Long and short scale

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Value of 10,000,000,000 according to the long scale: ten billion - German Reich postage stamp (1923)
Value of 10,000,000,000 according to the short scale: ten trillion - Zimbabwe banknote (2008)

The long and short scales ( French Échelles longue et courte ) are two systems of number names in the Decadal Number System with different conventions for names of large numbers above the million. In addition to the long and short scale, there is also the term long and short division and long and short ladder in German . The latter goes back to the fact that the French word échelle means both scale and ladder.

The long scale ( échelle longue ) uses the word trillion for the number 10 12 , i.e. one million million or one thousand billion . This scale goes back to the French mathematician Nicolas Chuquet and his work Triparty en la science des nombres from 1484. The variant used today in Germany uses the ending "-arde" for 1000 times all million potencies (numbers in the form 1000 · 10 6 · n = 10 6 · n + 3 ).

The short scale ( échelle courte ) uses the word trillion for the number 10 9 , i.e. for one billion. The use of the short scale emerged in Italy, and especially in France, in the 17th century, when the traditional division of large numbers into groups of six began to move to groups of three for better readability. A minority of scholars believed that this reform should also change the meaning of the number names themselves. Especially in the USA and Brazil , this short scale officially applies today. In English-speaking financial circles, the US variant has dominated almost entirely outside of the US for several decades.

Although the two scales have existed side by side for several hundred years, the French terms échelle longue and échelle courte that characterize them were only introduced in 1975 by the French mathematician Geneviève Guitel .

distribution

Worldwide use of the long and short scale
  • long scale
    		•
  • both scales
    		•
  • short scale
    		•
  • other systems
    		•

    In the 19th and up to the second third of the 20th century, the long scale was used uniformly in Great Britain , whereas the short scale was used in the USA , so that at that time it was also referred to as the British and American system. However, the short scale has been used semi-officially in Great Britain since 1974, making this description obsolete.

    In addition to the USA, Great Britain and Brazil , the short scale also applies in Australia, New Zealand, Ireland and the English-speaking part of Canada. A variant of the short scale, which also uses the word “billion” for 10 9 analogous to the long scale, applies in Russia , Turkey , Israel , all Arabic-speaking countries and many African countries.

    In France , usage was inconsistent during the 19th century: most of the French encyclopedias of the period used the échelle courte . The original system of the échelle longue is either not mentioned there or is described as obsolete. In 1961, France officially returned to the long scale ( échelle longue ), so that there was uniform use in Europe until the departure of Great Britain in 1974.

    The 11th General Conference on Weights and Measures , the highest organ of the Meter Convention , i.e. the SI system, notes the misunderstanding of the terms parts per billion (abbreviated ppb ) and parts per trillion (abbreviated ppt ) due to the coexistence of long and short scales. The conference recommends avoiding these confusing terms and their abbreviations.

    Comparison of the scales

    Short scale Long scale tens
    potency         		Resolutions
    Surname Systematics Chuquet with -arde Systematics
    [Unit] Thousand 1 - 1 [Unit] [Unit] Million 0 10 0 [Unit]
    thousand Thousand 1 + 0 thousand thousand Million ½ 10 3 kilo
    million Thousand 1 + 1 million million Million 1 10 6 Mega
    Bi llion Thousand 1 + 2 A thousand million Milli arde Million 1½ 10 9 Giga
    Tri llion Thousand 1 + 3 trillion Bi llion Million 2 10 12 Tera
    Quadr illion Thousand 1 + 4 A thousand trillion Billi arde Million 2½ 10 15 Peta
    Quint illion Thousand 1 + 5 Trillion Tri llion Million 3 10 18 Exa
    Sext illion Thousand 1 + 6 A thousand trillion Trilli arde Million 3½ 10 21 Zetta
    Sept illion Thousand 1 + 7 Quadrillion quadr illion Million 4 10 24 Yotta

    For further numbers on the long scale see number names # Billion, Billiard and beyond ; the short scale is shown in the English language Wikipedia.

    The prefixes of the numbers on the long scale always correspond exactly to the logarithm of the number to the base one million. The short scale has a similar system - but here the prefixes are not the logarithm to the base one million, but the logarithm to the base thousand, reduced by one .

    Other systems

    In Asia in particular there are other systems that are incompatible with the long and short scales. In the Chinese number system , which is also mostly used in Japan and Korea , counts in steps of ten thousand. There are also other names in India ( Lakh , Crore ).

    See also

    Web links

    Individual evidence

    1. ↑ Fabian Maysenhölder: Why is the English trillion not a trillion? In: n-tv knowledge. May 10, 2016. Retrieved November 22, 2017 .
    2. ↑ Christoph Clauser : Introduction to Geophysics: Global physical fields and processes in the earth . Springer-Verlag, 2014, ISBN 978-3-642-04496-0 , pp. 346 .
    3. ↑ Berthold Schuppar, Hans Humenberger: Elementary numerics for the secondary level . Springer-Verlag, 2015, ISBN 978-3-662-43479-6 , pp. 69 .
    4. ^ Geneviève Guitel: Histoire comparée des numérations écrites . Flammarion, Paris 1975, ISBN 978-2-08-211104-1 , pp. 51-52, 566-574 (French).
    5. ↑ Billion (definition). (PDF) Minutes of Parliament, December 20, 1974, Hansard 1803-2005 (English)
    6. ↑ Fluter , Issue 41, 2011/2012, p. 23; Federal Agency for Political Education .
    7. ↑ billion . In: Al Jazem English-Arabic online dictionary . Publisher: Encyclopedia Britannica
    8. ↑ trillion . In: Al Jazem English-Arabic online dictionary . Publisher: Encyclopedia Britannica
    9. ↑ Decree No. 61-501 of 3 may 1961 relatif aux units de mesure . ( Memento of July 17, 2012 in the Internet Archive ) (PDF) Journal officiel , May 20, 1961 (French)
    10. ↑ Section 5.3.7 Stating values ​​of dimensionless quantities, or quantities of dimension one. In: SI Brochure: The International System of Units (SI) [8th edition, 2006; updated in 2014]. Bureau International des Poids et Mesures, 2014, accessed November 22, 2017 .
    11. ↑ Names of large numbers in the English language Wikipedia.