Long scale

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 only 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) referred to as "British" and "American" usage, respectively. However, by the end of the 20th century most English-speaking countries had almost universally adopted the short scale, so the phrases "British usage" and "American usage" are now confusing.

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

"Long scale" and "short scale" are not familiar terms in English, but once explained they are easily understood and unambiguous. Therefore, articles such as Billion and Names of large numbers, discussing numeric nomenclature, use the phrases "long scale" and "short scale" to refer to the two systems.

Comparison

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: France's International Conférence des Poids et des Mesures proposed to return to the long scale.
• 1961: The Journal Officiel (the French official gazette) confirmed the official French usage of the long scale (Décret 61-501, page 14, note 3A).
• 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, 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

All other countries using French-derived numbering systems use the long scale. Examples:

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

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

In Italian, the word 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 incorrect pattern, 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

Some official recognition is given in Australia to a variant of the long form system which uses thousand million to mean 10⁹ and billion to mean 10¹². Many newspapers and publications also use short form, however. The current recommendation by AusInfo, the Government printing service, and the legal definition, are currently the short form (AusInfo, Style Guide for Authors, Editors and Printers).

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. One problem is that in computing contexts the prefix may be interpreted as the binary prefix with the same name but a somewhat different value.