngram viewer.
  5. ^ a b c d e f g h i j k Smith, David Eugene (1953) [first published 1925]. History of Mathematics. Vol. II. Courier Dover Publications. p. 81. ISBN 978-0-486-20430-7.
  6. ^ a b "Wortschatz-Lexikon: Milliarde" (in German). Universität Leipzig: Wortschatz-Lexikon. Archived from the original on 27 September 2011. Retrieved 19 August 2011.
  7. ^ a b "Wortschatz-Lexikon: Billion" (in German). Universität Leipzig: Wortschatz-Lexikon. Archived from the original on 7 August 2011. Retrieved 19 August 2011.
  8. ^ a b "Wortschatz-Lexikon: Billiarde" (in German). Universität Leipzig: Wortschatz-Lexikon. Archived from the original on 27 September 2011. Retrieved 28 July 2011.
  9. ^ a b "Wortschatz-Lexikon: Trilliarde" (in German). Universität Leipzig: Wortschatz-Lexikon. Archived from the original on 27 September 2011. Retrieved 28 July 2011.
  10. ^ a b c d e f "Direttiva CEE / CEEA / CE 1994 n. 55, p.12" (PDF) (in Italian). Italian Government. 21 November 1994. Retrieved 24 July 2011.
  11. ^ 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.
  12. ^ a b c d ""BILLION" (DEFINITION) — HC Deb 20 December 1974 vol 883 cc711W–712W". Hansard Written Answers. Parliamentary Debates (Hansard). 20 December 1972. Retrieved 2 April 2009.
  13. ^ a b c d O'Donnell, Frank (30 July 2004). "Britain's £1 trillion debt mountain – How many zeros is that?". The Scotsman. Retrieved 31 January 2008.
  14. ^ "Who wants to be a trillionaire?". BBC News. 7 May 2007. Retrieved 11 May 2010.
  15. ^ a b c Comrie, Bernard (24 March 1996). "billion:summary". Linguist List (Mailing list). Retrieved 24 July 2011.
  16. ^ a b c "Oxford Dictionaries: How many is a billion?". Oxford University Press. Archived from the original on 12 January 2017. Retrieved 7 May 2018.
  17. ^ "Oxford Dictionaries: Billion". Oxford University Press. Archived from the original on 11 August 2011. Retrieved 24 July 2011.
  18. ^ a b Nielsen, Ron (2006). The Little Green Handbook. Macmillan Publishers. p. 290. ISBN 978-0-312-42581-4.
  19. ^ Adam, Jehan (1475). Traicté en arismetique pour la practique par gectouers... (MS 3143) (in Middle French). Paris: Bibliothèque Sainte-Geneviève.
  20. ^ "HOMMES DE SCIENCE, LIVRES DE SAVANTS A LA BIBLIOTHÈQUE SAINTE-GENEVIÈVE, Livres de savants II". Traicté en arismetique pour la practique par gectouers… (in French). Bibliothèque Sainte-Geneviève. 2005. Archived from the original on 25 October 2014. Retrieved 25 October 2014.
  21. ^ Thorndike, Lynn (1926). "The Arithmetic of Jehan Adam, 1475 A.D". The American Mathematical Monthly. 1926 (January). Mathematical Association of America: 24–28. doi:10.2307/2298533. JSTOR 2298533.
  22. ^ a b Chuquet, Nicolas (1880) [written 1484]. "Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien". Bulletino di Bibliographia e di Storia delle Scienze Matematische e Fisische (in Middle French). XIII (1880). Bologna: Aristide Marre: 593–594. ISSN 1123-5209. Retrieved 17 July 2011.
  23. ^ Chuquet, Nicolas (1880) [written 1484]. "Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien" (in Middle French). miakinen.net. Retrieved 1 March 2008.
  24. ^ Flegg, Graham (23–30 December 1976). "Tracing the origins of One, Two, Three". New Scientist. 72 (1032). Reed Business Information: 747. ISSN 0262-4079. Retrieved 17 July 2011.[permanent dead link]
  25. ^ a b Budaeus, Guilielmus (1516). De Asse et partibus eius Libri quinque (in Latin). pp. folio 93.
  26. ^ Littré, Émile (1873–1874). Dictionnaire de la langue française. Paris, France: L. Hachette. p. 347. Ce n'est qu'au milieu du XVIIe siècle qu'il fut réglé que les tranches, au lieu d'être de six en six chiffres, seraient de trois en trois chiffres; ce qui revint à diviser par 1000 l'ancien billion, l'ancien trillion, etc. [It was only in the middle of the 17th century that it was settled that the slices, instead of being from six to six digits, would be from three to three digits; which resulted in dividing by 1000 the old billion, the old trillion, and so on.]
  27. ^ Houck (1676). Arithmetic. Netherlands. p. 2.
  28. ^ Dictionnaire de l'académie françoise (4th ed.). Paris, France: Institut de France. 1762. p. 177.
  29. ^ Dictionnaire de l'Académie française (6th ed.). Paris, France. 1835. p. 189.
  30. ^ Dictionnaire de l'Académie française (7th ed.). Paris, France: Institut de France. 1877. p. 182.
  31. ^ Dictionnaire de l'Académie française (8th ed.). Paris, France: Institut de France. 1932–1935. p. 144.
  32. ^ a b "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. ^ a b "Resolution 12 of the 11th meeting of the CGPM (1960)". BIPM. Retrieved 28 July 2011.
  35. ^ The International System of Units (SI) (PDF) (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. Archived from the original (PDF) on 25 July 2011. Retrieved 24 July 2011.
  36. ^ Thompson, Ambler; Taylor, Barry N. (30 March 2008). "Guide for the Use of the International System of Units (SI), NIST SP – 811". NIST. US: National Institute of Standards and Technology: 21. Archived from the original on 8 March 2021. Retrieved 13 September 2014.
  37. ^ a b "Décret 61-501" (PDF). Journal Officiel (in French). French Government: 4587 note 3a, and erratum on page 7572. 11 August 1961 [commissioned 3 May 1961 published 20 May 1961]. Archived from the original (PDF) on 20 January 2010. Retrieved 31 January 2008.
  38. ^ "BBC News: Zimbabweans play the zero game". BBC. 23 July 2008. Retrieved 13 July 2012.
  39. ^ "BBC News: Zimbabwe rolls out Z$100tr note". BBC. 16 January 2009. Retrieved 24 July 2010.
  40. ^ "BBC News: Zimbabwe abandons its currency". BBC. 29 January 2009. Retrieved 13 July 2012.
  41. ^ "US National Debt Clock". Retrieved 24 November 2022.
  42. ^ a b "RBA: Definition of billion". Reserve Bank of Australia. Retrieved 22 August 2011.
  43. ^ a b "BBC News: Who wants to be a trillionaire?". BBC. 7 May 2007. Retrieved 11 May 2010.
  44. ^ a b "billion". Cambridge Dictionaries Online. Cambridge University Press. Retrieved 21 August 2011.[permanent dead link]
  45. ^ a b "trillion". Cambridge Dictionaries Online. Cambridge University Press. Retrieved 21 August 2011.[permanent dead link]
  46. ^ a b "Al Jazem English-Arabic online dictionary: Billion". Al Jazem English-Arabic online dictionary. Encyclopædia Britannica. Retrieved 6 June 2012.
  47. ^ a b "Al Jazem English-Arabic online dictionary:Trillion". Al Jazem English-Arabic online dictionary. Encyclopædia Britannica. Retrieved 6 June 2012.
  48. ^ a b Robson S. O. (Stuart O.), Singgih Wibisono, Yacinta Kurniasih. Javanese English dictionary Tuttle Publishing: 2002, ISBN 0-7946-0000-X, 821 pages
  49. ^ Avram, Mioara; Sala, Marius (2000), May We Introduce the Romanian Language to You?, Editura Fundatiei Culturale Române, p. 151, ISBN 9789735772246, the numeral miliard "billion"
  50. ^ "De Geïntegreerde Taal-Bank: miljard" (in Dutch). Instituut voor Nederlandse Lexicologie. Retrieved 19 August 2011.
  51. ^ "De Geïntegreerde Taal-Bank: biljoen" (in Dutch). Instituut voor Nederlandse Lexicologie. Retrieved 19 August 2011.
  52. ^ a b "French Larousse: milliard" (in French). Éditions Larousse. Archived from the original on 18 March 2012. Retrieved 19 August 2011.
  53. ^ a b "French Larousse: billion" (in French). Éditions Larousse. Archived from the original on 18 March 2012. Retrieved 19 August 2011.
  54. ^ "billion". Dictionnaire de l'Académie française (in French) (9th ed.). Académie française. 1992. Retrieved 17 January 2016. BILLION (les deux l se prononcent sans mouillure) n. m. XVe siècle, byllion, « un million de millions »; XVIe siècle, « mille millions ». Altération arbitraire de l'initiale de million, d'après la particule latine bi-, « deux fois ».
    Rare. Mille millions. Syn. vieilli de Milliard. Selon un décret de 1961, le mot Billion a reçu une nouvelle valeur, à savoir un million de millions (1012), qui n'est pas entrée dans l'usage.     [BILLION (the two Ls are pronounced without palatalisation) masculine noun. Spelled byllion in the 15th century when it meant a million millions; in the 16th century it meant a thousand millions. It is an arbitrary alteration of the start of million by inserting the Latin prefix bi-, meaning twice. Now rarely used. It means a thousand millions. It is an outdated synonym of Milliard. According to a decree of 1961, the word Billion received a new value, to wit a million millions (1012), which has not come into common usage.]    [permanent dead link]
  55. ^ a b "Diccionario Panhispánico de Dudas: millardo" (in Spanish). Real Academia Española. Retrieved 19 August 2011.
  56. ^ a b "Diccionario Panhispánico de Dudas: billon" (in Spanish). Real Academia Española. Retrieved 24 July 2010.
  57. ^ "Diccionario de la lengua española" (in Spanish). Real Academia Española. Retrieved 2 July 2018.
  58. ^ a b "Italian-English Larousse: bilione". Éditions Larousse. Archived from the original on 18 March 2012. Retrieved 21 August 2011.
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  60. ^ "Canadian government standards website". Canadian Government. 2010. Retrieved 15 September 2010.
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  63. ^ "'Groen boek': mooiste, beste, gebruikersvriendelikste" (in Afrikaans). Naspers:Media24. Archived from the original on 14 July 2014. Retrieved 16 July 2014.
  64. ^ Gupta, S.V. (2010). Units of measurement: past, present and future: international system of units. Springer. pp. 12 (Section 1.2.8 Numeration). ISBN 978-3642007385. Retrieved 22 August 2011.
  65. ^ Foundalis, Harry. "Greek Numbers and Numerals (Ancient and Modern)". Retrieved 20 May 2007.
  66. ^ "BBC: GCSE Bitesize – The origins of the universe". BBC. Retrieved 28 July 2011.
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