Long and short scales

Long scale is the English translation of the French term "échelle longue", which designates a system of numeric names in which the word billion means a million millions.

Short scale is the English translation of the French term "échelle courte", which designates a system of numeric names in which the word billion means a thousand millions.

For most of the nineteenth and twentieth centuries, Great Britain uniformly used the long scale, while the United States of America used the short scale, so the two systems were often (and accurately at that time) referred to as "British" and "American" usage, respectively. However, by the end of the 20th century, almost all English-speaking countries had universally adopted the short scale, so the phrases "British usage" and "American usage" are now misleading.

Both systems have been used in France at various times in history, but France has now settled with the long scale, in common with most other European languages.

Usage note: some Wikipedia articles use the terms "long scale" and "short scale," although they are not presently standard terms in English, because they are unambiguous and easily understood, and because there is no better substitute.

Comparison

Value		Short Scale	Long Scale
103 =	1 000	thousand	thousand
106 =	1 000 000	million	million
109 =	1 000 000 000	billion	milliard (or thousand million)
1012 =	1 000 000 000 000	trillion	billion
1015 =	1 000 000 000 000 000	quadrillion	billiard (or thousand billion)
1018 =	1 000 000 000 000 000 000	quintillion	trillion

For a more extensive table, see names of large numbers.

History

• 1475: Jehan Adam recorded the words "bymillion" and "trimillion" (for 10¹² and 10¹⁸)
• 1484: French mathematician Nicolas Chuquet, in his article "Triparty en la science de nombres"[1], used the words byllion, tryllion, quadrillion, quyllion, sixlion, septyllion, ottyllion, and nonyllion to refer to 10¹², 10¹⁸, etc.; Chuquet's work had little direct influence because it was not published until the 1870s, but most of it was copied (without attribution) by Estienne de la Roche for a portion of his 1520 book, Larismetique
• ca. 1550: Pelletier retained Chuquet's long scale but suggested the name milliard in place of "thousand million". This word was widely adopted in England, Germany, and the rest of Europe.
• Early 17th century: In France and Italy, a minority of scientists changed the sense of "billion" to 10⁹
• Middle 18th century: The reformed meaning of the term "billion" was brought to the British American colonies
• Early 19th century: France partially converted to the short scale, and was followed by the USA, which began teaching it in schools.
• 1926: H. W. Fowler's Modern English Usage noted "It should be remembered that this word ["billion"] does not mean in American use (which follows the French) what it means in British. For to us it means the second power of a million, i.e. a million millions (1,000,000,000,000); for Americans it means a thousand multiplied by itself twice, or a thousand millions (1,000,000,000), what we call a milliard. Since billion in our sense is useless except to astronomers, it is a pity that we do not conform."
• 1948: The Conférence Générale des Poids et des Mesures, meeting in France, proposed to return to the long scale.
• 1961: The Journal Officiel (the French official gazette) confirmed the official French use of the long scale (Décret 61-501, page 4587, note 3, as modified by the erratum on page 7572).
• 1974: British prime minister Harold Wilson abandoned the long scale meaning of billion (10¹²), explaining before the House of Commons that "billion" from now on in British government statistics has the short scale meaning of 10⁹, in common with the U.S.
• 1994: The Italian government officially confirmed the long scale use of the term "billion" (Direttiva CE 1994 n. 55, page 12).
• End of 20th century: As a result of US influence, the short scale usage came to be used officially by all English-speaking countries.

Current usage

Short scale countries

The following countries use the short scale:

• Most English-speaking countries — the U.S., Canada, United Kingdom, Ireland, Australia, etc.
• Brazil, which despite speaking a variant of Portuguese, uses 10⁹ = bilhão, 10¹² = trilhão, etc.
• Puerto Rico, a Spanish-speaking US territory uses 10⁹ = billón, 10¹² = trillón, etc.
• Russia and Turkey, where 10⁹ is commonly called "milliard" but the short scale is used for 10¹² and above .
• Greece, which uses 10⁹ = disekatommyrio ("bi-hundred-myriad"), 10¹² = trisekatommyrio, ("tri-hundred-myriad"), etc

Long scale countries

The following countries use the Long scale:

• All other countries using French-derived numbering systems

Examples:

French, Danish and Norwegian milliard, German Milliarde, Dutch miljard, Hebrew milliard, Spanish millardo, Italian miliardo, Polish miliard, Swedish miljard or milliard, Finnish miljardi, Latvian miljards, Czech miliarda, Romanian miliard and Slovenian, Croatian and Serbian milijarda all equal 10⁹.

French, Norwegian and Danish billion, German Billion, Dutch biljoen, Spanish billón, Polish and Serbian bilion, Swedish billion or biljon, Finnish biljoona, Croatian bilijun, Portuguese (Portugal) bilião, Slovenian bilijon - all equal 10¹².

Italian usage

In Italian, the word bilione officially means 10¹². Colloquially, bilione can mean both 10⁹ and 10¹²; trilione both 10¹² and (rarer) 10¹⁸ and so on. Therefore, in order to avoid ambiguity, hardly anybody uses them. Forms such as mille miliardi (a thousand milliards) for 10¹², un milione di miliardi for 10¹⁵, un miliardo di miliardi for 10¹⁸, mille miliardi di miliardi for 10²¹ are much more common.

UK usage

The term "milliard" is now obsolete in British English and "billion" has meant nothing except 10⁹ in all published writing for many years now. Both the UK government and the BBC use the short scale exclusively in all contexts. Anyone deliberately using billion to mean 10¹² in British English is likely to be misunderstood.

However, the long scale understanding still persists, and not only among older people. As numbers this large are rare in everyday life, a significant proportion of lay readers will interpret "billion" as 10¹² ("a million million"), even if they are young enough to have been taught otherwise at school. Following this pattern incorrectly, some will even extrapolate "trillion" as a (long scale) billion billions (10²⁴) rather than the actual long scale 10¹⁸ or the short scale 10¹².

For the above reasons, avoiding the words "billion", "trillion" etc. may be advisable when writing for the general public.

Australian usage

In Australia, some documents use the term thousand million for 10⁹ in cases where two amounts are being compared using a common unit of one 'million'. The current recommendation by AusInfo, the Government printing service, and the legal definition, is the short scale (AusInfo, Style Guide for Authors, Editors and Printers). Education, media outlets, and literature all use the short scale in line with other English speaking countries.

Esperanto usage

The official Esperanto words biliono, triliono etc. are ambiguous, and the inherently international nature of Esperanto communication compounds the problem by preventing any national presumption in favour of long or short scale. Ambiguity may be avoided by the use of the unofficial but generally-recognised suffix -iliono appended to a numeral indicating the power of a million, e.g. duiliono (from du meaning "two") = (10⁶)² = 10¹², triiliono = 10¹⁸, etc. Miliardo is an unambiguous term for 10⁹.

Alternative approaches

Unambiguous ways of identifying large numbers include:

• Combinations of the unambiguous word 'million', for example: 10⁹ = "one thousand million"; 10¹² = "one million million". This becomes rather unwieldy for numbers above 10¹².

• Combination of numbers with more than 3 digits with million, as in 15,300 million.

• Scientific notation, including its engineering notation variant, for example 10⁹, 10¹². This is the most common practice among scientists and mathematicians, and is both unambiguous and convenient.

• SI prefixes, for example, giga for 10⁹ and tera for 10¹². In information technology contexts, the prefix is sometimes used as a power of 2¹⁰ instead of 10³, but there is an attempt at introducing a binary prefix system to eliminate this inambiguity.