Thelong and short scales are twopowers of ten number naming systems that are consistent with each other for smallernumbers, but are contradictory for larger numbers.[1][2] Other numbering systems, particularly inEast Asia andSouth Asia, have large number naming that differs from both the long and the short scales. Such numbering systems include theIndian numbering system andChinese,Japanese, andKorean numerals.[1][2] 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 areFrench-speaking,German-speaking andSpanish-speaking.[3] Use of the short scale is found in mostEnglish-speaking andArabic-speaking countries, most Eurasian post-communist countries, andBrazil.
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 scalebillion is one thousand million (109), whereas in the long scale,billion is one million million (1012), making the word 'billion' afalse 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, theInternational System of Units (SI) recommends using themetric prefixes to indicate magnitude. For example,giga- is always 109, which is 'billion' in short scale but 'milliard' in long scale.
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 integersn.[4][1][2]
In some languages, the long scale uses additional names for the intermediate multipliers, replacing the ending-ion with-iard; for example, the next multiplier aftermillion ismilliard (109); after abillion it isbilliard (1015). Hence, a long scalen-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 |
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 |
| . . . | . . . |
One way to avoid confusion between the two scales is to usepositional 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,[5] though this also becomes unwieldy with longer numbers.Methods that are better at longer numbers include:
1.2e10). This is the most common practice among scientists and mathematicians, but can be cumbersome in spoken word.Although this situation has been developing since the 1200s, the first recorded use of the termsshort scale (French:échelle courte) andlong scale (French:échelle longue) was by the French mathematicianGeneviève Guitel in 1975.[1][2]
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.[8] It has since become common in otherEnglish-speaking nations and several other countries. For most of the 19th and early 20th centuries, theUnited Kingdom largely used the long scale,[4][9] whereas theUnited States used the short scale,[9] so that the two systems were often referred to asBritish andAmerican in theEnglish language. After several decades of increasing informal British usage of the short scale, in 1974 the government of the UK adopted it,[10] and it is used for all official purposes.[11][12][13][14][15][16] The British usage and American usage are now identical.
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, butFrance andItaly use the long scale.
The pre-1974 former British English wordbillion, post-1961 current French wordbillion, post-1994 current Italian wordbilione, Spanishbillón, GermanBillion, Dutchbiljoen, Danishbillion, Swedishbiljon, Finnishbiljoona, Slovenianbilijon, Polishbilion, and European Portuguese wordbilião (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), andnotbillion (109 in the short scale).
On the other hand, the pre-1961 former French wordbillion, pre-1994 former Italian wordbilione, Brazilian Portuguese wordbilhão, and Welsh wordbiliwn all refer to 109, being short scale terms. Each of these words translates to the American English or post-1974 British English wordbillion (109 in the short scale).
The termbillion originally meant 1012 when introduced.[8] In long scale countries,milliard was defined to its current value of 109, leavingbillion at its original 1012 value and so on for the larger numbers.[8] Some of these countries, but not all, introduced new wordsbilliard,trilliard, etc. as intermediate terms.[17][18][19][20][21] In some short scale countries,milliard was defined to 109 andbillion dropped altogether, withtrillion redefined down to 1012 and so on for the larger numbers.[8] In many short scale countries,milliard was dropped altogether andbillion was redefined down to 109, adjusting downwards the value oftrillion and all the larger numbers.
The wordmillion derives from the Old Frenchmilion from the earlier Old Italianmilione, an intensification of the Latin word,mille, a thousand. That is, amillion is abig thousand, much as agreat gross is a dozen gross or 12 × 144 =1728.[8]
The wordmilliard, 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 usesbillion, and not used in British English, which preferred to usethousand million before the current usage ofbillion. The financial termyard, which derives frommilliard, is used on financial markets, as, unlike the termbillion, it is internationally unambiguous and phonetically distinct frommillion. Likewise, many long scale countries use the wordbilliard (or similar) for one thousand long scale billions (i.e., 1015), and the wordtrilliard (or similar) for one thousand long scale trillions (i.e., 1021), etc.[17][18][19][20][21]
| Date | Event |
|---|---|
| 13th century | The wordmillion was not used in any language before the 13th century. The monk and polymathMaximus Planudes (c. 1260–1305) was among the first recorded users of the word to document Mediterranean trade between Constantinople and Italian states.[8] 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 |  Piers Plowman, a 17th-century copy of the original 14th-century allegorical narrative poem byWilliam Langland
Translation:
|
| 1475 | FrenchmathematicianJehan Adam, writing inMiddle French, recorded the wordsbymillion andtrimillion as meaning 1012 and 1018 respectively in a manuscriptTraicté en arismetique pour la practique par gectouers, now held in theBibliothèque Sainte-Geneviève inParis.[22][23][24]
Translation:
|
| 1484 |  Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien an extract from Chuquet's original 1484 manuscript
Translation:
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)
Translation:
|
| 1549 | The influential French mathematicianJacques Pelletier du Mans used the namemilliard (ormilliart) to mean 1012, attributing the term to the earlier usage byGuillaume Budé[28] |
| 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 usingbillion to mean 109,trillion to mean 1012, etc.[29] This usage formed the origins of the later short scale. The majority of scientists either continued to saythousand million or changed the meaning of the Pelletier term,milliard, from "million of millions" down to "thousand million".[8] This meaning ofmilliard has been occasionally used in England,[9] 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 ofmilliard as 109 occurred in the Netherlands.[8][30]
Translation:
|
| 1729 | The short-scale meaning of the termbillion had already been brought to the British American colonies. The first American appearance of the short scale value ofbillion as 109 was published in theGreenwood Book of 1729, written anonymously by Prof.Isaac Greenwood ofHarvard College.[8] |
| Late 18th century | As early as 1762 (and through at least the early 20th century), the dictionary of theAcadémie française definedbillion as a term of arithmetic meaning a thousand millions.[31][32][33][34] |
| 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 | 
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 9thGeneral 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.[35] 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.[35][36] |
| 1960 | The 11thGeneral Conference on Weights and Measures adopted theInternational System of Units (SI), with its own set of numeric prefixes.[6] 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.[37] TheNational Institute of Standards and Technology within the US also considers that it is best that they be avoided entirely.[38] |
| 1961 | TheFrench Government confirmed their official usage of the long scale in theJournal officiel (the official French Government gazette).[39] |
| 1974 | 
TheBBC 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 (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 mathematicianGeneviève Guitel introduced the termslong scale (French:échelle longue) andshort scale (French:échelle courte) to refer to the two numbering systems.[1][2] |
| 1994 | TheItalian Government confirmed their official usage of the long scale.[21] |
Most English-language countries and regions use the short scale with 109 beingbillion. For example:[shortscale note 1]
Australia[shortscale note 2][40]
Canada (English-speaking)seeUsing bothbelow
Ireland (English-speaking,Irish:billiún,trilliún)
United Kingdom[shortscale note 3][10][11][41][13][14]
United States[shortscale note 4][42][43]MostArabic-language countries and regions use the short scale with 109 beingمليارmilyar, except for a few countries like Saudi Arabia and the UAE which use the word بليونbillion for 109. For example:[shortscale note 5][44][45]
Other countries also use a word similar totrillion to mean 1012, etc. Whilst a few of these countries like English use a word similar tobillion to mean 109, most like Arabic have kept a traditionally long scale word similar tomilliard for 109. Some examples of short scale use, and the words used for 109 and 1012, are
The long scale is used by mostContinental European countries and by most other countries whose languages derive from Continental Europe (with the notable exceptions of Albania, Greece, Romania[47] and Brazil). These countries use a word similar tobillion to mean 1012. Some use a word similar tomilliard to mean 109, while others use a word or phrase equivalent tothousand millions.
MostDutch-language countries and regions use the long scale with 109 =miljard.[48][49]
MostFrench-language countries and regions use the long scale with 109 =milliard, for example:[longscale note 1][50][51]
Canada (Canadian French)seeUsing bothbelow
FranceGerman-language countries and regions use the long scale with 109 =Milliarde.
With the notable exception of Brazil, a short scale country, mostPortuguese-language countries and regions use the long scale with 109 =mil milhõesormilhar de milhões.
MostSpanish-language countries and regions use the long scale, for example:[longscale note 2][53][54]
Some examples of long scale use, and the words used for 109 and 1012, are:
Czech Republic (miliarda,bilion)
Denmark (milliard,billion)
Esperanto (miliardo,duiliono)[longscale note 3][56]
Finland (miljardi,biljoona;Swedish:miljard,biljon)
Iran (Persian:میلیاردmiliyard,بیلیونbillion,تریلیونtrillion)[citation needed]
Italy (miliardo,bilione)[longscale note 4][21][57]
Norway (Bokmål:milliard,billion;Nynorsk:milliard,billion)
Poland (miliard,bilion)
Romania[58] (miliard,bilion). There are ambiguities for numbers above 1012.[59]
Sweden (miljard,biljon)
Switzerland (French:milliard,billion;German:Milliarde,Billion; Italian:miliardo,bilione;Romansh:milliarda,billiun[60])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 |
|---|---|---|
| Canada[shortscale longscale note 1] | Canadian English (109 =billion, 1012 =trillion) | Canadian French (109 =milliard, 1012 =billion[62] ormille milliards). |
| English (109 =billion, 1012 =trillion) | French (109 =milliard, 1012 =billion) | |
| South African English (109 =billion, 1012 =trillion) | Afrikaans (109 =miljard, 1012 =biljoen) | |
 Puerto Rico | Economic and technical (109 =billón, 1012 =trillón) | Latin American export publications (109 =millardo ormil millones, 1012 =billón) |
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 Maldives Nepal Pakistan | Indian numbering system | Traditional 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 |
| East Asian numbering system: | Traditionalmyriad system for the larger numbers; special words and symbols up to 1068 | |
 Greece | Calque of the short scale | Names of the short scale have not been loaned butcalqued intoGreek, based on the native Greek word for million,εκατομμύριοekatommyrio ("hundred-myriad", i.e. 100 × 10,000):
|
 Laos | Lao numerals | Traditional system |
 Mongolia | Mongolian numerals | Traditionalmyriad system for the larger numbers; special words up to 1067 |
 Sri Lanka | Traditional systems | |
 Thailand | Thai numerals | Traditional system based on millions |
 Vietnam | Vietnamese numerals | Traditional system(s) based on thousands |
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) |
{{cite book}}:ISBN / Date incompatibility (help){{cite book}}:ISBN / Date incompatibility (help)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.]
the numeralmiliard "billion"
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 ».[BILLION (the two Ls are pronounced without palatalisation) masculine noun. Spelledbyllion in the 15th century when it meanta million millions; in the 16th century it meanta thousand millions. It is an arbitrary alteration of the start ofmillion by inserting the Latin prefixbi-, meaningtwice. Now rarely used. It meansa thousand millions. It is an outdated synonym ofMilliard. According to a decree of 1961, the wordBillion received a new value, to wit a million millions (1012), which has not come into common usage.][permanent dead link]
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.