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Long and short scales
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The long and short scales are two different numerical systems used throughout the world:
- Short scale is the English translation of the French term échelle courte. It refers to a system of numeric names in which every new term greater than million is 1,000 times the previous term: "billion" means "a thousand millions" (109), "trillion" means "a thousand billions" (1012), and so on.
- Long scale is the English translation of the French term échelle longue.
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Encyclopedia
The long and short scales are two different numerical systems used throughout the world:
- Short scale is the English translation of the French term échelle courte. It refers to a system of numeric names in which every new term greater than million is 1,000 times the previous term: "billion" means "a thousand millions" (109), "trillion" means "a thousand billions" (1012), and so on.
- Long scale is the English translation of the French term échelle longue. It refers to a system of numeric names in which every new term greater than million is 1,000,000 times the previous term: "billion" (from bi and million) means "a million to the power of two" or "a million millions" (1012), "trillion" (from tri and million) means "a million to the power of three" or "a million billions" (1018), and so on.
Note that the difference between the two scales grows as numbers get larger. Million is the same in both scales, but the long-scale billion is a thousand times larger than the short-scale billion, the long-scale trillion is a million times larger than the short-scale trillion, and so on.
For most of the 19th and 20th centuries, the United Kingdom uniformly used the long scale, while the United States of America used the short scale, so that usage of the two systems was often referred to as "British" and "American" respectively. In 1974 the government of the UK abandoned the long scale, so that the UK now exclusively applies the short scale interpretation in mass media and official usage. Although some residual usage of the long scale continues in the UK, the phrases "British usage" and "American usage" are no longer accurate or helpful characterizations. The two systems can be a subject of controversy and can arouse emotion. Usage changes can evoke resentment in adherents to the older system, while national differences of any kind can acquire patriotic overtones.
Comparison
For a more extensive table, see names of large numbers.
| Value | Value Expanded | Short Scale | Short Scale Logic | Long Scale | Long Scale Logic |
|---|
| 10 0 = | 1 | one | 1,000 1 - 1 | one | 1,000,000 0.0 | | 10 3 = | 1,000 | thousand | 1,000 1 + 0 | thousand | 1,000,000 0.5 | | 10 6 = | 1,000,000 | million | 1,000 1 + 1 | million | 1,000,000 1.0 | | 10 9 = | 1,000,000,000 | billion | 1,000 1 + 2 | thousand million (sometimes milliard) | 1,000,000 1.5 | | 1012 = | 1,000,000,000,000 | trillion | 1,000 1 + 3 | billion | 1,000,000 2.0 | | 1015 = | 1,000,000,000,000,000 | quadrillion | 1,000 1 + 4 | thousand billion (sometimes billiard) | 1,000,000 2.5 | | 1018 = | 1,000,000,000,000,000,000 | quintillion | 1,000 1 + 5 | trillion | 1,000,000 3.0 | | 1021 = | 1,000,000,000,000,000,000,000 | sextillion | 1,000 1 + 6 | thousand trillion (sometimes trilliard)
| 1,000,000 3.5 |
Bi refers to 2 and tri refers to 3, etc. The relationship between the names and the corresponding numbers is as follows.
- short scale: Million is thousand × (thousand)1 = 106; Billion is thousand × (thousand)2 = 109; Trillion is thousand × (thousand)3 = 1012; etc.
To get from one named order of magnitude to the next, multiply by a thousand.
- long scale: Million is (million)1 = 106; Billion is (million)2 = 1012; Trillion is (million)3 = 1018; etc.
To get from one named order of magnitude to the next, multiply by a million.
In other words, a billion (bi / two) has twice as many zeros as a million, and a trillion (tri / three) has three times as many zeros as a million, etc.
The word "milliard", or its translation, is found in European languages and can be used 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 it is unambiguous, unlike "billion". Likewise, some long scale countries use a word similar to billiard for a thousand long scale billions (i.e. 1015), a word similar to trilliard 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 using 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 used both systems at various times in their history. Nowadays, the United Kingdom officially uses the short scale, but France and Italy (and most other European countries) officially use the long scale. The French word billion, the German word Billion, the Dutch word biljoen, the Swedish word biljon, the Finnish word biljoona, the Danish word billion, the Spanish word billón and the Portuguese word biliăo all refer to 1012, being long scale terms. However, each of these words translates to the English word "trillion" (1012 in the short scale), and not "billion" (109 in the short scale). Brazilian Portuguese, on the other hand, employs short scale, and "bilhăo" (note the alternate spelling to the European Portuguese variant) corresponds to the American "billion". See Current usage below.
Timeline
| 1475 | French mathematician Jehan Adam recorded the words "bymillion" and "trimillion" as meaning 1012 and 1018 respectively. | | 1484 | French mathematician Nicolas Chuquet, in his article "Triparty en la science des nombres", used the words byllion, tryllion, quadrillion, quyllion, sixlion, septyllion, ottyllion, and nonyllion to refer to 1012, 1018, etc. Chuquet's work was not published until the 1870s, but most of it was copied without attribution by Estienne de La Roche and published in his 1520 book, L'arismetique. | | 1549 | Jacques Peletier used the name milliard (“milliart”) for "Million de Millions", i.e. 1012. He attributed this meaning to earlier usage by Guillaume Budé (1467-1540), a French scholar. | | During 17th century | The traditional six-digit groups were split up into three-digit groups. In France and Italy, some scientists then began using "billion" to mean 109. The majority either continued to say "thousand million" or used the Peletier term, milliard, to mean "thousand million", instead of "million of millions". The word milliard was used in England but was widely adopted in France, Germany, Italy and the rest of Europe, for those keeping Chuquet's original long scale billion. | | Mid 18th century | The short-scale meaning of the term "billion" was brought to the British American colonies. | | 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 "a now obsolete system". | | 1926 | 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."
| | 1948 | The 9th General Conference on Weights and Measures proposed the universal use of the long scale, inviting the short scale countries to return or convert. The proposal was considered but not adopted. | | 1960 | The 11th General Conference on Weights and Measures adopted the International System of Units (SI), with its own set of numeric prefixes. SI is therefore independent of the number scale being used. SI also notes the language-dependence of some larger number names and advises against using ambiguous terms such as billion, trillion, etc. . | | 1961 | France confirmed their official usage of the long scale in the Journal Officiel (the official French Government gazette). | | 1974 | British prime minister Harold Wilson explained to the House of Commons that UK government statistics would from then on use the short scale. During the last quarter of 20th century, most other English-speaking countries (Ireland, Australia, New Zealand, and South Africa) followed this lead and switched to the short scale use. However, in all these countries, some limited long scale use persists and the official status of the short scale use is not clear. | | 1975 | French mathematician Genevičve Guitel introduced the terms échelle courte (short scale) and échelle longue (long scale) to refer to the two numbering systems. | | 1994 | The Italian government confirmed their official long scale usage of the term "billion" . |
The origin of the word "million" seems to derive from the Old French Milion, thought to derive from Old Italian milione, an intensification of mille, a thousand. That is, a "million" is a "big thousand", much as "1728" (a dozen gross) is a "great gross".
Current usage
Short scale countries / regions
- 106 = one million, 109 = one billion, 1012 = one trillion, etc.
English language-speaking countries / regions
Most English-language countries use the short scale. For example:
Other languages and countries
- (Brazilian Portuguese: bilhăo = 109, trilhăo = 1012, etc.)
Short scale use with long scale milliard
Some countries adopted the short scale for the seldom-occurring higher numbers (such as 1012), but kept the traditional word "milliard" instead of the short-scale "billion". Countries that adopt this usage include:
Short scale use but with other terminology
- (e?at?µµ???? ekatommyrio "hundred-myriad" = 106; d?se?at?µµ???? disekatommyrio "bi-hundred-myriad" = 109; t??se?at?µµ???? trisekatommyrio "tri-hundred-myriad" = 1012; tet????? e?at?µµ???? tetrakis ekatommyrio "tetra-hundred-myriad" = 1015, and so on.)
Long scale countries
- 106 = one million, 109 = one milliard / thousand million, 1012 = one billion, 1015 = one billiard / thousand billion, 1018 = one trillion, etc.
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 Greece and Brazil). Many of these countries use a word similar to milliard to mean 109, and/or a word similar to billion to mean 1012. Some examples of long scale use, and the words used for 109 and 1012, are:
Both long and short scales countries
- , a Spanish-speaking US Commonwealth territory, generally uses short scale (billón = 109, trillón = 1012) in economic and technical matters, but the long scale (millardo or mil millones = 109, billón = 1012) is used in publications intended for a Latin American audience outside Puerto Rico.
Neither short nor long scale countries
The following countries have their own numbering systems and use neither short nor long scales:
English language countries
- Apart from the United States, the long scale was used for centuries in many English language countries before being superseded in recent times by short scale usage. Because of this history, some long scale use persists and the official status of the short scale in these countries is sometimes obscure.
UK usage
- "Billion" has meant 109 in most sectors of official published writing for many years now. The UK government, BBC, and most other broadcast or published mass media, have used the short scale exclusively in all contexts since the mid 1970s. Use of billion in British English can be ambiguous.
- Before the widespread use of "billion" for 109, UK usage generally referred to thousand million rather than milliard. The long scale term "milliard", for 109, is obsolete in British English (though its derivation "yard" is still used as slang in the London money, foreign exchange and bond markets).
US usage
- In the United States of America, the short scale has been taught in school since the early 19th century. It is therefore used exclusively.
Australian usage
- In Australia, some documents use the term thousand million for 109 in cases where two amounts are being compared using a common unit of one 'million'. As of 1999, the Australian Government's financial department did not consider short scale to be standard, but used it occasionally. The current recommendation by the Australian Department of Finance and Administration (formerly known as AusInfo), and the legal definition, is the short scale. Education, media outlets, and literature all use the short scale in line with other English-speaking countries.
South African Usage
- Since South Africa uses both the Long scale (in Afrikaans) and the Short scale (in English) chances for ambiguity is rife. Some Afrikaans publications briefly attempted usage of the "American System" but that has led to comment in the papers and has been disparaged by the "Taalkommissie" (The Afrikaans Language Commission of the South African Academy of Science and Art) and has thus, to most appearances, been abandoned.
Indian, Pakistani & Bangladeshi usage
- Outside of financial media, the use of "billion" by Indian & Pakistani English speakers highly depends on their educational background. Some may continue to use the traditional British long scale. In everyday life, Indian & Pakistanis largely use their own common number system, commonly referred to as Indian numbering system - for instance, Bangladeshi, Pakistani & Indian English commonly use the words lakh to denote 100 thousand, and crore to denote ten million (i.e. 100 lakhs). This is because of shared History of these countries.
Italian language usage
Italy – with France – was one of the two European countries partially converted to the short scale during the 19th century, but returned to the original long scale in 20th century.
In Italian, the word bilione officially means 1012. Colloquially, bilione can mean both 109 and 1012; trilione both 1012 and (rarer) 1018 and so on. Therefore, in order to avoid ambiguity, they are seldom used. Forms such as mille miliardi (a thousand milliards) for 1012, un milione di miliardi for 1015, un miliardo di miliardi for 1018, mille miliardi di miliardi for 1021 are more common.
Esperanto language usage
The Esperanto 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 . 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 numeral indicating the power of a million, e.g. duiliono (from du meaning "two") = biliono (1012); triiliono = triliono (1018), etc. Miliardo is an unambiguous term for 109.
Use of "thousand milliard"
In those countries using the term "milliard", the term "thousand milliard" is occasionally used, but only in budgetary contexts. One milliard currency units has become the major budgetary unit, as in the national debt of Germany at the end of 2004 was about 1418 milliard euros. In all other contexts in these same countries, 1012 is always termed "billion" and not "thousand milliard".
Alternative approaches
Unambiguous ways of identifying large numbers include:
- In written communications, the simplest solution for moderately large numbers is simply to write the full amount- i.e., 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 with more than 3 digits with million, as in 15,300 million.
- Scientific notation (standard form), including its engineering notation variant, for example 109, 1012, or in writing using the computer programming notation (1e9, 1e12, etc). This is the most common practice among scientists and mathematicians, and is both unambiguous and convenient.
- SI prefixes, for example, giga for 109 and tera for 1012. The International System of Units (SI) is independent of whichever scale is being used.
See also
External links
Current UK usage
- a 2007 BBC page on actual common media usage of trillion.
- A 1996 email list message, comparing the two scales usage in different languages.
Traditional UK usage
- a traditional UK viewpoint.
- a 1999 webpage comparing the long and short scale numbers, which only considers traditional UK numbering.
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