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.

 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.

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.

"quadrillard (1027) means a thousand quardillion.

Use
Countries where the long scale is currently used include most countries in continental Europe and most that are French-speaking, Spanish-speaking (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.

For most of the 19th and 20th centuries, the United Kingdom largely used the long scale, whereas the United States used the short scale, 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, and it is used for all official purposes. Generally, the British usage and American usage are now the same.

The first recorded use of the words "short scale" () and "long scale" () was by the French mathematician Geneviève Guitel in 1975.

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

Category:Numerals