The long and short scales are two of several large-number naming systems used throughout
the world for integer powers of ten: Long scale: Every new term greater than million
is one million times larger than the previous term. Thus, billion means a million millions,
trillion means a million billions, and so on.
Short scale: Every new term greater than million is one thousand times larger than the previous
term. Thus, billion means a thousand millions, trillion means a thousand billions, and so
on. For integers less than a thousand million,
the two scales are identical. At and above a thousand million, the two scales diverge
by using the same words for different number values. These "false friends" can be a source
of misunderstanding. Many countries, including most in continental
Europe and Latin America, use the long scale whereas most English-speaking countries and
Arabic-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 both the long and short scales.
For most of the 19th century and into the early 20th century, the United Kingdom largely
used the long scale, while the United States of America 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 British usage of the short scale, in 1974, the government
of the UK fully adopted it, which is reflected in its mass media and official usage. With
very few exceptions, the British usage and American usage are now identical.
The first recorded use of the terms short scale and long scale was by the French mathematician
Geneviève Guitel in 1975.
Comparison At and above a thousand million, 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. In the short scale, the
prefixes refer to one less than the exponent. The relationship between the numeric values
and the corresponding names in the two scales can be described as:
The relationship between the names and the corresponding numeric values in the two scales
can be described as: The root mil in "million" does not refer to
the numeral "one". The word million derives from the Old French milion from the earlier
Old Italian milione, an intensification of the Latin word mille, a thousand. That is,
a million is a "big thousand", much as a "great gross" is a dozen gross or 1728.
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, unlike the term billion, it is internationally unambiguous and phonetically
distinct from million. Likewise, many long scale countries use the word billiard for
a thousand long scale billions, and the word trilliard for a thousand long scale trillions,
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; Polish bilion, Spanish billón;
Slovenian bilijon and the European Portuguese word bilião 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, and not billion. 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.
The terms billion and milliard both originally meant 1012 when introduced.
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. Some of these countries,
but not all, introduced new words billiard, trilliard, etc. as intermediate terms.
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.
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.
Timeline Current usage
Short scale users English-speaking
106 = one million, 109 = one billion, 1012 = one trillion, etc.
Most English-language countries and regions use the short scale with 109 = billion. For
example:
Arabic-speaking 106 = میليون million, 109 = میليار
milyar, 1012 = تريليون trilyon, etc. Most Arabic-language countries and regions
use the short scale with 109 = میليار milyar. For example:
Other short scale 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 like English use a word similar
to billion to mean 109, most like Arabic 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:
With other terminology Greece
Long scale users The traditional long scale is used by most
Continental European countries and by most other countries whose languages derive from
Continental Europe. These countries use a word similar to billion to mean 1012. Some
use a word similar to milliard to mean 109, while others use a word or phrase equivalent
to thousand millions. Spanish-speaking
106 = millón, 109 = mil millones or millardo, 1012 = billón, etc.
Most Spanish-language countries and regions use the long scale with 109 = mil millones,
for example:
French-speaking 106 = million, 109 = milliard, 1012 = billion,
etc. Most French-language countries and regions
use the long scale, for example:
Portuguese-speaking 106 = milhão, 109 = mil milhões or milhar
de milhões, 1012 = bilião With the notable exception of Brazil, a short
scale country, most Portuguese-language countries and regions use the long scale, for example:
Dutch-speaking 106 = miljoen, 109 = miljard, 1012 =biljoen
Most Dutch-language countries and regions use the long scale, for example:
Other long scale 106 = one million, 109 = one milliard / thousand
million, 1012 = one billion, 1015 = one billiard / thousand billion, 1018 = one trillion, etc.
Some examples of long scale use, and the words used for 109 and 1012, are:
Other long scale languages Esperanto language
Using both 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 OR one milliard / thousand million, 1012 = EITHER
one trillion OR one billion, etc. Using neither
The following 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 most continents, with usage dependent on the language used. Examples include:
Notes on current usage Short scale
^ 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.
^ 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, and the legal definition,
is the short scale. 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'.
^ Filipino usage: Some short-scale words have been adopted into Filipino.
^ 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.
Before the widespread use of billion for 109, UK usage generally referred to thousand million
rather than milliard. 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. ^ 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. ^ Arabic language countries: Most Arabic-language
countries use: 106 = میليون million, 109 = میليار milyar, 1012 = تريليون
trilyon, etc. ^ Indonesian usage: Large numbers are common
in Indonesia, in part because its currency is generally expressed in large numbers. The
term juta, equivalent to million, is generally common in daily life. Indonesia officially
employs the term miliar 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 or more rarely
sejuta juta are also used for 1012 less often. Terms greater than triliun are not very familiar
to Indonesians. Long scale
^ Spanish language countries: Spanish-speaking countries sometimes use millardo for 109,
but mil millones is used more frequently. The word billón is sometimes used in the
short scale sense in those countries more influenced by the United States, but this
is considered unacceptable. ^ 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.
^ 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. In Italian, the word bilione officially means
1012, trilione means 1018, etc.. Colloquially, bilione can mean both 109 and 1012; trilione
can mean both 1012 and 1018 and so on. Therefore, in order to avoid ambiguity, they are seldom
used. Forms such as miliardo for 109, mille miliardi for 1012, un milione di miliardi
for 1015, un miliardo di miliardi for 1018, mille miliardi di miliardi for 1021 are more
common. ^ 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. 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 numeral indicating the power
of a million, e.g. duiliono = biliono = 1012, triiliono = triliono = 1018, etc. following
the 1×106X long scale convention. Miliardo is an unambiguous term for 109, and generally
the suffix -iliardo, for values 1×106X+3, for example triliardo = 1021 and so forth.
Both long and short scale ^ 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. ^ South African usage: South Africa uses both
the long scale and the short scale. Unlike the 1974 UK switch, the switch from long scale
to short scale took time. As of 2011 most English language publications use 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"
and has thus, to most appearances, been abandoned. Neither long nor short scale
^ 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 and
arab to denote thousand million. Alternative approaches
Unambiguous ways of identifying large numbers include:
In written communications, the simplest solution for moderately large numbers is to write the
full amount, for example 1,000,000,000,000 rather than, say, 1 trillion or 1 billion.
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 Scientific notation, or its engineering notation
variant, or the computing variant E notation 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 and terawatt, respectively. The International System of Units is independent
of whichever scale is being used. Use with non-SI units is uncommon.
See also
References
External links BBC News article: "Is trillion the new billion?"