From Surf Wiki (app.surf) — the open knowledge base

Long and short scales

Two meanings of "billion" and "trillion"

Summary

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. |author-link= Geneviève Guitel |author-link= Geneviève Guitel 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. 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. 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.

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.

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, |access-date= 28 July 2011 Methods that are better at longer numbers include:

Scientific notation (for example 1.2), or its engineering notation variant (for example 12), 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). 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. |access-date= 19 November 2025

History

Although this situation has been developing since the 1200s, the first recorded use of the terms short scale () and long scale () was by the French mathematician Geneviève Guitel in 1975.

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. 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,{{cite book |access-date= 26 April 2014 |author-link= Henry Watson Fowler whereas the United States used the short scale, 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, |access-date= 2 April 2009}} and it is used for all official purposes. |access-date= 31 January 2008}} |author-link= Bernard Comrie |mailing-list= Linguist List |access-date= 24 July 2011}} |archive-url= https://web.archive.org/web/20170112163426/https://en.oxforddictionaries.com/explore/how-many-is-a-billion |url-status= dead |archive-date= 12 January 2017 |access-date= 7 May 2018}} |archive-url= https://web.archive.org/web/20110811080212/http://oxforddictionaries.com/definition/billion |url-status= dead |archive-date= 11 August 2011 |access-date= 24 July 2011}} |url-access= registration

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. 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. Some of these countries, but not all, introduced new words billiard, trilliard, etc. as intermediate terms. 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. 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. |author-link= David Eugene Smith |orig-year= first published 1925

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. |access-date= 24 July 2011}}

;Timeline

Date	Event
13th century	The word million was not used in any language before the 13th century. The monk and polymath Maximus Planudes (–1305) was among the first recorded users of the word to document Mediterranean trade between Constantinople and Italian states. 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	[[File:Piers Plowman.jpg	thumb	upright	]] The word million entered the English language. One of the earliest references is William Langland's Piers Plowman (written –1387 in Middle English), with
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.{{Cite book
1484	[[File:Chuquet.gif	thumb	right	]] French mathematician Nicolas Chuquet, in his article Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien,
1516	[[File:Guillaume Budé, by Jean Clouet.jpg	thumb	upright	]] 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.
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
17th century	With the increased usage of large numbers, the traditional punctuation of large numbers into six-digit groups evolved into three-digit group punctuation. In some places, the large number names were then applied to the smaller numbers, following the new punctuation scheme. Thus, in France and Italy, some scientists then began using billion to mean 109, trillion to mean 1012, etc. This usage formed the origins of the later short scale. The majority of scientists either continued to say thousand million or changed the meaning of the Pelletier term, milliard, from "million of millions" down to "thousand million". This meaning of milliard has been occasionally used in England, but was widely adopted in France, Germany, Italy and the rest of Europe, for those keeping the original long scale billion from Adam, Chuquet and Pelletier.
1676	The first published use of milliard as 109 occurred in the Netherlands.{{Cite book
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.
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.
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	[[File:FowlersModernEnglishUsageFrontispiece.jpg	thumb	upright	]] H. W. Fowler's A Dictionary of Modern English Usage noted
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.
1960	The 11th General Conference on Weights and Measures adopted the International System of Units (SI), with its own set of numeric prefixes.
1961	The French Government confirmed their official usage of the long scale in the Journal officiel (the official French Government gazette).
1974	[[File:Lord Harold Wilson Allan Warren.jpg	thumb	upright	]] 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, reported in Hansard for 20 December 1974:
1975	French mathematician Geneviève Guitel introduced the terms long scale () and short scale () to refer to the two numbering systems.
1994	The Italian Government confirmed their official usage of the long scale.

Current usage

colwidth=10em}}

]]

Short scale users

English-speaking

Most English-language countries and regions use the short scale with 109 being billion. For example:

{{#tag:ref|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. |access-date= 22 August 2011}} 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'. |group="shortscale note"}}
(English-speaking) see Using both below
(English-speaking, , trilliún)
{{#tag:ref|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.{{Cite news |access-date= 11 May 2010
{{#tag:ref|American usage: In the United States, the short scale has been taught in school since the early 19th century. It is therefore used exclusively.{{cite encyclopedia |access-date= 21 August 2011 |access-date= 21 August 2011

Arabic-speaking

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:{{#tag:ref|Arabic language countries: Most Arabic-language countries use: 106, مليون million; 109, مليار milyar; 1012, ترليون trilyon; etc.{{cite web |access-date= 6 June 2012 |access-date= 6 June 2012}}

Other short scale

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

(bilhão, trilhão)
(miliar, triliun)
(Hebrew: מיליארד milyard, טריליון trilyon)
(миллиард milliard, триллион trillion)
(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 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

Most Dutch-language countries and regions use the long scale with 109 = miljard.{{cite web |access-date= 19 August 2011 |access-date= 19 August 2011

French-speaking

Most French-language countries and regions use the long scale with 109 = milliard, for example:{{#TAG:REF|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. However the 9th edition of the dictionary of the describes billion as an outdated synonym of milliard, and says that the new meaning of 1012 was decreed in 1961, but never caught on.{{cite encyclopedia |access-date= 17 January 2016 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.|trans-quote=BILLION (the two Ls are pronounced without palatalisation) masculine noun. Spelled byllion in the 15th century when it meant a million millions; in the 16th century it meant a thousand millions. It is an arbitrary alteration of the start of million by inserting the Latin prefix bi-, meaning twice. Now rarely used. It means a thousand millions. It is an outdated synonym of Milliard. According to a decree of 1961, the word Billion received a new value, to wit a million millions (1012), which has not come into common usage.

(Canadian French) see Using both below

German-speaking

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

Portuguese-speaking

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

Most Spanish-language countries and regions use the long scale, for example:{{#tag:ref|Spanish language countries: Spanish-speaking countries sometimes use millardo (milliard) |access-date= 19 August 2011 |access-date= 24 July 2010}} 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). |access-date= 2 July 2018}}

(mil millones or millardo)
(millardo or typ. mil millones)

Other long scale

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

(miliarda, bilion)
(milliard, billion)
Flag of Esperanto.svg Esperanto (miliardo, duiliono) {{#TAG:REF|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.{{cite web |author-link= Bertilo Wennergren |access-date= 15 September 2010
(miljardi, biljoona; Swedish: miljard, biljon)
(Persian: میلیارد miliyard, بیلیون billion, تریلیون trillion)
(miliardo, bilione)
(Bokmål: milliard, billion; Nynorsk: milliard, billion)
(miliard, bilion)
(miliard, bilion). There are ambiguities for numbers above 1012.
(miljard, biljon)
(French: milliard, billion; German: Milliarde, Billion; Italian: miliardo, bilione; Romansh: milliarda, billiun{{cite web |access-date= 15 August 2011}})

Using both

Some countries use either the short or long scales, depending on the internal language being used or the context.

Country or territory	Short scale usage	Long scale usage
{{#tag:ref	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.	title= Canadian government standards website	publisher= Canadian Government
	English (109 = billion, 1012 = trillion)	fr	milliard}}, 1012 = billion)
	South African English (109 = billion, 1012 = trillion)	af	miljard}}, 1012 = biljoen)
	es	billón}}, 1012 = trillón)	es	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

Indian numbering system	Traditional system for everyday use, but short or long scale may also be in use {{#tag:ref	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.{{Cite book
	Dzongkha numerals	Traditional system
	Khmer numerals	Traditional system
	East Asian numbering system:	Traditional myriad system for the larger numbers; special words and symbols up to 1068
	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):
	Lao numerals	Traditional system
	Mongolian numerals	Traditional myriad system for the larger numbers; special words up to 1067
		Traditional systems
	Thai numerals	Traditional system based on millions
	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

Long scale

Both long and short scale

Neither long nor short scale

References

"Authoritative Real Academia Española (RAE) dictionary: billón".
(7 May 2007). "Who wants to be a trillionaire?". BBC News.
Littré, Émile. (1873–1874). "Dictionnaire de la langue française". L. Hachette.
. (1762). ["Dictionnaire de l'académie françoise"](https://books.google.com/books?id=0oM-AAAAcAAJ&q=Dictionnaire+de+l'Académie+Française&pg=PA1). *Institut de France*.
. (1835). ["Dictionnaire de l'Académie française"](http://portail.atilf.fr/cgi-bin/dico1look.pl?strippedhw=billion&dicoid=ACAD1835&headword=&dicoid=ACAD1835).
. (1877). ["Dictionnaire de l'Académie française"](https://books.google.com/books?id=P2whAQAAMAAJ&q=Dictionnaire+de+l'Académie+Française&pg=PR23). *Institut de France*.
. (1932–1935). ["Dictionnaire de l'Académie française"](http://portail.atilf.fr/cgi-bin/dico1look.pl?strippedhw=billion&headword=&docyear=ALL&dicoid=ACAD1932&articletype=1). *Institut de France*.
Robson S. O. (Stuart O.), Singgih Wibisono, Yacinta Kurniasih. ''Javanese English dictionary'' Tuttle Publishing: 2002, {{ISBN. 0-7946-0000-X, 821 pages
(2000). "May We Introduce the Romanian Language to You?". Editura Fundatiei Culturale Române.
"French Larousse: milliard". [[Éditions Larousse]].
"French Larousse: billion". Éditions Larousse.
"Italian-English Larousse: bilione". Éditions Larousse.
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.
(2016). "Scara numerică". [[Dicționarul explicativ al limbii române.
(13 May 2013). "billion". Granddictionnaire.com.
"Taalkommissie se reaksie op biljoen, triljoen". [[Naspers]]: [[Media24]].
"'Groen boek': mooiste, beste, gebruikersvriendelikste". Naspers:Media24.

Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

numerals numeral-systems

Want to explore this topic further?

Ask Mako anything about Long and short scales — get instant answers, deeper analysis, and related topics.

Research with Mako

Free with your Surf account

Content sourced from Wikipedia, available under CC BY-SA 4.0.

This content may have been generated or modified by AI. CloudSurf Software LLC is not responsible for the accuracy, completeness, or reliability of AI-generated content. Always verify important information from primary sources.

Report