Long and short scales

The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries use the short scale. In all such countries, the number names are translated into the local language, but retain a name similarity due to shared etymology. Some languages, particularly in East Asia and South Asia, have large number naming systems that are different from the long and short scales.^[1][2]

Long scale is the English translation of the French term échelle longue. It refers to a system of large-number names in which every new term greater than million is 1,000,000 times the previous term: billion means a million millions (10¹²), trillion means a million billions (10¹⁸), and so on.^[1][2]

Short scale is the English translation of the French term échelle courte. It refers to a system of large-number names in which every new term greater than million is 1,000 times the previous term: billion means a thousand millions (10⁹), trillion means a thousand billions (10¹²), and so on.^[1][2]

For integers less than a thousand million (< 10⁹), the two scales are identical. At and above a thousand million (≥ 10⁹), the two scales diverge by using the same words for different number values. These "false friends" can be a source of misunderstanding.

For most of the 19th and 20th centuries, the United Kingdom uniformly used the long scale,^[3] while the United States of America used the short scale,^[3] so that the two systems were often referred to as British and American in the English language. In 1974, the government of the UK switched to the short scale, a change that is reflected in its mass media and official usage.^{[4][5][6][7][8][9]} Although some residual usage of the long scale continues in the UK,^[10][11] the phrases British usage and American usage are no longer accurate characterisations. Usage of the two systems can be a subject of controversy. Differences in opinion as to which system should be used can evoke resentment between adherents, while national differences of any kind can acquire jingoistic overtones.^[11]

The first recorded use of the terms échelle courte and échelle longue was by the French mathematician Geneviève Guitel in 1975.^[1][2]

Comparison

The same numerical value has two different names, depending on whether the value is being expressed in the long or short scale. Equivalently, the same name has two different numerical values depending on whether it is being used in the long or short scale.

Each scale has a logical justification to explain the use of each such differing numerical name and value within that scale. The short scale logic is based on powers of one thousand, whereas the long scale logic is based on powers of one million. In both scales, the prefix bi- refers to "2" and tri- refers to "3", etc. However only in the long scale do the prefixes beyond one million indicate the actual power or exponent (of 1,000,000). In the short scale, the prefixes refer to one less than the exponent (of 1,000).

The relationship between the numeric values and the corresponding names in the two scales can be described as:

The root mil in "million" does not refer to the numeral "one". Rather, it refers to the Latin word for "thousand" (milia).

The relationship between the names and the corresponding numeric values in the two scales can be described as:

The word milliard, or its translation, is found in many European languages and is used in those languages for 10⁹. However, it is unknown in American English, which uses billion, and not used in British English, which preferred to use thousand million before the current usage of billion. The financial term yard, which derives from milliard, is used on financial markets, as it is unambiguous, unlike billion. Likewise, many long scale countries use the word billiard (or similar) for a thousand long scale billions (i.e. 10¹⁵), and the word trilliard (or similar) for a thousand long scale trillions (i.e. 10²¹), etc.

History

The existence of the different scales means that care must be taken when comparing large numbers between languages or countries, or when interpreting old documents in countries where the dominant scale has changed over time. For example, British-English, French, and Italian historical documents can refer to either the short or long scale, depending on the date of the document, since each of the three countries has used both systems at various times in its history. Today, the United Kingdom officially uses the short scale, but France and Italy use the long scale.

The pre-1974 former British English word billion, post-1961 current French word billion, post-1994 current Italian word bilione, German Billion; Dutch biljoen; Swedish biljon; Finnish biljoona; Danish billion; Spanish billón and the European Portuguese word bilião (with an alternate spelling to the Brazilian Portuguese variant) all refer to 10¹², being long-scale terms. Therefore, each of these words translates to the American English or post-1974 modern British English word: trillion (10¹² in the short scale), and not billion (10⁹ in the short scale).

On the other hand, the pre-1961 former French word billion, pre-1994 former Italian word bilione, Brazilian Portuguese word bilhão and the Welsh word biliwn all refer to 10⁹, being short scale terms. Each of these words translates to the American English or post-1974 modern British English word billion (10⁹ in the short scale).

The terms billion and milliard both originally meant 10¹² when introduced.^[12]

• In long scale countries, milliard was redefined down to its current value of 10⁹, leaving billion at its original 10¹² value and so on for the larger numbers.^[12] Some of these countries, but not all, introduced new words billiard, trilliard, etc. as intermediate terms.^[13][14][15]
• In some short scale countries, milliard was redefined down to 10⁹ and billion dropped altogether, with trillion redefined down to 10¹² and so on for the larger numbers.^[12]
• In many short scale countries, milliard was dropped altogether and billion was redefined down to 10⁹, adjusting downwards the value of trillion and all the larger numbers.

The word million derives from the Old French Milion from the earlier Old Italian milione, an intensification of mille, a thousand. That is, a million is a "big thousand", much as a "great gross" is a dozen gross or 1728.^[12]

Timeline

Current usage

Short scale countries and regions

English language-speaking countries and regions ^{[shortscale note 1]}

10⁶ = one million, 10⁹ = one billion, 10¹² = one trillion, etc.

Most English-language countries use the short scale with 10⁹ = billion. For example:

Other short scale countries and regions

10⁶ = one million, 10⁹ = one milliard / billion, 10¹² = one trillion, etc.

Other countries also use a word similar to trillion to mean 10¹², etc. While a few of these countries use a word similar to billion to mean 10⁹, most have kept a traditional long scale word similar to "milliard" for 10⁹. Some examples of short scale use, and the words used for 10⁹ and 10¹², are:

Short scale use but with other terminology

 Greece (εκατομμύριο ekatommyrio "hundred-myriad" = 10⁶; δισεκατομμύριο disekatommyrio "bi+hundred-myriad" = 10⁹; τρισεκατομμύριο trisekatommyrio "tri+hundred-myriad" = 10¹²; τετράκις εκατομμύριο tetrakis ekatommyrio "quadri+hundred-myriad" = 10¹⁵, and so on.)^[36]

Long scale countries and languages

10⁶ = one million, 10⁹ = one milliard / thousand million, 10¹² = one billion, 10¹⁵ = one billiard / thousand billion, 10¹⁸ = one trillion, etc.

The traditional long scale is used by most Continental European countries and by most other countries whose languages derive from Continental Europe (with the notable exceptions of Greece, Romania, Bulgaria and Brazil). These countries use a word similar to billion to mean 10¹². Some use a word similar to milliard to mean 10⁹, while others use something equivalent to thousand millions. Some examples of long scale use, and the words used for 10⁹ and 10¹², are:

Esperanto language   (miliardo, duiliono) ^{[longscale note 4]}

Both long and short scale countries

Some countries use either the Short or Long scales, depending on the internal language being used or the context.

10⁶ = one million, 10⁹ = EITHER one billion (Short Scale) OR one milliard / thousand million (Long Scale), 10¹² = EITHER one trillion (Short Scale) OR one billion (Long Scale), etc.

Neither short nor long scale countries

The following Asian countries have their own numbering systems and use neither short nor long scales:

Presence on most continents

The long and short scales are both present on all continents, with usage dependent on the language used. Examples include:

Alternative approaches

Unambiguous ways of identifying large numbers include:

• In written communications, the simplest solution for moderately large numbers is simply to write the full amount, for example 1,000,000,000,000 rather than, say, 1 trillion (short scale) or 1 billion (long scale).
• 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 of more than 3 digits with the unambiguous word million, for example 13,600 million^[50]
• Scientific notation (also known as standard form or exponential notation, for example 1×10⁹, 1×10¹⁰, 1×10¹¹, 1×10¹², etc.), or its engineering notation variant (for example 1×10⁹, 10×10⁹, 100×10⁹, 1×10¹², etc.), or the computing variant E notation (for example 1e9, 1e10, 1e11, 1e12, etc.) This is the most common practice among scientists and mathematicians, and is both unambiguous and convenient.
• SI prefixes in combination with SI units, for example, giga for 10⁹ and tera for 10¹² can give Gigawatt (=10⁹ W) and Terawatt (=10¹² W), respectively. The International System of Units (SI) is independent of whichever scale is being used.^[22] Use with non-SI units (e.g. "giga-dollars", "giga-miles") is uncommon.

Notes on current usage

Short scale

1. ^ English language countries: Apart from the United States, the long scale was used for centuries in many English language countries before being superseded in recent times by short scale usage. Because of this history, some long scale use persists and the official status of the short scale in anglophone countries other than the UK and US is sometimes obscure.
2. ^ Australian usage: In Australia, education, media outlets, and literature all use the short scale in line with other English-speaking countries. The current recommendation by the Australian Government Department of Finance and Deregulation (formerly known as AusInfo), and the legal definition, is the short scale.^[25] As recently as 1999, the same department did not consider short scale to be standard, but only used it occasionally. Some documents use the term thousand million for 10⁹ in cases where two amounts are being compared using a common unit of one 'million'.
3. ^ Filipino usage: Some short-scale words have been adopted into Filipino.
4. ^ British usage: Billion has meant 10⁹ in most sectors of official published writing for many years now. The UK government, the BBC, and most other broadcast or published mass media, have used the short scale in all contexts since the mid-1970s.^[4][5][6][7]
   Before the widespread use of billion for 10⁹, UK usage generally referred to thousand million rather than milliard.^[8] The long scale term milliard, for 10⁹, is obsolete in British English, though its derivative, yard, is still used as slang in the London money, foreign exchange, and bond markets.
5. ^ American usage: In the United States of America, the short scale has been taught in school since the early 19th century. It is therefore used exclusively.^[26][27]
6. ^ Indonesian usage: Large numbers are common in Indonesia, in part because its currency (rupiah) is generally expressed in large numbers (the lowest common circulating denomination is Rp100 with Rp1000 is considered as base unit). The term juta, equivalent to million (10⁶), is generally common in daily life. Indonesia officially employs the term miliar (derived from the long scale Dutch word miljard) for the number 10⁹, with no exception. For 10¹² and greater, Indonesia follows the short scale, thus 10¹² is named triliun. The term seribu miliar (a thousand milliards) or more rarely sejuta juta (a million millions) are also used for 10¹² less often. Terms greater than triliun are not very familiar to Indonesians.^[31]

Long scale

1. ^ French usage: France, with Italy, was one of two European countries which converted from the long scale to the short scale during the 19th century, but returned to the original long scale during the 20th century. In 1961, the French Government confirmed their long scale status.^[24][37][38]
2. ^ Italian usage: Italy, with France, was one of the two European countries which partially converted from the long scale to the short scale during the 19th century, but returned to the original long scale in the 20th century. In 1994, the Italian Government confirmed its long scale status.^[15]
   In Italian, the word bilione officially means 10¹², trilione means 10¹⁸, etc.. Colloquially, bilione^[41] can mean both 10⁹ and 10¹²; trilione can mean both 10¹² and (rarer) 10¹⁸ and so on. Therefore, in order to avoid ambiguity, they are seldom used. Forms such as miliardo (milliard) for 10⁹, mille miliardi (a thousand milliards) for 10¹², un milione di miliardi (a million milliards) for 10¹⁵, un miliardo di miliardi (a milliard of milliards) for 10¹⁸, mille miliardi di miliardi (a thousand milliard of milliards) for 10²¹ are more common.^[15]
3. ^ Spanish usage: Spanish-speaking countries sometimes use millardo (milliard)^[44] for 10⁹, but mil millones (thousand millions) is used more frequently. The word billón is sometimes incorrectly used in the short scale sense in those countries more influenced by the United States, but this is considered unacceptable.^[45]
4. ^ Esperanto language usage: The Esperanto language words biliono, triliono etc. used to be ambiguous, and both long or short scale were used and presented in dictionaries. The current edition of the main Esperanto dictionary PIV however recommends the long scale meanings, as does the grammar PMEG.^[47] Ambiguity may be avoided by the use of the unofficial but generally-recognised suffix -iliono, whose function is analogous to the long scale, i.e. it is appended to a (single) numeral indicating the power of a million, e.g. duiliono (from du meaning "two") = biliono = 10¹², triiliono = triliono = 10¹⁸, etc. following the 1×10^6X long scale convention. Miliardo is an unambiguous term for 10⁹, and generally the suffix -iliardo, for values 1×10^6X+3, for example triliardo = 10²¹ and so forth.

Both long and short scale

1. ^ Canadian usage: Both scales are in use currently in Canada. English-speaking regions use the short scale exclusively, while French-speaking regions use the long scale.^[48]
2. ^ South African usage: South Africa uses both the long scale (in Afrikaans and sometimes English) and the short scale (in English). Unlike the 1974 UK switch, the switch from long scale to short scale took time with most English publications now (2011) using the short scale. Some Afrikaans publications briefly attempted usage of the "American System" but that has led to comment in the papers and has been disparaged by the "Taalkommissie" (The Afrikaans Language Commission of the South African Academy of Science and Art) and has thus, to most appearances, been abandoned.
3. ^ Romanian usage: Up to and including 10⁹, Romania uses a standard long scale: milion = 10⁶; miliard = 10⁹; Above 10⁹, the short scale is used: trilion = 10¹². The official status of either scale is far from clear.

Neither long nor short scale

1. ^ Indian, Pakistani and Bangladeshi usage: Outside of financial media, the use of billion by Bangladeshi, Indian and Pakistani English speakers highly depends on their educational background. Some may continue to use the traditional British long scale. In everyday life, Bangladeshis, Indians and Pakistanis largely use their own common number system, commonly referred to as the Indian numbering system – for instance, Bangladeshi, Pakistani, and Indian English commonly use the words lakh to denote 100 thousand, crore to denote ten million (i.e. 100 lakhs) and arab to denote thousand million.^[49]

See also

External links

• BBC News article: "Is trillion the new billion?"

References