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Short scale is the English translation of the French term échelle courte, which designates a system of numeric names in which the word billion means a thousand millions.

Long scale is the English translation of the French term échelle longue, which designates a system of numeric names in which the word billion means a million millions.

For most of the nineteenth and twentieth centuries, the United Kingdom uniformly used the long scale, while the United States of America used the short scale, so the two systems were often (and accurately at that time) referred to as "British" and "American" usage, respectively. However, today the United Kingdom uses the short scale so widely that the term "British usage" is no longer an appropriate phrase.

Both systems have been used in France at various times in history, but France has now settled with the long scale, in common with most other European countries.

Usage note: some articles use the terms long and short scale^[1] – although not presently standard terms in English – because they are unambiguous and easily understood.

Contents 1 Comparison 2 History 3 Current usage 3.1 Neither short nor long scale countries 3.2 Short scale countries 3.2.1 English-speaking countries 3.2.2 Other countries 3.2.2.1 with milliard use 3.2.2.2 without milliard use 3.3 Long scale countries 3.3.1 Most other countries 3.4 Notes 3.4.1 Use of "thousand milliard" 3.4.2 Italian usage 3.4.3 English-speaking countries 3.4.3.1 US usage 3.4.3.2 Elsewhere 3.4.3.2.1 UK usage 3.4.3.2.2 Australian usage 3.4.3.2.3 Indian usage 3.4.4 Esperanto usage 4 Alternative approaches 5 References

[edit] Comparison

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

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

Since bi refers to 2 and tri refers to 3, the logic in the names is:

• short scale:  Billion is thousand times thousand ²  =  10 ⁹.  Trillion is thousand times thousand ³  =  10 ¹².

To get from one named order of magnitude to the next, multiply by a thousand.

• long scale:  Million is million ¹  =  10 ⁶.  Billion is million ²  =  10 ¹².  Trillion is million ³  =  10 ¹⁸.

To get from one named order of magnitude to the next, multiply by a million.

The old word "milliard", also found in many other languages, can be used for 10⁹ but is unknown in American English and not used in British English - however, 'Yard', which derives from 'milliard', is used on financial markets, as unlike 'billion' it is unambiguous.

[edit] History

1475	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" [2] [3], 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 1600s	The traditional six-digit-groups were split up. Therefore, in France and Italy, some scientists began using "billion" to mean 109. The majority either continued to say "thousand million", even with the three-digit-groups, or started using the Peletier term, milliard, as a synonym for "thousand million". This word was widely adopted in England, Germany, and the rest of Europe, including France and Italy, for those keeping Chuquet's original long scale billion.
Mid 1700s	The short-scale meaning of the term "billion" was brought to the British American colonies.
Early 1800s	France widely converted to the short scale, and was followed by the USA, 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 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."
1948	The General Conference on Weights and Measures proposed the universal use of the long scale, inviting the short scale countries to return.
1961	The Journal Officiel (the official French gazette) confirmed the official French use of the long scale (Décret 61-501, page 4587, note 3 and erratum on page 7572).
1974	British prime minister Harold Wilson explained to the House of Commons that UK government statistics would from now on use the short scale. [4] During the last quarter of 20th c., most other English-speaking countries 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.
1994	The Italian government officially confirmed the long scale. (Direttiva CE 1994 n. 55, page 12).

[edit] Current usage

[edit] Neither short nor long scale countries

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

• China - see Chinese large numbers.  which features symbols for all the myriads up to 10 ⁴⁴.
• India - see Indian numbering system  which is commonly used. For Indian English speakers see below.
• Japan - see Japanese numerals  Particular number names exist up to a billion  ^[1], next to a myriad system for the higher numbers  ^[2].
• Korea - see Korean numerals  which uses a traditional myriad system for the larger numbers, with special words and symbols up to 10 ⁴⁸.
• Greece - see Greek numerals  which uses 10⁹ = disekatommyrio ("bi-hundred-myriad"), 10¹² = trisekatommyrio, ("tri-hundred-myriad"), etc.

[edit] Short scale countries

[edit] English-speaking countries

Most English-speaking countries currently use the Short Scale, for example:

• U.S.A.
• English-speaking Canada
• United Kingdom
• Ireland
• Australia

[edit] Other countries

[edit] with milliard use

• Russia, миллиард (milliard) in Russian, where 10⁹ is commonly called "milliard", actually a long scale term, but the short scale is used for 10¹² and above
• Turkey, milyar in Turkish, where 10⁹ is commonly called "milliard", actually a long scale term, but the short scale is used for 10¹² and above
• Denmark, milliard in Danish, where 10⁹ is commonly called "milliard", actually a long scale term, but the short scale is used for 10¹² and above
• Bulgaria, милиард in Bulgarian, where 10⁹ is commonly called "milliard", actually a long scale term, but the short scale is used for 10¹² and above

[edit] without milliard use

• Brazil, which despite speaking a variant of Portuguese, uses 10⁹ = bilhão, 10¹² = trilhão, etc.
• Puerto Rico, a Spanish-speaking US territory, generally uses Short Scale (10⁹ = billón, 10¹² = trillón) in economic and technical matters, but the Long Scale is used publications intended for a Latin American audience outside Puerto Rico.

[edit] Long scale countries

[edit] Most other countries

Examples:

Milliard:  French, Danish and Norwegian milliard, German Milliarde, Dutch miljard, Hungarian milliárd, Hebrew milliard, Spanish millardo, but more frequently one says "mil millones", Italian miliardo, Polish miliard, Swedish miljard (or less common milliard), Finnish miljardi, Latvian miljards, Czech miliarda, Romanian miliard and Slovenian, Croatian, Serbian milijarda and Icelandic milljarður  - all equal 10⁹.

Billion:  French, Norwegian and Danish billion, German Billion, Dutch biljoen, Hungarian billió, Spanish billón, Polish and Serbian bilion, Swedish biljon (or less common billion), Finnish biljoona, Croatian bilijun, Portuguese (Portugal) bilião, Slovenian bilijon, Icelandic billjón  - all equal 10¹².

[edit] Notes

[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] Italian 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, hardly anybody uses them. 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 much more common.

[edit] English-speaking countries

[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] Elsewhere

In all other English-speaking countries, the long scale was used for centuries. Because of this, some long scale use persists and the official status of the short scale use in these countries is therefore obscure.

[edit] UK usage

The term "milliard" is now obsolete in British English (though its derivation "yard" is still used as slang in the London money, foreign exchange and bond markets) and "billion" has meant nothing except 10⁹ in all published writing for many years now. Both the UK government and the BBC use the short scale exclusively in all contexts. Anyone using billion to mean 10¹² in British English is likely to be misunderstood.

However, some long scale understanding still persists, and not only among older people. As numbers this large are rare in everyday life, a significant proportion of lay readers will interpret "billion" as 10¹² ("a million million"), even if they are young enough to have been taught otherwise at school.

For the above reasons, avoiding the words "billion", "trillion" etc. may be advisable when writing for the general public.

[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 [5]. 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] Indian usage

Like the other English speaking countries, also India is currently strongly influenced by the usual U.S. short scale use. However – outside of financial media – the use of Indian English speakers highly depends on their education background. Many Indians may continue to use the traditional British long scale. In everyday life, Indians largely use their own system.

[edit] Esperanto usage

The official Esperanto words biliono, triliono etc. are ambiguous, and the inherently international nature of Esperanto communication compounds the problem by preventing any national presumption in favour of long or short scale. Ambiguity may be avoided by the use of the unofficial but generally-recognised suffix -iliono appended to a numeral indicating the power of a million, e.g. duiliono (from du meaning "two") = (10⁶)² = 10¹², triiliono = 10¹⁸, etc. Miliardo is an unambiguous term for 10⁹.

[edit] Alternative approaches

Unambiguous ways of identifying large numbers include:

• 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. In information technology contexts, these SI prefixes are sometimes used as powers of 2¹⁰ (= 1024) instead of powers of 10³ (= 1000) , but there is an attempt at introducing a binary prefix system to eliminate this ambiguity.

[edit] References

• [1] ↑  The first attested use of the terms échelle courte – échelle longue was by the French mathematician Geneviève Guitel in "Histoire comparée des numérations écrites", Geneviève Guitel, Éd. Flammarion, Paris, 1975, p. 51-52, also p. 566-574, the chapter "Les grands nombres en numération parlée" (English: The large numbers in oral numeration).
• [2] ↑  Respective mention in Nicolas Chuquet's manuscript published by www.miakinen.net.
• [3] ↑  Entire transcription − by florencetime.net − of Nicolas Chuquet's chapter concerning the names of great numbers in "Triparty en la science des nombres" (ISSN 9012-9458).
• Referencing 1974 decision by Harold Wilson to change numbering systems, Scotsman, 30 July 2004
• Names for large numbers, Russ Rowlett, University of North Carolina, 1 Nov. 2001. (proposal for new names in the short scale system: it replaces billion by "gillion", cf. giga, then it uses greek prefixes. Rowlett's proposal used the terms American and European instead of Short and Long Scale respectively. Note that North America uses both long and short scales depending on the language, English or Canadian-French; and Europe uses both, the long scale in most countries of continental Europe, short scale is currently used in the United Kingdom and Ireland.)
• AskOxford: How many is a billion?.de:Lange und kurze Leiter

fr:Échelles longue et courte la:Scalae longae et breves nl:Korte en lange schaalverdeling ru:Системы наименования чисел zh:数量命名中的级差