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Scale

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:

Long scale

Every new term greater than million is one million times larger than the previous term. Thus, billion means a million millions (1012), trillion means a million billions (1018), and so on. Thus, an n-illion equals 106n.

Short scale

Every new term greater than million is one thousand times larger than the previous term. Thus, billion means a thousand millions (109), trillion means a thousand billions (1012), and so on. Thus, an n-illion equals 103n + 3.

For whole numbers less than a thousand million (< 109) the two scales are identical. From a thousand million up (≥ 109) the two scales diverge, using the same words for different numbers; this can cause misunderstanding.

Countries where the long scale is currently used include most countries in continental Europe and most French-speaking, Spanish-speaking, 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 country, but are similar everywhere due to shared etymology (e.g., billion is billón in Spanish). Some languages, particularly in East Asia and South Asia, have large number naming systems that are different from both the long and short scales, 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 purposes including official. With very few exceptions, the British usage and American usage are now identical.

The first recorded use of the terms short scale (French: échelle courte) and long scale (French: échelle longue) was by the French mathematician Geneviève Guitel in 1975.