Long and short scales

The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.

For the use of "long scale" and "short scale" in connection with musical instruments, see Scale length (string instruments).

For whole numbers smaller than 1,000,000,000 (10⁹), such as one thousand or one million, the two scales are identical. For larger numbers, starting with 10⁹, the two systems differ. For identical names, the long scale proceeds by powers of one million, whereas the short scale proceeds by powers of one thousand. For example, one billion is one thousand millions in the short scale, while it is one million millions in the long scale. The long scale system introduces new terms for the intervening values, typically replacing the word ending -ion with -iard.

Scales

In both short and long scale naming, names are given each multiplication step for increments of the base-10 exponent of three, i.e. for each integer n in the sequence of multipliers 10³ⁿ. For certain multipliers, including those for all numbers smaller than 10⁹, both systems use the same names. The differences arise from the assignment of identical names to specific values of n, for numbers starting with 10⁹, for which n=3. In the short scale system, the identical names are for n=3, 4, 5, ..., while the long scale places them at n=4, 6, 8, etc.

Short scale

In the short scale, billion means a thousand millions (1,000,000,000 which is 10⁹), trillion means one thousand billions (10¹²), and so on. Thus, an n-illion equals 10³ⁿ⁺³.[1]

Long scale

In the long scale, billion means one million million (10¹²) and trillion means one million billions (10¹⁸), and so on. Therefore, an n-illion equals 10⁶ⁿ.[2][3] In some languages, the long scale introduces new names for the interleaving multipliers, replacing the ending -ion with -iard; for example, the next multiplier after million is milliard, after billion it is billiard. Hence, an n-iard equals 10⁶ⁿ⁺³.

Use

Countries with usage of the long scale include most countries in continental Europe, and most that are French-speaking, Spanish-speaking[4] and Portuguese-speaking countries (except Brazil).

The short scale is used in most English-speaking and Arabic-speaking countries, in Brazil, and in several other countries.

Number names are rendered in the language of the country, but are similar due to shared etymology. Some languages, particularly in East Asia and South Asia, have large number naming systems that are different from both the long and short scales, for example the Indian numbering system.[2][3]

For most of the 19th and 20th centuries, the United Kingdom largely used the long scale,[5][1] whereas the United States used the short scale,[5] 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,[6] and it is used for all official purposes.[7][8][9][10][11] With very few exceptions,[12] the British usage and American usage are now identical.

The first recorded use of the terms short scale (French: échelle courte) and long scale (French: échelle longue) was by the French mathematician Geneviève Guitel in 1975.[2][3]

To avoid confusion resulting from the coexistence of short and long term in any language, the International System of Units (SI) recommends using the metric prefix to indicate orders of magnitude, but it is only relevant to scientific applications, and not (for example) to finance. Unlike words like billion and million, metric prefixes keep the same meaning regardless of the country and the language.

Comparison

The relationship between the numeric values and the corresponding names in the two scales can be described as:

Value in scientific notation	Metric prefix		Value in positional notation	Short scale		Long scale
	Prefix	Symbol		Name	Logic	Name	Alternative name	Logic
10^0			1	one		one
10^1	deca	da	10	ten		ten
10^2	hecto	h	100	hundred		hundred
10^3	kilo	k	1,000	thousand		thousand
10^6	mega	M	1,000,000	million	1,000 × 1,000^1	million		1,000,000^1
10^9	giga	G	1,000,000,000	billion	1,000 × 1,000^2	thousand million	milliard	1,000 × 1,000,000^1
10^12	tera	T	1,000,000,000,000	trillion	1,000 × 1,000^3	billion		1,000,000^2
10^15	peta	P	1,000,000,000,000,000	quadrillion	1,000 × 1,000^4	thousand billion	billiard	1,000 × 1,000,000^2
10^18	exa	E	1,000,000,000,000,000,000	quintillion	1,000 × 1,000^5	trillion		1,000,000^3
10^21	zetta	Z	1,000,000,000,000,000,000,000	sextillion	1,000 × 1,000^6	thousand trillion	trilliard	1,000 × 1,000,000^3
10^24	yotta	Y	1,000,000,000,000,000,000,000,000	septillion	1,000 × 1,000^7	quadrillion		1,000,000^4

The relationship between the names and the corresponding numeric values in the two scales can be described as:

Name	Short scale				Long scale
	Value in scientific notation	Metric prefix		Logic	Value in scientific notation	Metric prefix		Logic
		Prefix	Symbol			Prefix	Symbol
million	10^6	mega	M	1,000 × 1,000^1	10^6	mega	M	1,000,000^1
billion	10^9	giga	G	1,000 × 1,000^2	10^12	tera	T	1,000,000^2
trillion	10^12	tera	T	1,000 × 1,000^3	10^18	exa	E	1,000,000^3
quadrillion	10^15	peta	P	1,000 × 1,000^4	10^24	yotta	Y	1,000,000^4
etc.	To next named order of magnitude: multiply by 1,000				To next named order of magnitude: multiply by 1,000,000

The root mil in million does not refer to the numeral, 1. 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.[13]

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.[14][15][16][17][18]

History

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, German Billion; Dutch biljoen; Swedish biljon; Finnish biljoona; Danish billion; Polish bilion, Spanish billón; Slovenian bilijon and the 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 the 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.[13]

• 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.[13] Some of these countries, but not all, introduced new words billiard, trilliard, etc. as intermediate terms.[14][15][16][17][18]
• 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.[13]
• 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.

Timeline

Date	Event
13th century	The word million was not used in any language before the 13th century. Maximus Planudes (c. 1260–1305) was among the first recorded users.[13]
Late 14th century	Piers Plowman, a 17th-century copy of the original 14th-century allegorical narrative poem by William Langland The word million entered the English language. One of the earliest references is William Langland's Piers Plowman (written c. 1360–1387 in Middle English),[13] with Coueyte not his goodes For millions of moneye Translation: Covet not his goods for millions of money
1475	French mathematician Jehan Adam, writing in Middle French, recorded the words bymillion and trimillion as meaning 10^12 and 10^18 respectively in a manuscript Traicté en arismetique pour la practique par gectouers, now held in the Bibliothèque Sainte-Geneviève in Paris.[19][20][21] ... item noctes que le premier greton dembas vault ung, le second vault dix, le trois vault cent, le quart vult [sic] mille, le Ve vault dix M, le VIe vault cent M, le VIIe vault Milion, Le VIIIe vault dix Million, Le IXe vault cent Millions, Le Xe vault Mil Millions, Le XIe vault dix mil Millions, Le XIIe vault Cent mil Millions, Le XIIIe vault bymillion, Le XIIIIe vault dix bymillions, Le XVe vault cent mil [sic] bymillions, Le XVIe vault mil bymillions, Le XVIIe vault dix Mil bymillions, Le XVIIIe vault cent mil bymillions, Le XIXe vault trimillion, Le XXe vault dix trimillions ... Translation: ... Item note that the first counter from the bottom is worth one, the 2nd is worth ten, the 3rd is worth one hundred, the 4th is worth one thousand, the 5th is worth ten thousand, the 6th is worth one hundred thousand, the 7th is worth a million, the 8th is worth ten millions, the 9th is worth one hundred millions, the 10th is worth one thousand millions, the 11th is worth ten thousand millions, the 12th is worth one hundred thousand million, the 13th is worth a bymillion, the 14th is worth ten bymillions, the 15th is worth one [hundred] bymillions, the 16th is worth one thousand bymillions, the 17th is worth ten thousand bymillions, the 18th is worth hundred thousand bymillions, the 19th is worth a trimillion, the 20th is worth ten trimillions ...
1484	Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien an extract from Chuquet's original 1484 manuscript French mathematician Nicolas Chuquet, in his article Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien,[22][23][24] used the words byllion, tryllion, quadrillion, quyllion, sixlion, septyllion, ottyllion, and nonyllion to refer to 10^12, 10^18, ... 10^54. Most of the work was copied without attribution by Estienne de La Roche and published in his 1520 book, L'arismetique.[22] Chuquet's original article was rediscovered in the 1870s and then published for the first time in 1880. ... Item lon doit savoir que ung million vault mille milliers de unitez, et ung byllion vault mille milliers de millions, et [ung] tryllion vault mille milliers de byllions, et ung quadrillion vault mille milliers de tryllions et ainsi des aultres : Et de ce en est pose ung exemple nombre divise et punctoye ainsi que devant est dit, tout lequel nombre monte 745324 tryllions 804300 byllions 700023 millions 654321. Exemple : 745324'8043000'700023'654321 ... [sic] Translation: ...Item: one should know that a million is worth a thousand thousand units, and a byllion is worth a thousand thousand millions, and tryllion is worth a thousand thousand byllions, and a quadrillion is worth a thousand thousand tryllions, and so on for the others. And an example of this follows, a number divided up and punctuated as previously described, the whole number being 745324 tryllions, 804300 byllions 700023 millions 654321. Example: 745324'8043000'700023'654321 ... [sic] The extract from Chuquet's manuscript, the transcription and translation provided here all contain an original mistake: one too many zeros in the 804300 portion of the fully written out example: 745324'8043000 '700023'654321 ...
1516	Guilielmus Budaeus or Guillaume Budé (1467–1540) French mathematician Budaeus (Guillaume Budé), writing in Latin, used the term milliart to mean "ten myriad myriad" or 10^9 in his book De Asse et partibus eius Libri quinque.[25] .. hoc est decem myriadum myriadas:quod vno verbo nostrates abaci studiosi Milliartum appellant:quasi millionum millionem Translation: .. this is ten myriad myriads, which in one word our students of numbers call Milliart, as if a million millions
1549	The influential French mathematician Jacques Pelletier du Mans used the name milliard (or milliart) to mean 10^12, attributing the term to the earlier usage by Guillaume Budé[25]
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 10^9, trillion to mean 10^12, etc.[26] 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".[13] This meaning of milliard has been occasionally used in England,[5] 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 10^9 occurred in the Netherlands.[13][27] .. milliart/ofte duysent millioenen.. Translation: ..milliart / also thousand millions..
18th century	The short-scale meaning of the term billion was brought to the British American colonies. 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.[28][29][30][31]
1729	The first American appearance of the short scale value of billion as 10^9 was published in the Greenwood Book of 1729, written anonymously by Prof. Isaac Greenwood of Harvard College[13]
Early 19th century	France widely converted to the short scale, and was followed by the U.S., which began teaching it in schools. Many French encyclopedias of the 19th century either omitted the long scale system or called it "désormais obsolète", a now obsolete system. Nevertheless, by the mid 20th century France would officially convert back to the long scale.
1926	A Dictionary of Modern English Usage by H. W. Fowler H. W. Fowler's A Dictionary of Modern English Usage[5] noted It should be remembered that "billion" does not mean in American use (which follows the French) what it means in British. For to us it means the second power of a million, i.e. a million millions (1,000,000,000,000); for Americans it means a thousand multiplied by itself twice, or a thousand millions (1,000,000,000), what we call a milliard. Since billion in our sense is useless except to astronomers, it is a pity that we do not conform. Although American English usage did not change, within the next 50 years French usage changed from short scale to long and British English usage changed from long scale to short.
1948	The 9th General Conference on Weights and Measures received requests to establish an International System of Units. One such request was accompanied by a draft French Government discussion paper, which included a suggestion of universal use of the long scale, inviting the short-scale countries to return or convert.[32] This paper was widely distributed as the basis for further discussion. The matter of the International System of Units was eventually resolved at the 11th General Conference in 1960. The question of long scale versus short scale was not resolved and does not appear in the list of any conference resolutions.[32][33]
1960	The 11th General Conference on Weights and Measures adopted the International System of Units (SI), with its own set of numeric prefixes.[34] 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.[35] The National Institute of Standards and Technology within the US also considers that it is best that they be avoided entirely.[36]
1961	The French Government confirmed their official usage of the long scale in the Journal officiel (the official French Government gazette).[37]
1974	British prime minister Harold Wilson (1916–1995) British prime minister Harold Wilson explained in a written answer to the House of Commons that UK government statistics would from then on use the short scale.[7] Hansard,[6] for 20 December 1974, reported it Mr. Maxwell-Hyslop asked the Prime Minister whether he would make it the practice of his administration that when Ministers employ the word 'billion' in any official speeches, documents, or answers to Parliamentary Questions, they will, to avoid confusion, only do so in its British meaning of 1 million million and not in the sense in which it is used in the United States of America, which uses the term 'billion' to mean 1,000 million. The Prime Minister: No. The word 'billion' is now used internationally to mean 1,000 million and it would be confusing if British Ministers were to use it in any other sense. I accept that it could still be interpreted in this country as 1 million million and I shall ask my colleagues to ensure that, if they do use it, there should be no ambiguity as to its meaning. The BBC and other UK mass media quickly followed the government's lead within the UK. During the last quarter of the 20th century, most other English-speaking countries (the Republic of Ireland, Australia, New Zealand, South Africa, Zimbabwe, etc.) either also followed this lead or independently switched to the short scale use. However, in most of these countries, some limited long scale use persists and the official status of the short scale use is not clear.
1975	French mathematician Geneviève Guitel introduced the terms long scale (French: échelle longue) and short scale (French: échelle courte) to refer to the two numbering systems.[2][3]
1994	The Italian Government confirmed their official usage of the long scale.[18]

As large numbers in natural sciences are usually represented by metric prefixes, scientific notation or otherwise, the most commonplace occurrence of large numbers represented by long or short scale terms is in finance. The following table includes some historic examples related to hyper-inflation and other financial incidents.

Timeline

Date	Event
1923	10 Milliarden Mark (10^10 mark) stamp 1000 Mark German banknote, over-stamped in red with "Eine Milliarde Mark" (10^9 mark) Using German banknotes as wallpaper following the 1923 hyperinflation German hyperinflation in the 1920s Weimar Republic caused 'Eintausend Mark' (1000 Mark = 10^3 Mark) German banknotes to be over-stamped as 'Eine Milliarde Mark' (10^9 Mark). This introduced large-number names to the German populace. The Mark or Papiermark was replaced at the end of 1923 by the Rentenmark at an exchange rate of 1 Rentenmark = 1 billion (long scale) Papiermark = 10^12 Papiermark = 1 trillion (short scale) Papiermark
1946	10^20 Hungarian pengo banknote issued in 1946 Hyperinflation in Hungary in 1946 led to the introduction of the 10^20 pengo banknote. 100 million b-pengo (long scale) = 100 trillion (long scale) pengo = 10^20 pengo = 100 quintillion (short scale) pengo. On 1 August 1946, the forint was introduced at a rate of 1 forint = 400 quadrilliard (long scale) pengo = 4 × 10^29 pengo = 400 octillion (short scale) pengo.
1993	5 × 10^11 Yugoslav dinar banknotes from 1993 Hyperinflation in Yugoslavia led to the introduction of 5 × 10^11 dinar banknotes. 500 thousand million (long scale) dinars = 5 × 10^11 dinar banknotes = 500 billion (short scale) dinars. The later introduction of the new dinar came at an exchange rate of 1 new dinar = 1 × 10^27 dinars = ~1.3 × 10^27 pre 1990 dinars.
2009	10^14 Zimbabwean dollars banknote from 2009 Hyperinflation in Zimbabwe led to banknotes of 10^14 Zimbabwean dollars, marked "One Hundred Trillion Dollars" (short scale), being issued in 2009, shortly ahead of the currency being abandoned.[38][39][40] As of 2013, a new currency has yet to be announced – so foreign currencies are being used instead. 100 trillion (short scale) Zimbabwean dollars = 10^14 Zimbabwean dollars = 100 billion (long scale) Zimbabwean dollars = 10^27 pre-2006 Zimbabwean dollars = 1 quadrilliard (long scale) pre-2006 Zimbabwean dollars.
2013	As of 24 October 2013, the combined total public debt of the United States stood at $17.078 trillion.[41][42] 17 trillion (short scale) US Dollars = 1.7 × 10^13 US Dollars = 17 billion (long scale) US Dollars

Current usage

Short and long scale usage throughout the world

  Long scale

  Short scale

  Short scale (and milliard)

  Both scales

  Other naming system

  No data

Short scale users

English-speaking

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

Most English-language countries and regions use the short scale with 10⁹ being billion. For example:[shortscale note 1]

 American Samoa

 Anguilla

 Antigua and Barbuda

 Australia [shortscale note 2][43]

 Bahamas

 Barbados

 Belize   (English-speaking)

 Bermuda

 Botswana   (English-speaking)

 British Virgin Islands

 Cameroon   (English-speaking)

 Cayman Islands

 Cook Islands

 Dominica

 Eritrea

 Ethiopia

 Falkland Islands

 Fiji

 Gambia

 Ghana   (English-speaking)

 Gibraltar

 Grenada

 Guam

 Guernsey

 Guyana   (English-speaking)

 Hong Kong   (English-speaking)

 Ireland   (English-speaking, Irish: billiún, trilliún)

 Isle of Man

 Jamaica

 Jersey

 Kenya   (English-speaking)

 Kiribati

 Lesotho

 Liberia

 Malawi   (English-speaking)

 Malaysia   (English-speaking; Malay: bilion billion, trilion trillion)

 Malta   (English-speaking; Maltese: biljun, triljun)

 Marshall Islands

 Federated States of Micronesia

 Montserrat

 Nauru

 New Zealand

 Nigeria   (English-speaking)

 Niue

 Norfolk Island

 Northern Mariana Islands

 Palau

 Papua New Guinea   (English-speaking)

 Philippines   (English-speaking) [shortscale note 3]

 Pitcairn Islands

 Rwanda

 Saint Helena, Ascension and Tristan da Cunha

 Saint Kitts and Nevis

 Saint Lucia

 Saint Vincent and the Grenadines

 Samoa

 Sierra Leone

 Singapore   (English-speaking)

 Solomon Islands

 South Georgia and the South Sandwich Islands

 South Sudan   (English-speaking)

 Eswatini

 Tanzania   (English-speaking)

 Tokelau

 Tonga

 Trinidad and Tobago

 Turks and Caicos Islands

 Tuvalu

 Uganda   (English-speaking)

 United Kingdom   (see Wales below) [shortscale note 4][6][7][44][9][10]

 United States [shortscale note 5][45][46]

 United States Virgin Islands

 Zambia   (English-speaking)

 Zimbabwe   (English-speaking)[38][39][40]

Arabic-speaking

10⁶, مَلْيُوْن‎  malyoon; 10⁹, مِلْيَار‎  milyar; 10¹², تِرِلْيُوْن‎  tirilyoon; etc.

Most Arabic-language countries and regions use the short scale with 10⁹ being مليار‎ milyar, except for a few countries like Saudi Arabia and the UAE which use the word بليون billion for 10⁹. For example:[shortscale note 6][47][48]

 Algeria

 Bahrain

 Chad

 Comoros

 Djibouti

 Egypt

 Eritrea

 Iraq

 Jordan

 Kuwait

 Lebanon

 Libya

 Mauritania

 Morocco

 Oman

 Palestine

 Qatar

 Saudi Arabia

 Somalia

 Sudan

 Syria

 Tunisia

 United Arab Emirates

 Western Sahara

 Yemen

Other short scale

10⁶, one million; 10⁹, one milliard or one billion; 10¹², one trillion; etc.

Other countries also use a word similar to trillion to mean 10¹², etc. Whilst a few of these countries like English use a word similar to billion to mean 10⁹, most like Arabic have kept a traditional long scale word similar to milliard for 10⁹. Some examples of short scale use, and the words used for 10⁹ and 10¹², are

 Afghanistan   (Dari: میلیارد milyard or بیلیون billion, تریلیون trillion, Pashto: میلیارد milyard, بیلیون billion, تریلیون trillion)

 Albania   (miliard, trilion)[49]

 Armenia   (միլիարդ miliard, տրիլիոն trilion)

 Azerbaijan   (milyard, trilyon)

 Belarus   (мільярд milyard, трыльён trilyon)

 Brazil   (Brazilian Portuguese: bilhão, trilhão)

 Brunei   (Malay: bilion, trilion)

 Bulgaria   (милиард miliard, трилион trilion)

 Myanmar   (Burmese: ဘီလျံ, IPA: [bìljàɰ̃]; ထရီလျံ, [tʰəɹìljàɰ̃])[50]

 Cyprus   (Greek: δισεκατομμύριο disekatommyrio, τρισεκατομμύριο trisekatommyrio, Turkish: milyar, trilyon)

 Estonia   (miljard or biljon[shortscale note 7], triljon)[51][52][53]

 Georgia   (მილიარდი miliardi, ტრილიონი trilioni)

 Indonesia   (miliar, triliun)  [shortscale note 8][54]

 Israel   (Hebrew: מיליארד milyard, טריליון trilyon)

 Kazakhstan   (Kazakh: миллиард milliard, триллион trillion)

 Kyrgyzstan   (Kyrgyz: миллиард milliard, триллион trillion)

 Latvia   (miljards, triljons)

 Lithuania   (milijardas, trilijonas)

 Moldova   (Romanian:[55] miliard, trilion; Russian: миллиард milliard, триллион trillion)

 Russia   (миллиард milliard, триллион trillion)

 Tajikistan   (Tajik: миллиард milliard, триллион trillion)

 Turkey   (milyar, trilyon)

 Turkmenistan   (Turkmen: ; Russian: миллиард milliard, триллион trillion)

 Ukraine   (мільярд mil'yard, трильйон tryl'yon)

 Uzbekistan   (Uzbek: ; Russian: миллиард milliard, триллион trillion)

 Wales   (biliwn, triliwn) In some contexts a paraphrase is needed to resolve ambiguity, as the lenitive of both miliwn and biliwn is the same: filiwn.

Long scale users

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 Albania, Greece, Romania,[55] 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.

Spanish-speaking

10⁶, millón; 10⁹, mil millones or millardo; 10¹², billón; etc.

Most Spanish-language countries and regions use the long scale, for example:[longscale note 1][56][57]

 Argentina  

 Bolivia  

 Chile  

 Colombia  

 Costa Rica  

 Cuba  

 Dominican Republic  

 Ecuador  

 El Salvador  

 Equatorial Guinea  

 Guatemala   (millardo)

 Honduras   (millardo)

 Mexico   (mil millones or millardo)

 Nicaragua   (mil millones or millardo)

 Panama   (mil millones or millardo)

 Paraguay  

 Peru   (mil millones)

 Spain   (millardo or typ. mil millones)

 Uruguay  

 Venezuela  

French-speaking

10⁶, million; 10⁹, milliard; 10¹², billion; etc.

Most French-language countries and regions use the long scale with 10⁹ = milliard, for example:[longscale note 2][59][60]

 Belgium

 Benin

 Burkina Faso

 Central African Republic

 Democratic Republic of the Congo

 Republic of the Congo

 France

 French Polynesia

 French Southern and Antarctic Lands

 Gabon

 Guinea

 Haiti

 Ivory Coast   (Côte d'Ivoire)

 Mali

 Monaco

 New Caledonia

 Niger

 Saint Barthélemy

 Senegal

 Togo

 Wallis and Futuna

 Quebec

Portuguese-speaking

10⁶, milhão; 10⁹, mil milhões or milhar de milhões; 10¹², bilião;

With the notable exception of Brazil, a short scale country, most Portuguese-language countries and regions use the long scale with 10⁹ = mil de milhões or milhar de milhões, for example:

 Angola

 Cape Verde

 East Timor

 Guinea-Bissau

 Macau

 Mozambique

 Portugal

 São Tomé and Príncipe

Dutch-speaking

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

Most Dutch-language countries and regions use the long scale with 10⁹ = miljard, for example:[62][63]

 Aruba

 Belgium

 Curaçao

 Netherlands

 Sint Maarten

 Suriname

German-speaking

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

German-language countries and regions use the long scale with 10⁹ = Milliarde, for example:

 Austria   (Austrian German: Milliarde, Billion)

 Belgium   (German: Milliarde, Billion)

 Germany   (Milliarde, Billion)[14][15]

 Liechtenstein   (German: Milliarde, Billion)

Other long scale

10⁶, one million; 10⁹, one milliard or one thousand million; 10¹², one billion; etc.

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

 Andorra   (Catalan: miliard or typ. mil milions, bilió)

 Bosnia and Herzegovina   (Bosnian: milijarda, bilion; Croatian: milijarda, bilijun, Serbian: милијарда milijarda, билион bilion)

 Croatia   (milijarda, bilijun)

 Czech Republic   (miliarda, bilion)

 Denmark   (milliard, billion)

Esperanto   (miliardo, duiliono) [longscale note 3][64]

 Faroe Islands   (milliard, billión)

 Finland   (Finnish: miljardi, biljoona; Swedish: miljard, biljon)

 Greenland   (milliardi, billioni)

 Hungary   (milliárd, billió or ezermilliárd)

 Iceland   (milljarður, billjón)

 Iran   (Persian: میلیارد milyard, بیلیون billion, تریلیون trillion)

 Italy   (miliardo, bilione) [longscale note 4][18][65]

 Luxembourg   (French: milliard, billion; German: Milliarde, Billion; Luxembourgish: milliard, billioun)

 Madagascar   (French: milliard, billion; Malagasy: miliara, arivo miliara )

 Montenegro   (Montenegrin: milijarda, bilion)

 North Macedonia   (милијарда milijarda, билион bilion)

 Norway   (Bokmål: milliard, billion; Nynorsk: milliard, billion)

 Poland   (miliard, bilion)

 Romania[66]   (miliard, bilion). See also [67] for ambiguities above 10¹²).

 San Marino   (Italian: miliardo, bilione)

 Serbia   (милијарда milijarda, билион bilion)

 Slovakia   (miliarda, bilión)

 Slovenia   (milijarda, bilijon)

 Sweden   (miljard, biljon)

  Switzerland   (French: milliard, billion; German: Milliarde, Billion; Italian: miliardo, bilione, Romansh: milliarda, billiun[68] )

  Vatican City   (Italian: miliardo, bilione)

Using both

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

10⁶ = one million, 10⁹ = EITHER one billion (short scale) OR one milliard / thousand million (long scale), 10¹² = EITHER one trillion (short scale) OR one billion (long scale), etc.

Country or territory	Short scale usage	Long scale usage
Canada [shortscale longscale note 1]	Canadian English   (10^9 = billion, 10^12 = trillion)	Canadian French   (10^9 = milliard, 10^12 = billion[70] or mille milliards).
Mauritius;  Seychelles;  Vanuatu	English   (10^9 = billion, 10^12 = trillion)	French   (10^9 = milliard, 10^12 = billion)
Namibia  South Africa [shortscale longscale note 2]	South African English   (10^9 = billion, 10^12 = trillion)	Afrikaans   (10^9 = miljard, 10^12 = biljoen)
Puerto Rico	Economic & technical (10^9 = billón, 10^12 = trillón)	Latin American export publications (10^9 = millardo or mil millones, 10^12 = billón)

Using neither

The following countries use naming systems for large numbers that are not etymologically related to the short and long scales:

Country	Number system	Naming of large numbers
Bangladesh,    India,      Nepal,    Pakistan	Indian Numbering System	For everyday use, but short or long scale may also be in use [other scale note 1]
Bhutan	Dzongkha numerals	Traditional system
Cambodia	Khmer numerals	Traditional system
China  Taiwan  South Korea  North Korea  Japan	Chinese numerals Korean numerals Japanese numerals	Traditional myriad system for the larger numbers; special words and symbols up to 10^88
Greece	Calque of the short scale	Names of the short scale have not been loaned but calqued into Greek, based on the native Greek word for million, εκατομμύριο ekatommyrio ("hundred-myriad", i.e. 100×10000): δισεκατομμύριο disekatommyrio "bi+hundred-myriad" = 10^9 (short scale billion); τρισεκατομμύριο trisekatommyrio "tri+hundred-myriad" = 10^12 (short scale trillion); τετράκις εκατομμύριο tetrakis ekatommyrio "quadri+hundred-myriad" = 10^15 (short scale quadrillion), and so on.[74]
Laos	Lao numerals	Traditional system
Maldives,    Sri Lanka	Sinhala numerals Tamil numerals	Traditional systems
Mongolia	Mongolian numerals	Traditional myriad system for the larger numbers; special words up to 10^67
Thailand	Thai numerals	Traditional system based on millions
Vietnam	Vietnamese numerals	Traditional system(s) based on thousands

Presence on most 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	Arabic (Egypt, Libya, Tunisia), English (South Sudan), South African English	Afrikaans, French (Benin, Central African Republic, Gabon, 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	Burmese (Myanmar), Hebrew (Israel), Indonesian, Malaysian English, Philippine English, Kazakh, Uzbek, Kyrgyz	Portuguese (East Timor, Macau), Persian (Iran)
Europe	British English, Welsh, Estonian, Greek, Latvian, Lithuanian, Russian, Turkish, Ukrainian	Danish, Dutch, Finnish, French, German, Icelandic, Italian, Norwegian, Polish, Portuguese, Spanish, Swedish and most other languages of continental Europe
Oceania	Australian English, New Zealand English	French (French Polynesia, New Caledonia)

Notes on current usage

Short scale

1. English language countries: Apart from the United States, the long scale was used for centuries in many English language countries before being superseded in recent times by short scale usage. Because of this history, some long scale use persists[12] and the official status of the short scale in anglophone countries other than the UK and US is sometimes obscure.
2. Australian usage: In Australia, education, media outlets, and literature all use the short scale in line with other English-speaking countries. The current recommendation by the Australian Government Department of Finance and Deregulation (formerly known as AusInfo), and the legal definition, is the short scale.[43] As recently as 1999, the same department did not consider short scale to be standard, but only used it occasionally. Some documents use the term thousand million for 10⁹ in cases where two amounts are being compared using a common unit of one 'million'.
3. Filipino usage: Some short-scale words have been adopted into Filipino.
4. 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.[6][7][44][9]
   Before the widespread use of billion for 10⁹, UK usage generally referred to thousand million rather than milliard.[10] The long scale term milliard, for 10⁹, is obsolete in British English, though its derivative, yard, is still used as slang in the London money, foreign exchange, and bond markets.
5. American 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.[45][46]
6. Arabic language countries: Most Arabic-language countries use: 10⁶, مليون‎  million; 10⁹, مليار‎  milyar; 10¹², ترليون‎  trilyon; etc.[47][48]
7. Estonian usage: Biljon is used due to English influences and is less common than miljard.
8. Indonesian usage: Large numbers are common in Indonesia, in part because its currency (rupiah) is generally expressed in large numbers (the lowest common circulating denomination is Rp100 with Rp1000 is considered as base unit). The term juta, equivalent to million (10⁶), is generally common in daily life. Indonesia officially employs the term miliar (derived from the long scale Dutch word miljard) for the number 10⁹, with no exception. For 10¹² and greater, Indonesia follows the short scale, thus 10¹² is named triliun. The term seribu miliar (a thousand milliards) or more rarely sejuta juta (a million millions) are also used for 10¹² less often. Terms greater than triliun are not very familiar to Indonesians.[54]

Long scale

1. Spanish language countries: Spanish-speaking countries sometimes use millardo (milliard)[56] for 10⁹, but mil millones (thousand millions) is used more frequently. The word billón is sometimes used in the short scale sense in those countries more influenced by the United States, where "billion" means "one thousand millions". The usage of "billón" to mean "one thousand millions", controversial from the start, was denounced by the Royal Spanish Academy as recently as 2010,[57] 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).[58]
2. 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.[37][59][60] However the 9th edition of the dictionary of the Académie française describes billion as an outdated synonym of milliard, and says that the new meaning of 10¹² was decreed in 1961, but never caught on.[61]
3. Esperanto language usage: The Esperanto language 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.[64] Ambiguity may be avoided by the use of the unofficial but generally recognised suffix -iliono, whose function is analogous to the long scale, i.e. it is appended to a (single) numeral indicating the power of a million, e.g. duiliono (from du meaning "two") = biliono = 10¹², triiliono = triliono = 10¹⁸, etc. following the 1×10^6X long scale convention. Miliardo is an unambiguous term for 10⁹, and generally the suffix -iliardo, for values 1×10^6X+3, for example triliardo = 10²¹ and so forth.
4. Italian usage: Italy, with France, was one of the two European countries which partially converted from the long scale to the short scale during the 19th century, but returned to the original long scale in the 20th century. In 1994, the Italian Government confirmed its long scale status.[18]
   In Italian, the word bilione officially means 10¹², trilione means 10¹⁸, etc.. Colloquially, bilione[65] can mean both 10⁹ and 10¹²; trilione can mean both 10¹² and (rarer) 10¹⁸ and so on. Therefore, in order to avoid ambiguity, they are seldom used. Forms such as miliardo (milliard) for 10⁹, mille miliardi (a thousand milliards) for 10¹², un milione di miliardi (a million milliards) for 10¹⁵, un miliardo di miliardi (a milliard of milliards) for 10¹⁸, mille miliardi di miliardi (a thousand milliard of milliards) for 10²¹ are more common.[18]

Both long and short scale

1. Canadian usage: Both scales are in use currently in Canada. English-speaking regions use the short scale exclusively, while French-speaking regions use the long scale, though the Canadian government standards website recommends that in French billion and trillion be avoided, recommending milliard for 10⁹, and mille milliards (a thousand milliards) for 10¹².[69]
2. South African usage: South Africa uses both the long scale (in Afrikaans and sometimes English) and the short scale (in English). Unlike the 1974 UK switch, the switch from long scale to short scale took time. As of 2011 most English language publications use the short scale. Some Afrikaans publications briefly attempted usage of the "American System" but that has led to comment in the papers[71] and has been disparaged by the "Taalkommissie" (The Afrikaans Language Commission of the South African Academy of Science and Art)[72] and has thus, to most appearances, been abandoned.

Neither long nor short scale

1. Indian, Pakistani and Bangladeshi usage: Outside of financial media, the use of billion by Bangladeshi, Indian and Pakistani English speakers highly depends on their educational background. Some may continue to use the traditional British long scale. In everyday life, Bangladeshis, Indians and Pakistanis largely use their own common number system, commonly referred to as the Indian numbering system — for instance, Bangladeshi, Pakistani, and Indian English commonly use the words lakh to denote 100 thousand, crore to denote ten million (i.e. 100 lakhs) and arab to denote thousand million.[73]

Alternative approaches

Unambiguous ways of identifying large numbers include:

• In written communications, the simplest solution for moderately large numbers is to write the full amount, for example 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 of more than 3 digits with the unambiguous word million, for example 13,600 million[75]
• Scientific notation (also known as standard form or exponential notation, for example 1×10⁹, 1×10¹⁰, 1×10¹¹, 1×10¹², etc.), or its engineering notation variant (for example 1×10⁹, 10×10⁹, 100×10⁹, 1×10¹², etc.), or the computing variant E notation (for example 1e9, 1e10, 1e11, 1e12, etc.) This is the most common practice among scientists and mathematicians, and is both unambiguous and convenient.
• SI prefixes in combination with SI units, for example, giga for 10⁹ and tera for 10¹² can give gigawatt (=10⁹ W) and terawatt (=10¹² W), respectively. The International System of Units (SI) is independent of whichever scale is being used.[34] Use with non-SI units (e.g. "giga-dollars", "giga-miles") is uncommon although "megabucks" is in informal use representing a large sum of money rather than exactly a million dollars. k€ and M€ is more frequently encountered, although the official scheme places the Euro sign in front of the value. The SI-approach has the advantage to survive translations without ambiguity and is well understood in an IT context, especially in countries that have established SI-standards.

See also

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

References

1. British-English usage of 'Billion vs Thousand million vs Milliard'. Google Books ngram viewer. Google Inc. Retrieved 26 April 2014.
2. Guitel, Geneviève (1975). Histoire comparée des numérations écrites (in French). Paris: Flammarion. pp. 51–52. ISBN 978-2-08-211104-1.
3. Guitel, Geneviève (1975). ""Les grands nombres en numération parlée (État actuel de la question)", i.e. "The large numbers in oral numeration (Present state of the question)"". Histoire comparée des numérations écrites (in French). Paris: Flammarion. pp. 566–574. ISBN 978-2-08-211104-1.
4. "Authoritative [[Real Academia Española|RAE]] dictionary: billón". Archived from the original on 4 November 2015. Retrieved 12 March 2015.
5. Fowler, H. W. (1926). A Dictionary of Modern English Usage. Great Britain: Oxford University Press. pp. 52–53. ISBN 978-0-19-860506-5.
6. ""BILLION" (DEFINITION) — HC Deb 20 December 1974 vol 883 cc711W–712W". Hansard Written Answers. Hansard. 20 December 1972. Retrieved 2 April 2009.
7. O'Donnell, Frank (30 July 2004). "Britain's £1 trillion debt mountain – How many zeros is that?". The Scotsman. Retrieved 31 January 2008.
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11. "Oxford Dictionaries: Billion". Oxford University Press. Retrieved 24 July 2011.
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16. "Wortschatz-Lexikon: Billiarde" (in German). Universität Leipzig: Wortschatz-Lexikon. Archived from the original on 27 September 2011. Retrieved 28 July 2011.
17. "Wortschatz-Lexikon: Trilliarde" (in German). Universität Leipzig: Wortschatz-Lexikon. Archived from the original on 27 September 2011. Retrieved 28 July 2011.
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19. Adam, Jehan (1475). "Traicté en arismetique pour la practique par gectouers... (MS 3143)" (in Middle French). Paris: Bibliothèque Sainte-Geneviève. Cite journal requires |journal= (help)
20. "HOMMES DE SCIENCE, LIVRES DE SAVANTS A LA BIBLIOTHÈQUE SAINTE-GENEVIÈVE, Livres de savants II". Traicté en arismetique pour la practique par gectouers… (in French). Bibliothèque Sainte-Geneviève. 2005. Retrieved 25 October 2014.
21. Thorndike, Lynn (1926). "The Arithmetic of Jehan Adam, 1475 A.D". The American Mathematical Monthly. Mathematical Association of America. 1926 (January): 24–28. JSTOR 2298533.
22. Chuquet, Nicolas (1880) [written 1484]. "Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien". Bulletino di Bibliographia e di Storia delle Scienze Matematische e Fisische (in Middle French). Bologna: Aristide Marre. XIII (1880): 593–594. ISSN 1123-5209. Retrieved 17 July 2011.
23. Chuquet, Nicolas (1880) [written 1484]. "Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien" (in Middle French). miakinen.net. Retrieved 1 March 2008.
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26. Littré, Émile (1873–1874). Dictionnaire de la langue française. Paris, France: L. Hachette. p. 347. Ce n'est qu'au milieu du XVIIe siècle qu'il fut réglé que les tranches, au lieu d'être de six en six chiffres, seraient de trois en trois chiffres ; ce qui revint à diviser par 1000 l'ancien billion, l'ancien trillion, etc. [It was only in the middle of the 17th century that it was settled that the slices, instead of being from six to six digits, would be from three to three digits; which resulted in dividing by 1000 the old billion, the old trillion, and so on.]
27. Houck (1676). "Arithmetic". Netherlands: 2. Cite journal requires |journal= (help)
28. Dictionnaire de l'académie françoise (4th ed.). Paris, France: Institut de France. 1762. p. 177.
29. Dictionnaire de l'Académie française (6th ed.). Paris, France. 1835. p. 189.
30. Dictionnaire de l'Académie française (7th ed.). Paris, France: Institut de France. 1877. p. 182.
31. Dictionnaire de l'Académie française (8th ed.). Paris, France: Institut de France. 1932–1935. p. 144.
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34. "Resolution 12 of the 11th meeting of the CGPM (1960)". BIPM. Retrieved 28 July 2011.
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36. Thompson, Ambler; Taylor, Barry N. (30 March 2008). Guide for the Use of the International System of Units (SI), NIST SP – 811. US: National Institute of Standards and Technology. p. 21. Retrieved 13 September 2014.
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48. "Al Jazem English-Arabic online dictionary:Trillion". Al Jazem English-Arabic online dictionary. Encyclopædia Britannica. Retrieved 6 June 2012.
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50. "Britain to Reduce $4 billion from Defence". Bi-Weekly Eleven (in Burmese). Yangon. 3 (30). 15 October 2010.
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53. "Eesti õigekeelsussõnaraamat ÕS 2006: triljon" (in Estonian). Institute of the Estonian Language (Eesti Keele Instituut). 2006. Retrieved 13 August 2011.
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55. Avram, Mioara; Sala, Marius (2000), May We Introduce the Romanian Language to You?, Editura Fundatiei Culturale Române, p. 151, ISBN 9789735772246, the numeral miliard "billion"
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57. "Diccionario Panhispánico de Dudas: billon" (in Spanish). Real Academia Española. Retrieved 24 July 2010.
58. "Diccionario de la lengua española" (in Spanish). Real Academia Española. Retrieved 2 July 2018.
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61. "Definition of 'Billion' in the 9th edition of the Dictionnaire de l'Académie française". Académie française. 1992. Retrieved 17 January 2016. BILLION (les deux l se prononcent sans mouillure) n. m. XVe siècle, byllion, « un million de millions » ; XVIe siècle, « mille millions ». Altération arbitraire de l'initiale de million, d'après la particule latine bi-, « deux fois ».
    Rare. Mille millions. Syn. vieilli de Milliard. Selon un décret de 1961, le mot Billion a reçu une nouvelle valeur, à savoir un million de millions (10¹²), qui n'est pas entrée dans l'usage.
    
    This translates into English as : 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.
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External links

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