Editing Long and short scales (section)

{{Short description|Two meanings of "billion" and "trillion"}}
{{For|the concept related to musical instruments|Scale length (string instruments)}}
{{Good article}}
{{Use dmy dates|date=October 2019}} 

The '''long and short scales''' are two [[power of 10|powers of ten]] number naming systems that are consistent with each other for smaller [[order of magnitude|numbers]], but are contradictory for larger numbers.<ref name="Guitel1">
{{Cite book
 |last= Guitel |first= Geneviève
 |author-link= Geneviève Guitel
 |title= Histoire comparée des numérations écrites
 |publisher= [[Groupe Flammarion|Flammarion]]
 |year= 1975 |location= Paris
 |pages= 51–52 |language= fr |isbn= 978-2-08-211104-1}}
</ref><ref name="Guitel2">
{{Cite book
 |last= Guitel |first= Geneviève
 |author-link= Geneviève Guitel
 |title= Histoire comparée des numérations écrites |publisher= Flammarion
 |year= 1975 |location= Paris
 |pages= 566–574
 |chapter= "Les grands nombres en numération parlée (État actuel de la question)", ''i.e. "The large numbers in oral numeration (Present state of the question)"''
 |language= fr |isbn= 978-2-08-211104-1}}
</ref> Other numbering systems, particularly in [[East Asia]] and [[South Asia]], have large number naming that differs from both the long and short scales. Such numbering systems include the [[Indian numbering system]] and [[Chinese numerals|Chinese]], [[Japanese numerals#Powers of 10|Japanese]], and [[Korean Peninsula|Korean]] numerals.<ref name="Guitel1" /><ref name="Guitel2" /> Much of the remainder of the world adopted either the short or long scale. Countries using the long scale include most countries in continental Europe and most that are [[Geographical distribution of French speakers|French-speaking]], [[Geographical distribution of German speakers|German-speaking]] and [[Hispanophone|Spanish-speaking]].<ref>{{Cite web |url=http://lema.rae.es/drae/ |title=Authoritative Real Academia Española (RAE) dictionary: billón |access-date=12 March 2015 |archive-url=https://web.archive.org/web/20151104145435/http://lema.rae.es/drae/ |archive-date=4 November 2015 |url-status=dead }}</ref> Use of the short scale is found in most [[Anglophone|English]] and [[Arabic]] speaking countries, most Eurasian post-communist countries and [[Brazil]].

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 (10<sup>6</sup>), whereas the short scale grows by multiples of one thousand (10<sup>3</sup>). For example, the short scale ''billion'' is one thousand million (10<sup>9</sup>), whereas in the long scale, ''billion'' is one million million (10<sup>12</sup>), making the word [[false friends]] 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, the [[International System of Units]] (SI) recommends using the [[metric prefix]]es to indicate magnitude.
For example, [[giga]] is always 10<sup>9</sup>, which is billion in short scale but milliard in long scale.