# Long and short scales

The long and short scales are two of several large-number naming systems for integer powers of ten that use the same words with different meanings. The long scale is based on powers of one million (1,000,000), whereas the short scale is based on powers of one thousand (1,000).

For whole numbers less than a thousand million (< 109), the two scales are the same. From a thousand million up (≥ 109), the two scales differ ever more, using the same words for different numbers, which can cause misunderstanding.

## Short scale

Every next short "-illion" word greater than "million" is one thousand times as large as the previous term. Thus, a short:
"billion" (109) means a thousand million,
"trillion" (1012) means a thousand billion,
"quadrillion" (1015) means a thousand trillion, and so on. Thus, a short n-illion equals 103n + 3.[1][2]

## Long scale

Every next long "-illion" word greater than "million" is one million times as large as the previous term. So, the long:
"billion" (1012) means a million million,
"trillion" (1018) means a million billion,
"quadrillion" (1024) means a million trillion and so on. Thus, a long n-illion equals 106n.[1][2]

Every "-illiard" word is one thousand times as large as the previous "-illion" word. So:
"milliard" (109) means a thousand million,
"billiard" (1015) means a thousand billion,
"trilliard" (1021) means a thousand trillion and so on. Thus, a long n-illiard equals 106n+3.

## Use

Countries where the long scale is currently used include most countries in continental Europe and most that are French-speaking, Spanish-speaking[3] (except Spanish-speakers born into an English-speaking culture, e.g. Puerto Rico, because of its influence from English-speaking United States) and Portuguese-speaking countries, except Brazil.

The short scale is now used in most English-speaking and Arabic-speaking countries, in Brazil, in the former Soviet Union and several other countries.

Number names are rendered in the language of the countries, but are similar everywhere 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, as for example the Indian numbering system.[1][2]

For most of the 19th and 20th centuries, the United Kingdom largely used the long scale,[4][5] whereas the United States used the short scale,[4] 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] Generally,[12] the British usage and American usage are now the same.

The first recorded use of the words "short scale" (French: échelle courte) and "long scale" (French: échelle longue) was by the French mathematician Geneviève Guitel in 1975.[1][2]

To lessen the confusion from the use of both short and long terms in any language, the SI recommends using the Metric prefix, which keeps the same meaning regardless of the country and the language. Long and short scales remain in use for counting money.

## References

1. Guitel, Geneviève (1975). Histoire comparée des numérations écrites (in français). Paris: Flammarion. pp. 51–52. ISBN 978-2-08-211104-1.
2. 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 français). Paris: Flammarion. pp. 566–574. ISBN 978-2-08-211104-1.
3. "Authoritative [[Real Academia Española|RAE]] dictionary: billón". Archived from the original on 2015-11-04. Retrieved 2019-03-17.
4. Fowler, H. W. (1926). A Dictionary of Modern English Usage. Great Britain: Oxford University Press. pp. 52–53. ISBN 978-0-19-860506-5.
5. British-English usage of 'Billion vs Thousand million vs Milliard'. Google Books ngram viewer. Google Inc. Retrieved 26 April 2014.
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?. Retrieved 31 January 2008.
8. BBC News: Who wants to be a trillionaire?. BBC. 7 May 2007. Retrieved 11 May 2010.
9. Comrie, Bernard (24 March 1996). "billion:summary". Retrieved 24 July 2011.
10. "Oxford Dictionaries: How many is a billion?". Oxford University Press. Archived from the original on 8 May 2018. Retrieved 7 May 2018.
11. "Oxford Dictionaries: Billion". Oxford University Press. Archived from the original on 11 August 2011. Retrieved 24 July 2011.
12. Nielsen, Ron (2006). The Little Green Handbook. Macmillan Publishers. p. 290. ISBN 978-0-312-42581-4.