Long and short scales

Short description: Two meanings of "billion" and "trillion"

The long and short scales are two powers of ten number naming systems that are consistent with each other for smaller numbers, but are contradictory for larger numbers.[1][2] Other numbering systems, particularly in East Asia and South Asia, have large number naming that differs from both the long and the short scales. Such numbering systems include the Indian numbering system and Chinese, Japanese, and Korean numerals.[1][2] Much of the remainder of the world has adopted either the short or long scale. Countries using the long scale include most countries in continental Europe and most that are French-speaking, German-speaking and Spanish-speaking.[3] Use of the short scale is found in most English-speaking and Arabic-speaking countries, most Eurasian post-communist countries, and Brazil.

For powers of ten less than 9 (one, ten, hundred, thousand, and million), the short and long scales are identical; but, for larger powers of ten, the two systems differ in confusing ways. For identical names, the long scale grows by multiples of one million (106), whereas the short scale grows by multiples of one thousand (103). For example, the short scale billion is one thousand million (109), whereas in the long scale, billion is one million million (1012), making the word 'billion' a false friend between long- and short-scale languages. The long scale system includes additional names for interleaved values, typically replacing the word-ending '-ion' with '-iard'.

To avoid confusion, the International System of Units (SI) recommends using the metric prefixes to indicate magnitude. For example, giga\- is always 109, which is 'billion' in short scale but 'milliard' in long scale.

## Contents

* 1 Definition
* 2 Comparison
* 3 Avoiding confusion
* 4 History
* 5 Current usage
* 5.1 Short scale users
* 5.1.1 English-speaking
* 5.1.2 Arabic-speaking
* 5.1.3 Other short scale
* 5.2 Long scale users
* 5.2.1 Dutch-speaking
* 5.2.2 French-speaking
* 5.2.3 German-speaking
* 5.2.4 Portuguese-speaking
* 5.2.5 Spanish-speaking
* 5.2.6 Other long scale
* 5.3 Using both
* 5.4 Using neither
* 5.5 By continent
* 5.6 Notes on current usage
* 5.6.1 Short scale
* 5.6.2 Long scale
* 5.6.3 Both long and short scale
* 5.6.4 Neither long nor short scale
* 6 See also
* 7 References
* 8 External links

## Definition

In both scales, names are given to orders of magnitude at increments of 1000. Both systems use the same names for magnitudes less than 109. Differences arise from the use of identical names for larger magnitudes. For the same magnitude name (n-illion), the value is 103n+3 in the short scale but 106n in the long scale for positive integers n.[4][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-illiard equals 106n+3.

The following table shows the size of first few short and long scale magnitudes. Notice how billion and trillion are in both scales but have different sizes.

Quantity  | Short scale  | Long scale

|
|

106 | million  | million
109 | billion | milliard
1012 | trillion | billion
1015 | quadrillion | billiard
1018 | quintillion  | trillion
1021 | sextillion  | trilliard
1024 | septillion  | quadrillion
1027 | octillion  | quadrilliard

## Comparison

The following tables show the corresponding names and values of the two scales.

Note that instead of using an intermediate long scale word (illiard), a quantity is sometimes specified in terms of the smaller illion word. For example, "thousand billion" instead of "billiard".

Value  | Metric prefix  | Short scale  | Long scale

|
|
|

1  |  | one  | one
10  | deca  | ten  | ten
102 | hecto  | hundred  | hundred
103 | kilo  | thousand  | thousand
106 | mega  | million  | million
109 | giga  | billion  | milliard
1012 | tera  | trillion  | billion
1015 | peta  | quadrillion  | billiard
1018 | exa  | quintillion  | trillion
1021 | zetta  | sextillion  | trilliard
1024 | yotta  | septillion  | quadrillion
1027 | ronna  | octillion  | quadrilliard
1030 | quetta  | nonillion  | quintillion

The different sizes of the same name of the two scales can be described as:

Name  | Short scale  | Long scale

|
|

million  | 106 | 106
billion | 109 | 1012
trillion  | 1012 | 1018
quadrillion  | 1015 | 1024
quintillion  | 1018 | 1030
| .

.  | .

## Avoiding confusion

One way to avoid confusion between the two scales is to use positional notation. For example, 1,000,000,000,000 rather than 1 trillion (short scale) or 1 billion (long scale). This method becomes unwieldy for very large numbers.

Another way is to combine unambiguous words: ten, hundred, thousand, and million. For example: one thousand million and one million million,[5] though this also becomes unwieldy with longer numbers. Methods that are better at longer numbers include:

* Scientific notation (for example 1.2×1010), or its engineering notation variant (for example 12×109), or the computing variant E notation (for example `1.2e10`). This is the most common practice among scientists and mathematicians, but can be cumbersome in spoken word.

* SI metric prefixes. For example, giga for 109 and tera for 1012 can give gigawatt (109 W) and terawatt (1012 W).[6] These prefixes can be used unambiguously even with non-SI units. For example: giga-dollars, megabucks, k€, and M€. (An exception to this is digital storage, is still common practice to use prefixes incorrectly, such as using kilobyte to refer to 1024 bytes (a kibibyte) instead of 1000 bytes or using megabyte to refer to 1,048,576 bytes (a mebibyte) instead of 1,000,000. [7])

## History

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

The short scale was never widespread before its general adoption in the United States. It has been taught in American schools since the early 1800s.[8] It has since become common in other English-speaking nations and several other countries. For most of the 19th and early 20th centuries, the United Kingdom largely used the long scale,[4][9] whereas the United States used the short scale,[9] 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,[10] and it is used for all official purposes.[11][12][13][14][15][16] 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.[8] 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.[8] Some of these countries, but not all, introduced new words billiard, trilliard, etc. as intermediate terms.[17][18][19][20][21] 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.[8] 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.

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.[8]

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.[17][18][19][20][21]

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.[8] 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),[8] 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.[22][23][24]

> ... 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,[25][26][27] 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.[25] 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.[28]

> .. 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[28]
17th century
1676  | The first published use of milliard as 109 occurred in the Netherlands.[8][29]

> .. 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.[8]
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.[30][31][32][33]
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[9] 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.[34] 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.[34][35]
1960  | The 11th General Conference on Weights and Measures adopted the International System of Units (SI), with its own set of numeric prefixes.[6] 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.[36] The National Institute of Standards and Technology within the US also considers that it is best that they be avoided entirely.[37]
1961  | The French Government confirmed their official usage of the long scale in the Journal officiel (the official French Government gazette).[38]
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,[11] reported in Hansard for 20 December 1974:[10]

> 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.[21]

## Current usage

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

#### English-speaking

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]

* Australia[shortscale note 2][39]
* Canada (English-speaking) see Using both below
* Ireland (English-speaking, Irish: billiún, trilliún)
* United Kingdom[shortscale note 3][10][11][40][13][14]
* United States[shortscale note 4][41][42]

#### Arabic-speaking

106, مَلْيُوْن milyūn; 109, مِلْيَار milyar; 1012, تِرِلْيُوْن tirilyūn; 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][43][44]

* Algeria
* Egypt
* Iraq
* Morocco
* Saudi Arabia
* United Arab Emirates

#### Other short scale

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

* Brazil (bilhão, trilhão)
* Indonesia (miliar, triliun)[shortscale note 6][45]
* Israel (Hebrew: מיליארד milyard, טריליון trilyon)
* Russia (миллиард milliard, триллион trillion)
* Turkey (milyar, trilyon)

### 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[46] 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

106, miljoen; 109, miljard; 1012, biljoen; etc.

Most Dutch-language countries and regions use the long scale with 109 = miljard.[47][48]

#### French-speaking

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][49][50]

* Canada (Canadian French) see Using both below
* France

#### German-speaking

106, Million; 109, Milliarde; 1012, Billion; etc.

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

#### Portuguese-speaking

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

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][52][53]

* Argentina
* Mexico (mil millones or millardo)
* Spain (millardo or typ. mil millones)

#### Other long scale

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:

* Czech Republic (miliarda, bilion)
* Denmark (milliard, billion)
* Esperanto (miliardo, duiliono) [longscale note 3][55]
* Finland (miljardi, biljoona; Swedish: miljard, biljon)
* Iran (Persian: میلیارد miliyard, بیلیون billion, تریلیون trillion) *  Italy (miliardo, bilione) [longscale note 4][21][56]
* Norway (Bokmål: milliard, billion; Nynorsk: milliard, billion)
* Poland (miliard, bilion)
* Romania[57] (miliard, bilion). There are ambiguities for numbers above 1012.[58]
* Sweden (miljard, biljon)
* Switzerland (French: milliard, billion; German: Milliarde, Billion; Italian: miliardo, bilione; Romansh: milliarda, billiun[59])

### Using both

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).

* 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 and technical (109 = billón, 1012 = trillón)  | Latin American export publications (109 = millardo or mil millones, 1012 = billón)

### 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

|
|

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

* People's Republic of China
* Republic of China
* South Korea
* North Korea
* Japan

| East Asian numbering system:

* Chinese numerals
* Korean numerals
* Japanese numerals

| 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 |

* Sinhala numerals
* Tamil numerals

| Traditional systems
Thailand | Thai numerals | Traditional system based on millions
Vietnam | 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. For example:

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, 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, 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, Ukrainian, Estonian, Latvian, Lithuanian, Bulgarian, Romanian, Albanian, Turkish  | Dutch, French, German, Italian, Portuguese, Spanish, Danish, Swedish, Norwegian, Finnish, Icelandic, Polish, Czech, Slovak, Hungarian, Serbo-Croatian, Slovene, Macedonian
Oceania | Australian English, New Zealand English  | French (French Polynesia, New Caledonia)

### Notes on current usage

#### Short scale

1. ↑ English language countries: Apart from the United States, the long scale was used for centuries in many English language countries before being superseded in recent times by short scale usage. Because of this history, some long scale use persists[16] and the official status of the short scale in anglophone countries other than the UK and US is sometimes obscure.[8]
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.[39] 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.[10][11][40][13]

Before the widespread use of billion for 109, UK usage generally referred to thousand million rather than milliard.[14] 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.[41][42]
5. ↑ Arabic language countries: Most Arabic-language countries use: 106, مليون million; 109, مليار milyar; 1012, ترليون trilyon; etc.[43][44]
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.[45]

#### Long scale

1. ↑ French usage: France, with Italy, was one of two European countries which converted from the long scale to the short scale during the 19th century, but returned to the original long scale during the 20th century. In 1961, the French Government confirmed their long scale status.[38][49][50] 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.[51]
2. ↑ Spanish language countries: Spanish-speaking countries sometimes use millardo (milliard)[52] 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,[53] 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).[54]
3. ↑ Esperanto language usage: The Esperanto language words biliono, triliono etc. used to be ambiguous, and both long and 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.
4. ↑ 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.[21] In Italian, the word bilione officially means 1012, trilione means 1018, etc. Colloquially, bilione[56] can mean both 109 and 1012; trilione can mean both 1012 and (rarer) 1018 and so on. Therefore, in order to avoid ambiguity, they are seldom used. Forms such as miliardo (milliard) for 109, mille miliardi (a thousand milliards) for 1012, un milione di miliardi (a million milliards) for 1015, un miliardo di miliardi (a milliard of milliards) for 1018, mille miliardi di miliardi (a thousand milliard of milliards) for 1021 are more common.[21]

#### 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, 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[update] most English language publications use the short scale. Some Afrikaans publications briefly attempted usage of the "American System" but that has led to comment in the papers[62] and has been disparaged by the "Taalkommissie" (The Afrikaans Language Commission of the South African Academy of Science and Art)[63] and has thus, to most appearances, been abandoned.

#### Neither long nor short scale

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]

## See also

* Googol (number)
* Googolplex (number)
* Names of large numbers
* Names of small numbers
* Orders of magnitude (numbers)
* Hindu units of time which displays some similar issues
* Indian numbering system

## References

1. ↑ 1.0 1.1 1.2 1.3 1.4 Guitel, Geneviève (1975) (in fr). Histoire comparée des numérations écrites. Paris: Flammarion. pp. 51–52. ISBN 978-2-08-211104-1.
2. ↑ 2.0 2.1 2.2 2.3 2.4 Guitel, Geneviève (1975). "Les grands nombres en numération parlée (État actuel de la question) (The large numbers in oral numeration (Present state of the question))" (in fr). Histoire comparée des numérations écrites. Paris: Flammarion. pp. 566–574'. ISBN 978-2-08-211104-1.
3. ↑ "Authoritative Real Academia Española (RAE) dictionary: billón". http://lema.rae.es/drae/.
4. ↑ 4.0 4.1 British-English usage of 'Billion vs Thousand million vs Milliard'. Google Inc. https://books.google.com/ngrams/graph?content=billion,thousand+million,milliard&year_start=1808&year_end=1967&corpus=18&smoothing=3&share=. Retrieved 26 April 2014.
5. ↑ "BBC: GCSE Bitesize – The origins of the universe". BBC. http://www.bbc.co.uk/schools/gcsebitesize/science/edexcel/space/theoriginsoftheuniverserev1.shtml.
6. ↑ 6.0 6.1 "Resolution 12 of the 11th meeting of the CGPM (1960)". BIPM. http://www.bipm.org/jsp/en/ViewCGPMResolution.jsp?CGPM=11&RES=12.
7. ↑ "Understanding file sizes | Bytes, KB, MB, GB, TB, PB, EB, ZB, YB". geeksforgeeks.org. https://www.geeksforgeeks.org/computer-science-fundamentals/understanding-file-sizes-bytes-kb-mb-gb-tb-pb-eb-zb-yb/.
8. ↑ 8.00 8.01 8.02 8.03 8.04 8.05 8.06 8.07 8.08 8.09 Smith, David Eugene (1953). History of Mathematics. II. Courier Dover Publications. pp. 81. ISBN ((978-0-486-20430-7)). https://books.google.com/books?id=uTytJGnTf1kC&pg=PA81.
9. ↑ 9.0 9.1 9.2 Fowler, H. W. (1926). A Dictionary of Modern English Usage. Great Britain: Oxford University Press. pp. 52–53. ISBN ((978-0-19-860506-5)). https://books.google.com/books?id=hrtIDakUpA4C&q=billion&pg=PT169.
10. ↑ 10.0 10.1 10.2 10.3 ""BILLION" (DEFINITION) — HC Deb 20 December 1974 vol 883 cc711W–712W". Hansard Written Answers. Parliamentary Debates (Hansard). 20 December 1974. https://api.parliament.uk/historic-hansard/written-answers/1974/dec/20/billion-definition#S5CV0883P0_19741220_CWA_439.
11. ↑ 11.0 11.1 11.2 11.3 O'Donnell, Frank (30 July 2004). "Britain's £1 trillion debt mountain – How many zeros is that?". The Scotsman. http://news.scotsman.com/latestnews/Britains-1-trillion-debt-mountain.2550147.jp.
12. ↑ "Who wants to be a trillionaire?" (in en-GB). BBC News. 7 May 2007. http://news.bbc.co.uk/2/hi/programmes/more_or_less/6625545.stm.
13. ↑ 13.0 13.1 13.2 Comrie, Bernard (24 March 1996). "billion:summary". Linguist List (Mailing list). Retrieved 24 July 2011.
14. ↑ 14.0 14.1 14.2 "Oxford Dictionaries: How many is a billion?". Oxford University Press. https://en.oxforddictionaries.com/explore/how-many-is-a-billion/.
15. ↑ "Oxford Dictionaries: Billion". Oxford University Press. http://oxforddictionaries.com/definition/billion.
16. ↑ 16.0 16.1 Nielsen, Ron (2006). The Little Green Handbook. Macmillan Publishers. p. 290. ISBN 978-0-312-42581-4. https://archive.org/details/littlegreenhandb00ronn/page/290.
17. ↑ 17.0 17.1 "Wortschatz-Lexikon: Milliarde" (in de). Universität Leipzig: Wortschatz-Lexikon. http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Milliarde.
18. ↑ 18.0 18.1 "Wortschatz-Lexikon: Billion" (in de). Universität Leipzig: Wortschatz-Lexikon. http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Billion.
19. ↑ 19.0 19.1 "Wortschatz-Lexikon: Billiarde" (in de). Universität Leipzig: Wortschatz-Lexikon. http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Billiarde.
20. ↑ 20.0 20.1 "Wortschatz-Lexikon: Trilliarde" (in de). Universität Leipzig: Wortschatz-Lexikon. http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Trilliarde.
21. ↑ 21.0 21.1 21.2 21.3 21.4 21.5 "Direttiva CEE / CEEA / CE 1994 n. 55, p.12" (in it). Italian Government. 21 November 1994. http://www.frareg.com/news/legislazione/ambiente/direttiva_1994_55_CE.pdf.
22. ↑ Adam, Jehan (1475) (in frm). Traicté en arismetique pour la practique par gectouers... (MS 3143). Paris: Bibliothèque Sainte-Geneviève.
23. ↑ "HOMMES DE SCIENCE, LIVRES DE SAVANTS A LA BIBLIOTHÈQUE SAINTE-GENEVIÈVE, Livres de savants II" (in fr). Traicté en arismetique pour la practique par gectouers…. Bibliothèque Sainte-Geneviève. 2005. http://www-bsg.univ-paris1.fr/ExposVirtuelles/exposvirtuellesreserves/sciences/savants2.htm.
24. ↑ Thorndike, Lynn (1926). "The Arithmetic of Jehan Adam, 1475 A.D". The American Mathematical Monthly (Mathematical Association of America) 1926 (January): 24–28. doi:10.2307/2298533.
25. ↑ 25.0 25.1 Chuquet, Nicolas (1880). "Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien" (in frm). Bulletino di Bibliographia e di Storia delle Scienze Matematische e Fisische (Bologna: Aristide Marre) XIII (1880): 593–594. ISSN 1123-5209. http://www.miakinen.net/vrac/nombres#lettres_zillions. Retrieved 17 July 2011.
26. ↑ Chuquet, Nicolas (1880). "Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien" (in frm). miakinen.net. http://www.miakinen.net/vrac/nombres#lettres_zillions.
27. ↑ Flegg, Graham (23–30 December 1976). "Tracing the origins of One, Two, Three.". New Scientist (Reed Business Information) 72 (1032): 747. ISSN 0262-4079. https://books.google.com/books?id=obHSBCxiJ1YC&pg=PA747. Retrieved 17 July 2011.
28. ↑ 28.0 28.1 Budaeus, Guilielmus (1516) (in la). De Asse et partibus eius Libri quinque. pp. folio 93.
29. ↑ Houck (1676). Arithmetic. Netherlands. p. 2.
30. ↑ Dictionnaire de l'académie françoise (4th ed.). Paris, France: Institut de France. 1762. p. 177. https://books.google.com/books?id=0oM-AAAAcAAJ&q=Dictionnaire+de+l'Académie+Française&pg=PA1.
31. ↑ Dictionnaire de l'Académie française (6th ed.). Paris, France. 1835. p. 189. http://portail.atilf.fr/cgi-bin/dico1look.pl?strippedhw=billion&dicoid=ACAD1835&headword=&dicoid=ACAD1835.
32. ↑ Dictionnaire de l'Académie française (7th ed.). Paris, France: Institut de France. 1877. p. 182. https://books.google.com/books?id=P2whAQAAMAAJ&q=Dictionnaire+de+l'Académie+Française&pg=PR23.
33. ↑ Dictionnaire de l'Académie française (8th ed.). Paris, France: Institut de France. 1932–1935. p. 144. http://portail.atilf.fr/cgi-bin/dico1look.pl?strippedhw=billion&headword=&docyear=ALL&dicoid=ACAD1932&articletype=1.
34. ↑ 34.0 34.1 "Resolution 6 of the 9th meeting of the CGPM (1948)". BIPM. http://www.bipm.org/en/CGPM/db/9/6/.
35. ↑ "Resolution 6 of the 10th meeting of the CGPM (1954)". BIPM. http://www.bipm.org/en/CGPM/db/10/6/.
36. ↑ The International System of Units (SI) (8 ed.). BIPM. May 2006. pp. 134 / 5.3.7 Stating values of dimensionless quantities, or quantities of dimension one. ISBN 92-822-2213-6. http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf. Retrieved 24 July 2011.
37. ↑ 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. https://www.nist.gov/manuscript-publication-search.cfm?pub_id=200349. Retrieved 13 September 2014.
38. ↑ 38.0 38.1 "Décret 61-501" (in fr). Journal Officiel (French Government): 4587 note 3a, and erratum on page 7572. 11 August 1961. http://www.ensmp.net/pdf/1961/decr-61-0501.pdf. Retrieved 31 January 2008.
39. ↑ 39.0 39.1 "RBA: Definition of billion". Reserve Bank of Australia. http://www.rba.gov.au/glossary/index.html?search=billion.
40. ↑ 40.0 40.1 "BBC News: Who wants to be a trillionaire?". BBC. 7 May 2007. http://news.bbc.co.uk/1/hi/programmes/more_or_less/6625545.stm.
41. ↑ 41.0 41.1 "billion". Cambridge Dictionaries Online. Cambridge University Press. http://dictionaries.cambridge.org/define.asp?key=billion*1+0&dict=A. Retrieved 21 August 2011.
42. ↑ 42.0 42.1 "trillion". Cambridge Dictionaries Online. Cambridge University Press. http://dictionaries.cambridge.org/define.asp?key=trillion*1+0&dict=A.
43. ↑ 43.0 43.1 "Al Jazem English-Arabic online dictionary: Billion". Al Jazem English-Arabic online dictionary. Encyclopædia Britannica. http://www.aljazem.com/en/billion.
44. ↑ 44.0 44.1 "Al Jazem English-Arabic online dictionary:Trillion". Al Jazem English-Arabic online dictionary. Encyclopædia Britannica. http://www.aljazem.com/en/trillion.
45. ↑ 45.0 45.1 Robson S. O. (Stuart O.), Singgih Wibisono, Yacinta Kurniasih. Javanese English dictionary Tuttle Publishing: 2002, ISBN 0-7946-0000-X, 821 pages
46. ↑ 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""
47. ↑ "De Geïntegreerde Taal-Bank: miljard" (in nl). Instituut voor Nederlandse Lexicologie. http://www.wnt.inl.nl/iWDB/search?actie=article&wdb=WFT&id=63043&lemmodern=miljard.
48. ↑ "De Geïntegreerde Taal-Bank: biljoen" (in nl). Instituut voor Nederlandse Lexicologie. http://gtb.inl.nl/iWDB/search?actie=article&wdb=WFT&id=8253&lemmodern=biljoen.
49. ↑ 49.0 49.1 "French Larousse: milliard" (in fr). Éditions Larousse. http://www.larousse.com/en/dictionaries/french/milliard.
50. ↑ 50.0 50.1 "French Larousse: billion" (in fr). Éditions Larousse. http://www.larousse.com/en/dictionaries/french/billion.
51. ↑ "billion" (in fr). Dictionnaire de l'Académie française (9th ed.). Académie française. 1992. http://atilf.atilf.fr/dendien/scripts/generic/cherche.exe?15;s=802200930;;. 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.".
52. ↑ 52.0 52.1 "Diccionario Panhispánico de Dudas: millardo" (in es). Real Academia Española. http://buscon.rae.es/dpdI/SrvltConsulta?lema=millardo.
53. ↑ 53.0 53.1 "Diccionario Panhispánico de Dudas: billon" (in es). Real Academia Española. http://buscon.rae.es/dpdI/SrvltConsulta?lema=billon.
54. ↑ "Diccionario de la lengua española" (in es). Real Academia Española. http://dle.rae.es/?id=5WQzD1r.
55. ↑ 55.0 55.1 Wennergren, Bertilo (8 March 2008). "Plena Manlibro de Esperanta Gramatiko" (in eo). http://bertilow.com/pmeg/.
56. ↑ 56.0 56.1 "Italian-English Larousse: bilione". Éditions Larousse. http://www.larousse.com/en/dictionaries/italian-english/bilione/5726.
57. ↑ Institutul de Lingvistică „Iorgu Iordan – Alexandru Rosetti" al Academiei Române (2012), Dicționarul explicativ al limbii române (ediția a II-a revăzută și adăugită), Editura Univers Enciclopedic Gold
58. ↑ "Scara numerică" (in ro). dexonline.ro. 2016. http://dexonline.ro/articol/Scara_numerică.
59. ↑ "Switzerland: Words and Phrases". TRAMsoft Gmbh. 29 August 2009. http://www.about.ch/culture/languages/words_n_phrases.html#numbers.
60. ↑ "Canadian government standards website". Canadian Government. 2010. http://btb.termiumplus.gc.ca/tpv2alpha/alpha-eng.html?lang=eng&i=&index=frt&__index=frt&srchtxt=billion&comencsrch.x=12&comencsrch.y=10.
61. ↑ "billion". Granddictionnaire.com. 13 May 2013. http://www.granddictionnaire.com/ficheOqlf.aspx?Id_Fiche=8872290.
62. ↑ "Taalkommissie se reaksie op biljoen, triljoen" (in af). Naspers: Media24. http://152.111.1.88/argief/berigte/beeld/2008/02/20/B1/14/01milbiltril.html.
63. ↑ "'Groen boek': mooiste, beste, gebruikersvriendelikste" (in af). Naspers:Media24. http://152.111.1.87/argief/berigte/dieburger/2009/07/13/SK/9/BBfpistorAWS.html.
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. https://books.google.com/books?id=pHiKycrLmEQC&q=crore lakh arab&pg=PA12. Retrieved 22 August 2011.
65. ↑ Foundalis, Harry. "Greek Numbers and Numerals (Ancient and Modern)". http://www.foundalis.com/lan/grknum.htm.

## External links

* BBC News article: "Is trillion the new billion?"
* Live-Counter.com: How to visualize large numbers:"

* v
* t
* e

Large numbers

Examples in
numerical order|

* Thousand
* Ten thousand
* Hundred thousand
* Million
* Ten million
* Hundred million
* Billion
* Trillion
* Quadrillion
* Quintillion
* Sextillion
* Septillion
* Octillion
* Nonillion
* Decillion
* Googol
* Googolplex
* Skewes's number
* Moser's number
* Graham's number
* TREE(3)
* SSCG(3)
* Rayo's number
* Transfinite numbers

Expression
methods|

| Notations|

* Scientific notation
* Knuth's up-arrow notation
* Conway chained arrow notation
* Steinhaus–Moser notation

|

Operators|

* Hyperoperation
* Tetration
* Pentation
* Ackermann function
* Bowers's operators
* Grzegorczyk hierarchy

Related
articles
(alphabetical order)

* Extended real number line
* Gigantic prime
* Indefinite and fictitious numbers
* Infinitesimal
* Largest known prime number
* List of numbers
* Long and short scales
* Number systems
* Number names
* Orders of magnitude
* Power of two
* Power of 10
* Sagan Unit
* Titanic prime

* Names
* History

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Long and short scales. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Long_and_short_scales&oldid=4230355"
*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template