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Encyclopedia > Long and short scales

The long and short scales are two 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 is 1 000 times greater than 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 is 1 000 000 times greater than the previous term: "billion" means "a million millions" (1012), "trillion" means "a million billions" (1018), and so on.

Note that the difference between the two scales grows as numbers get larger. The long-scale billion is a thousand times larger than the short-scale billion, but the long-scale trillion is a million times larger than the short-scale trillion, and so on. The English language is a West Germanic language that originates in England. ... One thousand million (1,000,000,000) is the natural number following 999,999,999 and preceding 1,000,000,001. ... One million million (1,000,000,000,000) is the natural number following 999,999,999,999 and preceding 1,000,000,000,001. ... One million million (1,000,000,000,000) is the natural number following 999,999,999,999 and preceding 1,000,000,000,001. ... Look up exa- in Wiktionary, the free dictionary. ...


For most of the 19th and 20th centuries, the United Kingdom uniformly used the long scale, while the United States of America used the short scale, so that the two systems were often referred to as "British" and "American" usage respectively. Today, the UK uses the short scale exclusively in official and mass media usage and, although some long-scale usage still continues, the terms "British" and "American" no longer reflect usage. Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999... Popular press redirects here; note that the University of Wisconsin Press publishes under the imprint The Popular Press. Mass media is a term used to denote a section of the media specifically envisioned and designed to reach a very large audience such as the population of a nation state. ...

Contents

Comparison

For a more extensive table, see names of large numbers. // Throughout this article, exponential or scientific notation is used. ...

 Value   Short Scale    Short Scale Logic   Long Scale   Long Scale Logic  
 10 0  =   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  (or 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  (or 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

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

  • short scale:  Billion is thousand times thousand 2  =  109Trillion is thousand times thousand 3  =  1012.
To get from one named order of magnitude to the next, multiply by a thousand.
  • long scale:  Million is million1  =  106Billion is million2  =  1012Trillion is million3  =  1018.
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 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. Milliard is a French-derived word meaning the number 1,000,000,000 (109; one thousand million or a megamillion). ...


Historical and language context

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 documents from 1900 used long scale values, which are different from current British short scale usage. Both scales were used in France and Italy at various times in their history, but these countries (and most other European countries) now officially use long scale. For other uses, see Europe (disambiguation). ...


In addition, apparently identical words in different languages may mean different values. For example, the French word 'billion' (1012) translates to the English word 'trillion' (usually 1012), not 'billion' (usually 109). However, the German word 'Billion' and the Dutch word 'biljoen' both refer to 1012. See Current usage below.


History

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"[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 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 1700s The short-scale meaning of the term "billion" was brought to the British American colonies.
Early 1800s Flag of France France widely converted to the short scale, and was followed by the Flag of the United States United States, 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 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. [4].
1961 Flag of France France confirmed their official usage of the long scale in the Journal Officiel (the official French Government gazette).

(Décret 61-501, page 4587, and note 3 and erratum on page 7572. (French) [5]) Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Jehan Adam was a French mathematician who flourished in the 15th century. ... Nicolas Chuquet (born 1445 (some sources say c. ... Estienne de La Roche (1470 - 1530) was a French mathematician Born in Lyon, the family of Estienne of the Rock, in addition to living in this city, has a property with Villefranche; having lived during its youth, Estienne is sometimes known under the name of Estienne de Villefranche. ... Estienne de La Roche (1470-1530) was a French mathematician. ... Jacques Peletier du Mans (1517 Le Mans – 1582 Paris) was a humanist, poet and mathematician of the French Renaissance. ... Milliard is a French-derived word meaning the number 1,000,000,000 (109; one thousand million or a megamillion). ... Guillaume Budé (Latin: Guglielmus Budaeus) (January 26, 1467 – August 23, 1540) was a French scholar. ... (16th century - 17th century - 18th century - more centuries) As a means of recording the passage of time, the 17th century was that century which lasted from 1601-1700. ... Synonyms (in ancient Greek, συν (syn) = plus and όνομα (onoma) = name) are different words with similar or identical meanings. ... (17th century - 18th century - 19th century - more centuries) As a means of recording the passage of time, the 18th century refers to the century that lasted from 1701 through 1800. ... Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... Henry Watson Fowler (10 March 1858 - 26 December 1933) was an English schoolmaster, lexicographer and commentator on usage, notable for both Fowlers Modern English Usage (first published 1926) and his work on the Concise Oxford Dictionary. ... One million million (1,000,000,000,000) is the natural number following 999,999,999,999 and preceding 1,000,000,000,001. ... One thousand million (1,000,000,000) is the natural number following 999,999,999 and preceding 1,000,000,001. ... The General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures (CGPM, never GCWM). ... The General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures (CGPM, never GCWM). ... “SI” redirects here. ... Image File history File links This is a lossless scalable vector image. ...

1974 Flag of the United Kingdom United Kingdom prime minister Harold Wilson explained to the House of Commons that UK government statistics would from then on use the short scale [6][7]. During the last quarter of 20th century, most other English-speaking countries ( Flag of Ireland Ireland Flag of Australia Australia New Zealand New Zealand Flag of South Africa 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.
1994 Flag of Italy Italy confirmed their official usage of the long scale.

(Direttiva CE 1994 n. 55, page 12 (Italian) [8]). Image File history File links Flag_of_the_United_Kingdom. ... This article is about the field of statistics. ... Image File history File links Flag_of_Ireland. ... Image File history File links This is a lossless scalable vector image. ... Image File history File links Flag_of_New_Zealand. ... Image File history File links Flag_of_South_Africa. ... Geneviève Guitel is a French mathematician. ... Image File history File links Flag_of_Italy. ...

Current usage

Long scale countries

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

Most countries and languages in the world use the traditional long scale, with many using 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:

Flag of Argentina Argentina (mil millones, billón)
Flag of Austria Austria (Milliarde, Billion)
Flag of Belgium Belgium (French: milliard, billion; Dutch: miljard, biljoen; German: Milliarde, Billion)
Flag of the Netherlands Netherlands (Miljard, Biljoen)
Flag of Canada Canada (French-speaking: milliard, billion)
Flag of Croatia Croatia (milijarda, bilijun)
Flag of the Czech Republic Czech Republic (miliarda, bilion)
Flag of Denmark Denmark (milliard, billion)
Flag of Finland Finland (miljardi, biljoona)
Flag of France France (milliard, billion)
Flag of Germany Germany (Milliarde, Billion)
Flag of Hungary Hungary (milliárd, billió or ezer milliárd)
Flag of Iceland Iceland (milljarður, billjón)
Flag of Israel Israel (milliard, )
Flag of Italy Italy (miliardo, )
Flag of Lithuania Lithuania (milijardas, )
Flag of Norway Norway (milliard, billion)
Flag of Poland Poland (miliard, bilion)
Flag of Portugal Portugal (mil milhões, bilião or bilhão)
Flag of Romania Romania (miliard, )
Flag of Serbia Serbia (milijarda милијарда, bilion Биллион)
Flag of Slovakia Slovakia (miliarda, bilión)
Flag of Slovenia Slovenia (miliarda, bilijon)
Flag of Spain Spain (Spanish: millardo or typ. mil millones, billón, Catalan: miliard or typ. mil milions, bilió)
Flag of Sweden Sweden (miljard, biljon)
Flag of Switzerland Switzerland (French: milliard, billion; German: Milliarde, Billion; Italian: miliardo, )
Flag of Uruguay Uruguay (mil millones or millar, billón)

Image File history File links Flag_of_Argentina. ... Image File history File links Flag_of_Austria. ... Image File history File links Flag_of_Belgium_(civil). ... Image File history File links Flag_of_the_Netherlands. ... Image File history File links This is a lossless scalable vector image. ... French (français, langue française) is one of the most important Romance languages, outnumbered in speakers only by Spanish and Portuguese. ... Image File history File links Flag_of_Croatia. ... Image File history File links Flag_of_the_Czech_Republic. ... Image File history File links Flag_of_Denmark. ... Image File history File links Flag_of_Finland. ... Image File history File links This is a lossless scalable vector image. ... Image File history File links Flag_of_Germany. ... Image File history File links Flag_of_Hungary. ... Image File history File links Flag_of_Iceland. ... Image File history File links Flag_of_Israel. ... Image File history File links Flag_of_Italy. ... Image File history File links Flag_of_Lithuania. ... Image File history File links Flag_of_Norway. ... Image File history File links Flag_of_Poland. ... Image File history File links Flag_of_Portugal. ... Image File history File links Flag_of_Romania. ... Image File history File links Flag_of_Serbia. ... Anthem Serbia() on the European continent() Capital (and largest city) Belgrade Official languages Serbian 1 Recognised regional languages Hungarian, Croatian, Slovak, Romanian, Rusyn 2 Albanian 3 Government Semi-presidential republic  -  President Boris Tadić  -  Prime Minister Vojislav KoÅ¡tunica Establishment  -  Formation 812   -  Kingdom established 1217   -  Empire established 1346   -  Independence lost to... Image File history File links Flag_of_Slovakia. ... Image File history File links Flag_of_Slovenia. ... Image File history File links Flag_of_Spain. ... Catalan IPA: (català IPA: or []) is a Romance language, the national language of Andorra, and a co-official language in the Spanish autonomous communities of Balearic Islands, Catalonia and Valencia , and in the city of LAlguer in the Italian island of Sardinia. ... Image File history File links Flag_of_Sweden. ... Image File history File links Flag_of_Switzerland. ... Image File history File links Flag_of_Uruguay. ...

Short scale countries

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

English language-speaking countries

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

Flag of Australia Australia
Flag of Canada Canada (English-speaking)
Flag of Ireland Ireland
New Zealand New Zealand
Flag of South Africa South Africa
Flag of the United Kingdom United Kingdom - albeit with residual usage of the long-scale
Flag of the United States United States

Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... Image File history File links Flag_of_Ireland. ... Image File history File links Flag_of_New_Zealand. ... Image File history File links Flag_of_South_Africa. ... Image File history File links Flag_of_the_United_Kingdom. ... Image File history File links This is a lossless scalable vector image. ...

Other languages and countries
Flag of Brazil Brazil, which despite speaking Portuguese, uses 109 = bilhão, 1012 = trilhão, etc.

Image File history File links Flag_of_Brazil. ...

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:

Flag of Bulgaria Bulgaria (miliard милиард)   [citation needed]
Flag of Iran Iran [citation needed]
Flag of Latvia Latvia [citation needed]
Flag of Russia Russia (miliard миллиард)
Flag of Turkey Turkey (milyar)

Image File history File links Flag_of_Bulgaria. ... Image File history File links Flag_of_Iran. ... Image File history File links Flag_of_Latvia. ... Image File history File links Flag_of_Russia. ... Image File history File links Flag_of_Turkey. ...

Short scale use but with other terminology
Flag of Greece Greece, which despite using the word εκατομμύριο ("hundred-myriad") for 106 continues with terms for 109 (δισεκατομμύριο, "bi-hundred-myriad"), 1012 (τρισεκατομμύριο, "tri-hundred-myriad"), 1015 (τετράκις εκατομμύριο, "tetra-hundred-myriad"), and so on.[9]

Image File history File links Flag_of_Greece. ...

Both long and short scales countries

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

Image File history File links Flag_of_Puerto_Rico. ... In the terminology of the United States insular areas, a commonwealth is an organized territory that has established with the Federal Government a more highly developed relationship, usually embodied in a written mutual agreement. ...

Neither short nor long scale countries

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

Flag of the People's Republic of China China - see Chinese large numbers. - which features symbols for all the myriads up to 10 44.
Flag of India India - see Indian numbering system - which is commonly used. For Indian English speakers see below.
Flag of Japan Japan - see Japanese numerals: powers of 10 - which uses myriads as in Chinese.
Flag of South Korea South Korea  Flag of North Korea North Korea - see Korean numerals - which uses a traditional myriad system for the larger numbers, with special words and symbols up to 10 48.

Image File history File links Flag_of_the_Peoples_Republic_of_China. ... Chinese numerals are characters for writing numbers in Chinese. ... Look up myriad in Wiktionary, the free dictionary. ... Image File history File links Flag_of_India. ... The traditional, ancient Indian numbering system, used today in India, Pakistan, Bangladesh,Nepal and Myanmar (Burma), is based on a unique grouping of 2 decimal places, rather than the 3 decimal places commonplace in the West (China, Korea, and Japan, for instance, use 4). ... Image File history File links Flag_of_Japan. ... The system of Japanese numerals is the system of number names used in the Japanese language. ... Image File history File links Flag_of_South_Korea. ... Image File history File links Flag_of_North_Korea. ... Korean language has two regularly used sets of numerals, Sino-Korean and native Korean For both native and Sino-Korean numerals, the teens (11 through 19) are represented by a combination of tens and the ones places. ...

Notes on current usage

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.

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.

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, use the short scale exclusively in all contexts[6]. Anyone using billion to mean 1012 in British English may be misunderstood. However, this short scale usage is not uniformly accepted and the "traditional usage" of a billion to mean 1012 is not unknown.
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). Before the recent widespread use of "billion" for 109, UK usage generally referred to thousand million rather than milliard.

The United Kingdom is a unitary state and a democratic constitutional monarchy. ... For other uses, see BBC (disambiguation). ... Popular press redirects here; note that the University of Wisconsin Press publishes under the imprint The Popular Press. Mass media is a term used to denote a section of the media specifically envisioned and designed to reach a very large audience such as the population of a nation state. ...

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 [10]. 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.

Indian usage
Like the other English speaking countries, India also is currently strongly influenced by the standard U.S. short scale use. However (outside of financial media) the use of "billion" by Indian English speakers highly depends on their educational background. Some Indians may continue to use the traditional British long scale. In everyday life, Indians largely use their own system - for instance, Indian English commonly use the words lakh to denote 100 thousand, and crore to denote ten million (i.e. 100 lakhs).

The traditional, ancient Indian numbering system, used today in India, Pakistan, Bangladesh,Nepal and Myanmar (Burma), is based on a unique grouping of 2 decimal places, rather than the 3 decimal places commonplace in the West (China, Korea, and Japan, for instance, use 4). ... Indian English refers to the dialects or varieties of English spoken primarily in India, and/or by first generation Indian diaspora elsewhere in the world. ... A lakh (Hindi: लाख, Urdu: Ù„Ú©Ú¾, Bengali: , Tamil : இலட்சம்) is a unit in the Indian numbering system, widely used both in official and other contexts in Bangladesh, India, Sri Lanka, and Pakistan. ... A crore is a unit in the Indian numbering system, still widely used in Bangladesh, India, Myanmar, Sri Lanka, and Pakistan. ...

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 much more common [11].


Esperanto language 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.   is the most widely spoken constructed international auxiliary language. ...


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". Look up budget in Wiktionary, the free dictionary. ... Look up unit in Wiktionary, the free dictionary. ... Government debt (public debt, national debt) is money owed by government, at any level (central government, federal government, national government, municipal government, local government, regional government). ... For other uses, see Euro (disambiguation). ...


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. The International System of Units (SI) is independent of whichever scale is being used. In information technology contexts, these SI prefixes are sometimes used as powers of 210 (= 1024) instead of powers of 103 (= 1000), although there is a binary prefix system that can eliminate this ambiguity.

Scientific notation, also known as standard form, is a notation for writing numbers that is often used by scientists and mathematicians to make it easier to write large and small numbers. ... Engineering notation is scientific notation in which the powers of ten are limited to those where the exponent is a multiple of three, i. ... An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple. ... Look up giga- in Wiktionary, the free dictionary. ... Tera (symbol: T) is a prefix in the SI system of units denoting 1012, or 1 000 000 000 000. ... “SI” redirects here. ... // In computing, binary prefixes can be used to quantify large numbers where powers of two are more useful than powers of ten (such as computer memory sizes). ...

See also

// Throughout this article, exponential or scientific notation is used. ... This list compares various sizes of positive numbers, including counts of things, dimensionless numbers and probabilities. ... Look up billion in Wiktionary, the free dictionary. ... Trillion may mean either of the two numbers (see long and short scales for more detail): 1,000,000,000,000 (one million million; ) - increasingly common meaning in English language usage. ... Milliard is a French-derived word meaning the number 1,000,000,000 (109; one thousand million or a megamillion). ... Look up myriad in Wiktionary, the free dictionary. ... One thousand million (1,000,000,000) is the natural number following 999,999,999 and preceding 1,000,000,001. ... Jacques Peletier du Mans (1517 Le Mans – 1582 Paris) was a humanist, poet and mathematician of the French Renaissance. ... Nicolas Chuquet (born 1445 (some sources say c. ...

References

  1. ^ The first recorded use of the terms échelle courte and échelle longue was by the French mathematician Geneviève Guitel in 1975.
    See pp. 51–52 of Histoire comparée des numérations écrites, Geneviève Guitel, Éd. Flammarion, Paris, 1975 and also the chapter
    "Les grands nombres en numération parlée (État actuel de la question)", i.e. "The large numbers in oral numeration (Present state of the question)", pp. 566–574.
  2. ^ Nicolas Chuquet's manuscript   published by www.miakinen.net. (French)
  3. ^ Nicolas Chuquet's chapter  The names of great numbers in "Triparty en la science des nombres" (ISSN 9012-9458), transcription by Florencetime.net. (Widely in French.)
  4. ^ http://www.bipm.org/en/si/si_brochure/chapter5/5-3-7.html
  5. ^ Décret 61-501, page 4587, i.e. page 14 of 15 in this reference pdf and note 3 and erratum on page 7572, the last page of the pdf. (French)
  6. ^ a b The Scotsman newspaper - 30 July 2004 article referencing Harold Wilson's 1974 decision to change numbering systems
  7. ^ "Names for large numbers", Russ Rowlett, University of North Carolina, 1 Nov. 2001 - also contains a reference to Harold Wilson's 1974 decision. Otherwise, this article is an unadopted 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 ambiguous terms American and European instead of Short and Long Scale respectively. Note that North America uses both scales depending on the language (American English and Canadian English vs Canadian-French); South America uses both scales (Brazilian Portuguese vs Spanish) and Europe uses both scales (British English and Irish English vs most languages of continental Europe).
  8. ^ Direttiva CE 1994 n. 55, page 12). (Italian)
  9. ^ Greek Numbers and Numerals (Ancient and Modern), Harry Foundalis, part of a Greek tutorial at foundalis.com; accessed May 20, 2007.
  10. ^ http://www.finance.gov.au/publications/pdf/prelims.pdf
  11. ^ Federico Peiretti ("Archimede e i grandi numeri") (Italian)

Geneviève Guitel is a French mathematician. ... is the 211th day of the year (212th in leap years) in the Gregorian calendar. ... Year 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... Look up giga- in Wiktionary, the free dictionary. ... is the 140th day of the year (141st in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st Century. ...

External links

Modern UK usage

Traditional UK usage


  Results from FactBites:
 
Long and short scales | English | Dictionary & Translation by Babylon (140 words)
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.
Long and short scales - Wikipedia, the free encyclopedia (1761 words)
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.
  More results at FactBites »


 

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