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The long and short scales are two of the several different numerical systems used throughout the world:

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

Long scale is the English translation of the French term échelle longue. It refers to a system of numeric names in which every new term greater than million is 1,000,000 times the previous term: "billion" (from bi and million) means "a million to the power of two" or "a million millions" (10¹²), "trillion" (from tri and million) means "a million to the power of three" or "a million billions" (10¹⁸), and so on.

Note that the difference between the two scales grows as numbers get larger. Million is the same in both scales, but the long-scale billion is a thousand times larger than the short-scale billion, the long-scale trillion is a million times larger than the short-scale trillion, and so on.

For most of the 19th and 20th centuries, the United Kingdom uniformly used the long scale,^[2] while the United States of America used the short scale,^[2] so that usage of the two systems was often referred to as "British" and "American" respectively. In 1974 the government of the UK abandoned the long scale, so that the UK now exclusively applies the short scale interpretation in mass media and official usage.^[3][4][5][6] Although some residual usage of the long scale continues in the UK, the phrases "British usage" and "American usage" are no longer accurate or helpful characterizations. The two systems can be a subject of misunderstanding or controversy and can arouse emotion. Usage changes can evoke resentment in adherents to the older system, while national differences of any kind can acquire patriotic overtones. ^[7]

Other systems include the Chinese numbering system, Indian numbering system, Japanese numbering system and the Korean numbering system.

Contents 1 Comparison 2 History 2.1 Timeline 3 Current usage 3.1 Short scale countries / regions 3.1.1 English language-speaking countries / regions 3.1.2 Other languages and countries 3.1.3 Short scale use with long scale milliard 3.1.4 Short scale use but with other terminology 3.2 Long scale countries 3.3 Both long and short scales countries 3.4 Neither short nor long scale countries 4 Notes on current usage 4.1 English language countries 4.1.1 UK usage 4.1.2 US usage 4.1.3 Australian usage 4.1.4 Canadian usage 4.1.5 South African Usage 4.1.6 Indian, Pakistani & Bangladeshi usage 4.2 Italian language usage 4.3 Esperanto language usage 4.4 Presence on all continents 4.5 Use of "thousand milliard" 5 Alternative approaches 6 See also 7 References 8 External links 8.1 Current UK usage 8.2 Traditional UK usage

[edit] Comparison

For a more extensive table, see names of large numbers.

Value	Value Expanded	Short Scale	Short Scale Logic	Long Scale	Long Scale Logic
10 0  =	1	one	1,000 1 - 1	one	1,000,000  0.0
10 3  =	1,000	thousand	1,000 1 + 0	thousand	1,000,000  0.5
10 6  =	1,000,000	million	1,000 1 + 1	million	1,000,000  1.0
10 9  =	1,000,000,000	billion	1,000 1 + 2	thousand million  (sometimes milliard)	1,000,000  1.5
1012  =	1,000,000,000,000	trillion	1,000 1 + 3	billion	1,000,000  2.0
1015  =	1,000,000,000,000,000	quadrillion	1,000 1 + 4	thousand billion  (sometimes billiard)	1,000,000  2.5
1018  =	1,000,000,000,000,000,000	quintillion	1,000 1 + 5	trillion	1,000,000  3.0
1021  =	1,000,000,000,000,000,000,000	sextillion	1,000 1 + 6	thousand trillion  (sometimes trilliard)	1,000,000  3.5

Bi refers to 2 and tri refers to 3, etc. The relationship between the names and the corresponding numbers is as follows.

Short scale:	Million is thousand × (thousand)1  =  106;   Billion is thousand × (thousand)2  =  109;   Trillion is thousand × (thousand)3  =  1012; etc.
	To get from one named order of magnitude to the next, multiply by a thousand.
Long Scale:	Million is (million)1  =  106;   Billion is (million)2  =  1012;   Trillion is (million)3  =  1018; etc.
	To get from one named order of magnitude to the next, multiply by a million. In other words, a billion (bi / two) has twice as many zeros as a million, and a trillion (tri / three) has three times as many zeros as a million, etc.

The word "milliard", or its translation, is found in European languages and can be used for 10⁹. However, it is unknown in American English, which uses billion, and not used in British English, which preferred to use 'thousand million' before the current usage of 'billion'. The financial term "yard", which derives from "milliard", is used on financial markets, as it is unambiguous, unlike "billion". Likewise, some long scale countries use a word similar to billiard for a thousand long scale billions (i.e. 10¹⁵), a word similar to trilliard for a thousand long scale trillions (i.e. 10²¹), etc.

[edit] History

The existence of the different scales means that care must be taken when comparing large numbers between languages or countries, or when using 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 used both systems at various times in their history. Nowadays, the United Kingdom officially uses the short scale, but France and Italy (and most other European countries) officially use the long scale. The French word billion, the German word Billion, the Dutch word biljoen, the Swedish word biljon, the Finnish word biljoona, the Danish word billion, the Spanish word billón and the Portuguese word bilião all refer to 10¹², being long scale terms. However, each of these words translates to the English word "trillion" (10¹² in the short scale), and not "billion" (10⁹ in the short scale). On the other hand, the Brazilian Portuguese word bilhão (note the alternate spelling to the European Portuguese variant) and the Welsh word biliwn both refer to 10⁹, being short scale terms. Each of these words translate to the English word "billion" (10⁹ in the short scale). See Current usage below.

[edit] Timeline

1475	French mathematician Jehan Adam recorded the words "bymillion" and "trimillion" as meaning 1012 and 1018 respectively.
1484	French mathematician Nicolas Chuquet, in his article "Triparty en la science des nombres",[8] [9] used the words byllion, tryllion, quadrillion, quyllion, sixlion, septyllion, ottyllion, and nonyllion to refer to 1012, 1018, etc. Chuquet's work was not published until the 1870s, but most of it was copied without attribution by Estienne de La Roche and published in his 1520 book, L'arismetique.
1549	Jacques Peletier used the name milliard (“milliart”) for "Million de Millions", i.e. 1012. He attributed this meaning to earlier usage by Guillaume Budé (1467-1540), a French scholar.
During 17th century	The traditional six-digit groups were split up into three-digit groups. In France and Italy, some scientists then began using "billion" to mean 109. The majority either continued to say "thousand million" or used the Peletier term, milliard, to mean "thousand million", instead of "million of millions". The word milliard was used in England but was widely adopted in France, Germany, Italy and the rest of Europe, for those keeping Chuquet's original long scale billion.
Mid 18th century	The short-scale meaning of the term "billion" was brought to the British American colonies.
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 "a now obsolete system".
1926	H. W. Fowler's A Dictionary of Modern English Usage 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." [2]
1948	The 9th General Conference on Weights and Measures proposed the universal use of the long scale, inviting the short scale countries to return or convert. The proposal was considered but not adopted.
1960	The 11th General Conference on Weights and Measures adopted the International System of Units (SI), with its own set of numeric prefixes. 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. [10].
1961	The French Government confirmed their official usage of the long scale in the Journal Officiel (the official French Government gazette). [11]
1974	British prime minister Harold Wilson explained in a written answer to the House of Commons that UK government statistics would from then on use the short scale. Hansard, for the 20 December 1974, reported it: "Mr. Maxwell-Hyslop asked the Prime Minister whether he will make it the practice of his administration that when Ministers employ the word 'billion' in any official speeches, documents, or answers to Parliamentary Questions, they will, to avoid confusion, only do so in its British meaning of 1 million million and not in the sense in which it is used in the United States of America, which uses the term 'billion' to mean 1,000 million. The Prime Minister: No. The word 'billion' is now used internationally to mean 1,000 million and it would be confusing if British Ministers were to use it in any other sense. I accept that it could still be interpreted in this country as 1 million million and I shall ask my colleagues to ensure that, if they do use it, there should be no ambiguity as to its meaning."[3][4][12] During the last quarter of 20th century, most other English-speaking countries (Ireland, Australia, New Zealand, and South Africa) followed this lead and switched to the short scale use. However, in all these countries, some limited long scale use persists and the official status of the short scale use is not clear.
1975	French mathematician Geneviève Guitel introduced the terms échelle courte (short scale) and échelle longue (long scale) to refer to the two numbering systems. [1]
1994	The Italian government confirmed their official usage of the long scale [13].

The origin of the word "million" seems to derive from the Old French Milion, thought to derive from Old Italian milione, an intensification of mille, a thousand. That is, a "million" is a "big thousand", much as "1728" (a dozen gross) is a "great gross".

[edit] Current usage

[edit] Short scale countries / regions

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

[edit] English language-speaking countries / regions

Most English-language countries use the short scale. For example:

[edit] Other languages and countries

[edit] Short scale use with long scale milliard

Some countries adopted the short scale for the seldom-occurring higher numbers (such as 10¹²), but kept the traditional word "milliard" instead of the short-scale "billion". Countries that adopt this usage include:

[edit] Short scale use but with other terminology

 Greece (εκατομμύριο ekatommyrio "hundred-myriad" = 10⁶; δισεκατομμύριο disekatommyrio "bi-hundred-myriad" = 10⁹; τρισεκατομμύριο trisekatommyrio "tri-hundred-myriad" = 10¹²; τετράκις εκατομμύριο tetrakis ekatommyrio "tetra-hundred-myriad" = 10¹⁵, and so on.) ^[16]

[edit] Long scale countries

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

The traditional long scale is used by most Continental European countries and by most other countries whose languages derive from Continental Europe (with the notable exceptions of Greece and Brazil). Many of these countries use a word similar to milliard to mean 10⁹, and/or a word similar to billion to mean 10¹². Some examples of long scale use, and the words used for 10⁹ and 10¹², are:

[edit] Both long and short scales countries

 Canada – Canadian English language uses the Short Scale (billion = 10⁹, trillion = 10¹²); Canadian French language uses the Long Scale (milliard = 10⁹, billion = 10¹²).

 Puerto Rico – a Spanish-speaking US Commonwealth territory, generally uses short scale (billón = 10⁹, trillón = 10¹²) in economic and technical matters, but the long scale (millardo or mil millones = 10⁹, billón = 10¹²) is used in publications intended for a Latin American audience outside Puerto Rico.

 South Africa – South African English language uses the Short Scale (billion = 10⁹, trillion = 10¹²); Afrikaans language uses the Long Scale (miljard = 10⁹, biljoen = 10¹²).

[edit] Neither short nor long scale countries

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

Country	Numbering system	Notes
China	Modern Chinese large numbers.	Uses a traditional myriad system for the larger numbers, with special words and symbols up to 10 88.
India,  Pakistan and  Bangladesh	Indian numbering system	For everyday use, but short or long scale may also be in use; see below.
Japan	Japanese numerals: powers of 10	Uses a traditional myriad system for the larger numbers, with special words and symbols up to at least 10 68.
South Korea  North Korea	Korean numerals	Uses a traditional myriad system for the larger numbers, with special words and symbols up to 10 48.

[edit] Notes on current usage

[edit] English language countries

Apart from the United States, the long scale was used for centuries in many English language countries before being superseded in recent times by short scale usage. Because of this history, some long scale use persists and the official status of the short scale in these countries is sometimes obscure.

[edit] UK usage

"Billion" has meant 10⁹ in most sectors of official published writing for many years now. The UK government, BBC, and most other broadcast or published mass media, have used the short scale exclusively in all contexts since the mid 1970s. ^[3][4][5][6] Use of billion in British English can be ambiguous.

Before the widespread use of "billion" for 10⁹, UK usage generally referred to thousand million rather than milliard^[18][19]. The long scale term "milliard", for 10⁹, is obsolete in British English (though its derivation "yard" is still used as slang in the London money, foreign exchange and bond markets).

[edit] US usage

In the United States of America, the short scale has been taught in school since the early 19th century. It is therefore used exclusively.

[edit] Australian usage

In Australia, some documents use the term thousand million for 10⁹ in cases where two amounts are being compared using a common unit of one 'million'. As of 1999, the Australian Government's financial department did not consider short scale to be standard, but used it occasionally. The current recommendation by the Australian Department of Finance and Administration (formerly known as AusInfo), and the legal definition, is the short scale. Education, media outlets, and literature all use the short scale in line with other English-speaking countries.

[edit] Canadian usage

Since Canada uses both the Long scale (in French) and the Short scale (in English), the chance for ambiguity is rife.

[edit] South African Usage

Since South Africa uses both the Long scale (in Afrikaans) and the Short scale (in English), the chance for ambiguity is rife. Some Afrikaans publications briefly attempted usage of the "American System" but that has led to comment in the papers ^[20] and has been disparaged by the "Taalkommissie" (The Afrikaans Language Commission of the South African Academy of Science and Art) ^[21] and has thus, to most appearances, been abandoned.

[edit] Indian, Pakistani & Bangladeshi usage

Outside of financial media, the use of "billion" by Indian & Pakistani English speakers highly depends on their educational background. Some may continue to use the traditional British long scale. In everyday life, Indian & Pakistanis largely use their own common number system, commonly referred to as Indian numbering system - for instance, Bangladeshi, Pakistani & Indian English commonly use the words lakh to denote 100 thousand, and crore to denote ten million (i.e. 100 lakhs).

[edit] Italian language usage

Italy – with France – was one of the two European countries partially converted to the short scale during the 19th century, but returned to the original long scale in 20th century.

In Italian, the word bilione officially means 10¹². Colloquially, bilione can mean both 10⁹ and 10¹²; trilione both 10¹² and (rarer) 10¹⁸ and so on.^{[citation needed]} Therefore, in order to avoid ambiguity, they are seldom used. Forms such as mille miliardi (a thousand milliards) for 10¹², un milione di miliardi for 10¹⁵, un miliardo di miliardi for 10¹⁸, mille miliardi di miliardi for 10²¹ are more common. ^[22]

[edit] Esperanto language usage

The Esperanto words biliono, triliono etc. used to be ambiguous, and both long or short scale were used and presented in dictionaries. The current edition of the main Esperanto dictionary PIV however recommends the long scale meanings, as does the grammar PMEG. 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 numeral indicating the power of a million, e.g. duiliono (from du meaning "two") = biliono (10¹²); triiliono = triliono (10¹⁸), etc. Miliardo is an unambiguous term for 10⁹.

[edit] Presence on all continents

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

Continent	Short scale usage	Long scale usage
Africa	South African English	Afrikaans
North America	American English and Canadian English	Canadian French
South America	Brazilian Portuguese	Spanish
Europe	British English, Hiberno-English and Welsh	most languages of continental Europe

[edit] Use of "thousand milliard"

In those countries using the term "milliard", the term "thousand milliard" is occasionally used, but only in budgetary contexts. One milliard currency units has become the major budgetary unit, as in the national debt of Germany at the end of 2004 was about 1418 milliard euros. In all other contexts in these same countries, 10¹² is always termed "billion" and not "thousand milliard".

[edit] Alternative approaches

Unambiguous ways of identifying large numbers include:

• In written communications, the simplest solution for moderately large numbers is simply to write the full amount- i.e., 1,000,000,000,000 rather than, say, 1 trillion (short scale) or 1 billion (long scale).
• Combinations of the unambiguous word 'million', for example: 10⁹ = "one thousand million"; 10¹² = "one million million". This becomes rather unwieldy for numbers above 10¹².
• Combination of numbers with more than 3 digits with million, as in 15,300 million.
• Scientific notation (standard form), including its engineering notation variant, for example 10⁹, 10¹², or in writing using the computer programming notation (1e9, 1e12, etc). This is the most common practice among scientists and mathematicians, and is both unambiguous and convenient.
• SI prefixes, for example, giga for 10⁹ and tera for 10¹². The International System of Units (SI) is independent of whichever scale is being used.

[edit] See also

[edit] References

[edit] External links

[edit] Current UK usage

• "BILLION (DEFINITION)". Hansard. http://hansard.millbanksystems.com/written_answers/1974/dec/20/billion-definition#S5CV0883P0_19741220_CWA_439.  - the official Hansard report of 20 Dec 1974 when Harold Wilson defined 'Billion' for the UK Government.
• "Who wants to be a trillionaire?". BBC. http://news.bbc.co.uk/1/hi/programmes/more_or_less/6625545.stm.  - a 2007 BBC page on actual common media usage of trillion.
• "Linguist List 7.451". http://www.linguistlist.org/issues/7/7-451.html. - A 1996 email list message, comparing the two scales usage in different languages.

[edit] Traditional UK usage

• "AskOxford: How many is a billion?". http://www.askoxford.com/asktheexperts/faq/aboutwords/billion?view=uk.  - a traditional UK viewpoint.
• "Million, Billion, Trillion ...". http://www.jimloy.com/math/billion.htm.  - a 1999 webpage comparing the long and short scale numbers, which only considers traditional UK numbering.