Long and short scales

The long and short scales are two of several large-number naming systems used throughout the world for integer powers of ten:

Long scale: Every new term greater than million is one million times larger than the previous term. Thus, billion means a million millions (10¹²), trillion means a million billions (10¹⁸), and so on.

Short scale: Every new term greater than million is one thousand times larger than the previous term. Thus, billion means a thousand millions (10⁹), trillion means a thousand billions (10¹²), and so on.

For integers less than a thousand million (< 10⁹), the two scales are identical. At and above a thousand million (≥ 10⁹), the two scales diverge by using the same words for different number values. These "false friends" can be a source of misunderstanding.

Many countries, including most in continental Europe and Latin America, use the long scale whereas most English-speaking countries and Arabic-speaking countries use the short scale. In all such countries, the number names are translated into the local language, but retain a name similarity 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 most of the 19th century and into the early 20th century, the United Kingdom largely 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 in the English language. After several decades of increasing British usage of the short scale, in 1974, the government of the UK fully adopted it, which is reflected in its mass media and official usage. With very few exceptions, 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.

Comparison

At and above a thousand million (≥ 10⁹), the same numerical value has two different names, depending on whether the value is being expressed in the long or short scale. Equivalently, the same name has two different numerical values depending on whether it is being used in the long or short scale.

Each scale has a logical justification to explain the use of each such differing numerical name and value within that scale. The short-scale logic is based on powers of one thousand, whereas the long-scale logic is based on powers of one million. In both scales, the prefix bi- refers to "2" and tri- refers to "3", etc. However only in the long scale do the prefixes beyond one million indicate the actual power or exponent (of 1,000,000). In the short scale, the prefixes refer to one less than the exponent (of 1,000).

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 numerals	Short Scale		Long Scale
	Prefix	Symbol		Name	Logic	Name	Logic
100			1	One		One
101	Deca	D or da	10	Ten		Ten
102	Hecto	Lower h	100	Hundred		Hundred
103	Kilo	Lower k	1,000	Thousand		Thousand
104			10,000	Ten thousand		Ten thousand
105			100,000	Hundred thousand		Hundred thousand
106	Mega	M	1,000,000	Million	1,000×1,0001	Million	1,000,0001
109	Giga	G	1,000,000,000	Billion	1,000×1,0002	Milliard or thousand million
1012	Tera	T	1,000,000,000,000	Trillion	1,000×1,0003	Billion	1,000,0002
1015	Peta	P	1,000,000,000,000,000	Quadrillion	1,000×1,0004	Billiard or thousand billion
1018	Exa	E	1,000,000,000,000,000,000	Quintillion	1,000×1,0005	Trillion	1,000,0003
1021	Zetta	Z	1,000,000,000,000,000,000,000	Sextillion	1,000×1,0006	Trilliard or thousand trillion
1024	Yotta	Y	1,000,000,000,000,000,000,000,000	Septillion	1,000×1,0007	Quadrillion	1,000,0004
Etc.				To go from one named order of magnitude to the next: multiply by 1,000		To go from one named order of magnitude to the next: multiply by 1,000,000

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	106	Mega	M	1,000×1,0001	106	Mega	M	1,000,0001
Billion	109	Giga	G	1,000×1,0002	1012	Tera	T	1,000,0002
Trillion	1012	Tera	T	1,000×1,0003	1018	Exa	E	1,000,0003
Quadrillion	1015	Peta	P	1,000×1,0004	1024	Yotta	Y	1,000,0004
Etc.	To go from one named order of magnitude to the next: multiply by 1,000				To go from one named order of magnitude to the next: multiply by 1,000,000

The root mil in "million" does not refer to the numeral "one". 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 1728.

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

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 an alternate 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 modern 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 modern British English word billion (10⁹ in the short scale).

The terms billion and milliard both originally meant 10¹² when introduced.

• In long scale countries, milliard was redefined down 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 redefined down 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.

Timeline

Date	Event
1200s	The word million was not used in any language before the 13th century. Maximus Planudes (c. 1260–1305) was among the first recorded users.
Late 1300s	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), 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 1012 and 1018 respectively in a manuscript Traicté en arismetique pour la practique par gectouers, now held in the Bibliothèque Sainte-Geneviève in Paris. [... item noctes que le premier greton dembas vault ung, le second vault ... dix, le trois vault ... [sic] cent, le quart vult 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 Mill Millions, Le XIe vault dix mill Millions, Le XIIe vault Cent mil Millions, Le XIIIe vault bymillion, Le XIIIIe vault dix bymillions, Le XVe vault 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 ...] Error: {{Lang}}: text has italic markup (help) 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, used the words byllion, tryllion, quadrillion, quyllion, sixlion, septyllion, ottyllion, and nonyllion to refer to 1012, 1018, ... 1054. Most of the work was copied without attribution by Estienne de La Roche and published in his 1520 book, L'arismetique. 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 ...
1514	Guilielmus Budaeus or Guillaume Budé (1467–1540) French mathematician Budaeus (Guillaume Budé), writing in Latin, used the term milliart to mean "Millions of millions" or 1012 in his book De Asse et partibus eius Libri quinque. .. hoc est denas myriadum myriadas, quod vno verbo nostrates abaci studiosi Milliartum appellat, 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), attributing this meaning to the earlier usage by Guillaume Budé
1600s	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. 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. .. milliart/ofte duysent millioenen.. Translation: ..milliart / also thousand millions..
Early 1700s	The short-scale meaning of the term billion was brought to the British American colonies
1729	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
Early 1800s	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 had converted back to the long scale.
1923	10 Milliard Mark (1010 mark) stamp 1000 Mark German banknote, over-stamped in red with "Eine Milliarde Mark" (109 mark) Using German banknotes as wallpaper following the 1923 hyperinflation German hyperinflation in the 1920s Weimar Republic caused 'Eintausend Mark' (1000 Mark = 103 Mark) German banknotes to be over-stamped as 'Eine Milliarde Mark' (109 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 = 1012 Papiermark = 1 trillion (short scale) Papiermark
1926	A Dictionary of Modern English Usage by H. W. Fowler H. W. Fowler's A Dictionary of Modern English Usage noted: It should be remembered that "billion" does not mean in American use (which follows the French) what it means in British. For to us it means the second power of a million, i.e. a million millions (1,000,000,000,000); for Americans it means a thousand multiplied by itself twice, or a thousand millions (1,000,000,000), what we call a milliard. Since billion in our sense is useless except to astronomers, it is a pity that we do not conform. 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.
1946	1020 Hungarian pengő banknote issued in 1946 Sweeping up pengő banknotes in the street, following the 1946 introduction of the forint Sweeping up pengő banknotes in the street, following the 1946 introduction of the forint Hyperinflation in Hungary in 1946 led to the introduction of the 1020 pengő banknote. 100 million b-pengő (long scale) = 100 trillion (long scale) pengő = 1020 pengő = 100 quintillion (short scale) pengő. On 1 August 1946, the forint was introduced at a rate of: 1 forint = 400 quadrilliard (long scale) pengő = 4 x 1029 pengő = 400 octillion (short scale) pengő.
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. 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.
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. The National Institute of Standards and Technology within the USA also considers that it is best that they be avoided entirely.
1961	The French Government confirmed their official usage of the long scale in the Journal officiel (the official French Government gazette).
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. Hansard, for the 20 December 1974, reported it: Mr. Maxwell-Hyslop asked the Prime Minister whether he will make it the practice of his administration that when Ministers employ the word 'billion' in any official speeches, documents, or answers to Parliamentary Questions, they will, to avoid confusion, only do so in its British meaning of 1 million million and not in the sense in which it is used in the United States of America, which uses the term 'billion' to mean 1,000 million. The Prime Minister: No. The word 'billion' is now used internationally to mean 1,000 million and it would be confusing if British Ministers were to use it in any other sense. I accept that it could still be interpreted in this country as 1 million million and I shall ask my colleagues to ensure that, if they do use it, there should be no ambiguity as to its meaning. 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.
1993	5 x 1011 Yugoslav dinar banknotes from 1993 Hyperinflation in Yugoslavia led to the introduction of 5 x 1011 dinar banknotes. 500 thousand million (long scale) dinars = 5 x 1011 dinar banknotes = 500 billion (short scale) dinars. The later introduction of the new dinar came at an exchange rate of: 1 novi dinar = 1 × 1027 dinars = ~1.3 × 1027 pre 1990 dinars.
1994	The Italian Government confirmed their official usage of the long scale.
2009	1014 Zimbabwean dollars banknote from 2009 Hyperinflation in Zimbabwe led to banknotes of 1014 Zimbabwean dollars, marked "One Hundred Trillion Dollars" (short scale), being issued in 2009, shortly ahead of the currency being abandoned. As of 2013, a new currency has yet to be announced – so foreign currencies are being used instead. 100 trillion (short scale) Zimbabwean dollars = 1014 Zimbabwean dollars = 100 billion (long scale) Zimbabwean dollars = 1027 pre-2006 Zimbabwean dollars.
2013	As of 24 October 2013, the combined total public debt of the United States stood at $17.078 trillion. 17 trillion (short scale) US Dollars = 1.7 x 1013 US Dollars = 17 billion (long scale) US Dollars

Current usage

Short and long scale usage throughout the world

  Short scale

  Long scale

  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 = billion. For example:

American Samoa

Anguilla

Antigua and Barbuda

Australia

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   (English-speaking)

Nigeria   (English-speaking)

Niue

Norfolk Island

Northern Mariana Islands

Palau

Papua New Guinea   (English-speaking)

Philippines   (English-speaking)

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)

United States

United States Virgin Islands

Zambia   (English-speaking)

Zimbabwe   (English-speaking)

Arabic-speaking

10⁶ = میليون  million, 10⁹ = میليار  milyar, 10¹² = تريليون  trilyon, etc.

Most Arabic-language countries and regions use the short scale with 10⁹ = میليار   milyar. For example:

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 / billion, 10¹² = one trillion, etc.

Other countries also use a word similar to trillion to mean 10¹², etc. While 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)

Armenia   (միլիարդ miliard, տրիլիոն trilion)

Azerbaijan   (milyard, trilyon)

Belarus   (мільярд milyard, трыльён trilyon)

Brazil   (Brazilian Portuguese: bilhão, trilhão)

Brunei   (Brunei Malay: ; Malay: bilion, trilion)

Bulgaria   (милиард miliard, трилион trilion)

Myanmar   (Burmese: ‹See Tfd›ဘီလျံ, IPA: [bìljàɴ]; ‹See Tfd›ထရီလျံ, [tʰəɹìljàɴ])

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

Estonia   (miljard, triljon)

Georgia   (მილიარდი miliardi, ტრილიონი trilioni)

Indonesia   (miliar, triliun)  

Israel   (Hebrew: מיליארד millyard, טריליון trillyon)

Kazakhstan   (Kazakh: миллиард milliard, триллион trillion)

Kyrgyzstan   (Kyrgyz: миллиард milliard, триллион trillion)

Latvia   (miljards, triljons)

Lithuania   (milijardas, trilijonas)

Moldova   (Romanian / Moldovan: miliard, trilion; Russian: миллиард milliard, триллион trillion)

Romania   (miliard, trilion)

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)

With other terminology

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

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, Bulgaria, 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.

Spanish-speaking

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

Most Spanish-language countries and regions use the long scale with 10⁹ = mil millones, for example:

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  

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, for example:

Benin

Burkina Faso

Central African Republic

Democratic Republic of the Congo

Republic of the Congo

France

French Polynesia

French Southern and Antarctic Lands

Gabon

Guadeloupe

Guinea

Haiti

Ivory Coast   (Côte d'Ivoire)

Mali

Monaco

New Caledonia

Niger

Saint Barthélemy

Senegal

Togo

Wallis and Futuna

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, for example:

Angola

Cape Verde

East Timor

Guinea-Bissau

Macau

Mozambique

Portugal

São Tomé and Príncipe

Dutch-speaking

10⁶ = miljoen, 10⁹ = miljard, 10¹² =biljoen

Most Dutch-language countries and regions use the long scale, for example:

Aruba

Curaçao

Netherlands

Sint Maarten

Suriname

Other long scale

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

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

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

Austria   (Austrian German: Milliarde, Billion)

Belgium   (Belgian French: milliard, billion; Flemish: miljard, biljoen; German: Milliarde, Billion)

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

Croatia   (milijarda, bilijun)

Czech Republic   (miliarda, bilion)

Denmark   (milliard, billion)

Faroe Islands   (Danish: milliard, billion)

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

Germany   (Milliarde, Billion)

Hungary   (milliárd, billió or ezer milliárd)

Iceland   (milljarður, billjón)

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

Italy   (miliardo, bilione)

Liechtenstein   (German: Milliarde, Billion)

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

North Macedonia   (милијарда milijarda, билион bilion)

Madagascar   (French: milliard, billion; Malagasy: )

Montenegro   (Montenegrin: milijarda, bilion)

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

Poland   (miliard, bilion)

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 )

Vatican City   (Italian: miliardo, bilione)

Other long scale languages

Esperanto language   (miliardo, duiliono)

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	Canadian English   (109 = billion, 1012 = trillion)	Canadian French   (109 = milliard, 1012 = billion).
Mauritius Seychelles Vanuatu	English   (109 = billion, 1012 = trillion)	French   (109 = milliard, 1012 = billion)
Namibia South Africa	South African English   (109 = billion, 1012 = trillion)	Afrikaans   (109 = miljard, 1012 = biljoen)
Puerto Rico	Economic & technical (109 = billón, 1012 = trillón)	Latin American export publications (109 = millardo or mil millones, 1012 = billón)

Using neither

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

Country	Main article	Notes
Bangladesh,   India,   Nepal,   Pakistan	Indian Numbering System	For everyday use, but short or long scale may also be in use
Bhutan	Dzongkha numerals	Traditional system
Cambodia	Khmer numerals	Traditional system
China (People's Republic of China – PRC) Taiwan (Republic of China – ROC)	Chinese numerals	Traditional myriad system for the larger numbers; special words and symbols up to 1088
Greenland	Inuit numerals	Traditional system
Japan	Japanese numerals	Traditional myriad system for the larger numbers; special words and symbols up to 1088
North Korea South Korea	Korean numerals	Traditional myriad system for the larger numbers; special words and symbols up to 1088
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 1067
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	American Spanish (Argentina, Chile), French (France), Norwegian (Norway)
Asia	Burmese (Myanmar), Hebrew (Israel), Indonesian, Malaysian English, Persian (Iran), Philippine English,	Portuguese (East Timor, Macau)
Europe	British English, Hiberno-English, Scottish English, Welsh English, Welsh, Bulgarian, Estonian, Greek, Latvian, Lithuanian, 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)

Notes on current usage

Short scale

Long scale

Both long and short scale

Neither long nor short scale

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
• 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. Use with non-SI units (e.g. "giga-dollars", "giga-miles") is uncommon.

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

External links

• BBC News article: "Is trillion the new billion?"