Long and short scales

The long and short scales are two powers-of-ten number-naming systems that are consistent with each other for smaller numbers, but are distinct for larger numbers. Much of the world has adopted either the short or long scale. Countries using the long scale include most countries in continental Europe and most that are French-speaking, German-speaking and Spanish-speaking. Use of the short scale is found in most English-speaking, Arabic-speaking, and Hebrew-speaking countries, as well as most Eurasian post-communist countries, and Brazil.

For smaller powers of ten (one, ten, hundred, thousand, and million), the short and long scales are identical; but, for larger powers of ten, the two systems differ in confusing ways. The long scale grows between names by multiples of one million (10⁶) whereas the short scale grows by multiples of one thousand (10³). For example, the short scale billion is one thousand million (10⁹), whereas in the long scale, billion is one million million (10¹²), making the word 'billion' a false friend between long- and short-scale languages. The long scale system includes additional names for interleaved values, typically replacing the word-ending '-ion' with '-iard'.

To avoid confusion, the International System of Units (SI) recommends using the metric prefixes to indicate magnitude. For example, giga- is always 10⁹, which is 'billion' in short scale but 'milliard' in long scale.

Other numbering systems, particularly in East Asia and South Asia, have large number naming that differs from both the long and the short scales. Such numbering systems include the Indian numbering system and Chinese, Japanese, and Korean numerals. though this also becomes unwieldy with longer numbers.

Methods that are better at longer numbers include:

• Scientific notation (for example 1.2), or its engineering notation variant (for example 12), or the computing variant E notation (for example <code>1.2e10</code>). This is the most common practice among scientists and mathematicians, but can be cumbersome in spoken word.

• SI metric prefixes. For example, giga for 10⁹ and tera for 10¹² can give gigawatt (10⁹ W) and terawatt (10¹² W).

History

Although this situation has been developing since the 1200s, the first recorded use of the terms short scale () and long scale () was by the French mathematician Geneviève Guitel in 1975. whereas the United States used the short scale, and it is used for all official purposes. The British usage and American usage are now identical.

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, Spanish billón, German Billion, Dutch biljoen, Danish billion, Swedish biljon, Finnish biljoona, Slovenian bilijon, Polish bilion, and European Portuguese word bilião (with a different spelling to the Brazilian Portuguese variant, but in Brazil referring to short scale) all refer to 10¹², being long-scale terms. Therefore, each of these words translates to the American English or post-1974 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 Welsh word biliwn all refer to 10⁹, being short scale terms. Each of these words translates to the American English or post-1974 British English word billion (10⁹ in the short scale).

The term billion originally meant 10¹² when introduced.

The word milliard, or its translation, is found in many European languages and is used in those languages for 10⁹. However, it is not found 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 (or similar) for one thousand long scale billions (i.e., 10¹⁵), and the word trilliard (or similar) for one thousand long scale trillions (i.e., 10²¹), etc.

;Timeline

{| class="wikitable" style="width:100%;"

|-

! style="width:6%; vertical-align:top;"|&nbsp;Date

! style="width:94%; vertical-align:top;"|&nbsp;Event

|-

|valign="top"| 13th century

| The word million was not used in any language before the 13th century. The monk and polymath Maximus Planudes (–1305) was among the first recorded users of the word to document Mediterranean trade between Constantinople and Italian states.

Translation:

|-

| valign="top"|1484

|thumb|right| French mathematician Nicolas Chuquet, in his article Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien, used the words byllion, tryllion, quadrillion, quyllion, sixlion, septyllion, ottyllion, and nonyllion to refer to 10¹², 10¹⁸, ... 10⁵⁴. Most of the work was copied without attribution by Estienne de La Roche and published in his 1520 book, L'arismetique.

Translation:

|-

| valign="top"|1549

| The influential French mathematician Jacques Pelletier du Mans used the name milliard (or milliart) to mean 10¹², attributing the term to the earlier usage by Guillaume Budé This usage formed the origins of the later short scale. The majority of scientists either continued to say thousand million or changed the meaning of the Pelletier term, milliard, from "million of millions" down to "thousand million".

Translation:

|-

| valign="top"|1729

|The short-scale meaning of the term billion had already been brought to the British American colonies. The first American appearance of the short scale value of billion as 10⁹ was published in the Greenwood Book of 1729, written anonymously by Prof. Isaac Greenwood of Harvard College.

|-

| valign="top"|Early 19th century

|France widely converted to the short scale, and was followed by the U.S., which began teaching it in schools. Many French encyclopedias of the 19th century either omitted the long scale system or called it "désormais obsolète", a now obsolete system. Nevertheless, by the mid 20th century France would officially convert back to the long scale.

|-

| valign="top"|1926

|thumb|upright| H. W. Fowler's A Dictionary of Modern English Usage This paper was widely distributed as the basis for further discussion. The matter of the International System of Units was eventually resolved at the 11th General Conference in 1960. The question of long scale versus short scale was not resolved and does not appear in the list of any conference resolutions.

|-

| valign="top"|1960

|The 11th General Conference on Weights and Measures adopted the International System of Units (SI), with its own set of numeric prefixes. SI is therefore independent of the number scale being used. SI also notes the language-dependence of some larger-number names and advises against using ambiguous terms such as billion, trillion, etc. The National Institute of Standards and Technology within the US also considers that it is best that they be avoided entirely.

|-

| valign="top"|1961

|The French Government confirmed their official usage of the long scale in the Journal officiel (the official French Government gazette).

|-

| valign="top"|1974

|thumb|upright| British prime minister Harold Wilson explained in a written answer to the House of Commons that UK government statistics would from then on use 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'. |group="shortscale note" |group="shortscale note" |group="shortscale note"|group="shortscale note" 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 a word or phrase equivalent to thousand millions.

Dutch-speaking

Most Dutch-language countries and regions use the long scale with 10⁹ = .

French-speaking

Most French-language countries and regions use the long scale with 10⁹ = , for example: for 10⁹, but (thousand millions) is used more frequently. The word is sometimes used in the short scale sense in those countries more influenced by the United States, where "billion" means "one thousand millions". The usage of to mean "one thousand millions", controversial from the start, was denounced by the Royal Spanish Academy as recently as 2010, but was finally accepted in a later version of the official dictionary as standard usage among educated Spanish speakers in the United States (including Puerto Rico).|group="longscale note" Ambiguity may be avoided by the use of the unofficial but generally recognised suffix , 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. (from meaning "two") = = 10¹², = = 10¹⁸, etc. following the 1 long scale convention. is an unambiguous term for 10⁹, and generally the suffix , for values 1, for example = 10²¹ and so forth. |group="longscale note" can mean both 10⁹ and 10¹²; can mean both 10¹² and (rarer) 10¹⁸ and so on. Therefore, in order to avoid ambiguity, they are seldom used. Forms such as (milliard) for 10⁹, (a thousand milliards) for 10¹², (a million milliards) for 10¹⁵, (a milliard of milliards) for 10¹⁸, (a thousand milliard of milliards) for 10²¹ are more common. (, ). There are ambiguities for numbers above 10¹².

• (, )
• (French: , ; German: , ; Italian: , ; Romansh: , )

Using both

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

{| class="wikitable"

|-

! Country or territory

! Short scale usage

! Long scale usage

|-

|

|Canadian English (10⁹ = billion, 10¹² = trillion)

|Canadian French (10⁹ = , 10¹² = or ).

|-

|

|English (10⁹ = billion, 10¹² = trillion)

|French (10⁹ = , 10¹² = )

|-

|

|South African English (10⁹ = billion, 10¹² = trillion)

|Afrikaans (10⁹ = , 10¹² = )

|-

|<!--<br>a Spanish-speaking US Commonwealth territory-->

|Economic and technical (10⁹ = , 10¹² = )

|Latin American export publications (10⁹ = or , 10¹² = )

|}

Using neither

The following countries use naming systems for large numbers that are not etymologically related to the short and long scales:

{| class="wikitable"

! Country

! Number system

! Naming of large numbers

|-

|<br><br><br><br>||Indian numbering system||Traditional system for everyday use, but short or long scale may also be in use

|-

| || Dzongkha numerals || Traditional system

|-

| || Khmer numerals || Traditional system

|-

| || East Asian numbering system: || Traditional myriad system for the larger numbers; special words and symbols up to 10⁶⁸

|-

| || Calque of the short scale || Names of the short scale have not been loaned but calqued into Greek, based on the native Greek word for million, <!--εκατομμύριο--> ("hundred-myriad", i.e. 100&nbsp;×&nbsp;10,000):

• <!--δισεκατομμύριο--> "bi+hundred-myriad" = 10⁹ (short scale billion)
• <!--τρισεκατομμύριο--> "tri+hundred-myriad" = 10¹² (short scale trillion)
• "quadri+hundred-myriad" = 10¹⁵ (short scale quadrillion), and so on.

|-

| || Lao numerals || Traditional system

|-

| || Mongolian numerals || Traditional myriad system for the larger numbers; special words up to 10⁶⁷

|-

|<!--Sri Lanka--> || || Traditional systems

|-

| || Thai numerals || Traditional system based on millions

|-

| || Vietnamese numerals || Traditional system(s) based on thousands

|}

By continent

The long and short scales are both present on most continents, with usage dependent on the language used. For example:

{| class="wikitable"

!Continent

!Short scale usage

!Long scale usage

|-

|Africa

|Arabic (Egypt, Libya), South African English

|French (Benin, Guinea), Portuguese (Mozambique)

|-

|North America

|American English, Canadian English, U.S. Spanish

|Canadian French, Mexican Spanish

|-

|South America

|Brazilian Portuguese, English (Guyana)

|American Spanish, Dutch (Suriname), French (French Guiana)

|-

|Antarctica

|Australian English, British English, New Zealand English, Russian

|American Spanish (Argentina, Chile), French (France), Norwegian (Norway)

|-

|Asia

|Hebrew (Israel), Indonesian, Philippine English

|Persian (Iran), Portuguese (East Timor, Macau)

|-

|Europe

|British English, Russian, Ukrainian, Estonian, Latvian, Lithuanian, Bulgarian, Romanian, Albanian, Turkish

|Dutch, French, German, Italian, Portuguese, Spanish, Danish, Swedish, Norwegian, Finnish, Icelandic, Polish, Czech, Slovak, Hungarian, Serbo-Croatian, Slovene, Macedonian

|-

|Oceania

|Australian English, New Zealand English

|French (French Polynesia, New Caledonia)

|}

Notes on current usage

Short scale

Long scale

Both long and short scale

Neither long nor short scale

See also

• Googol (number)
• Googolplex (number)
• Names of large numbers
• Names of small numbers
• Orders of magnitude (numbers)
• Hindu units of time which displays some similar issues
• Indian numbering system

References

External links

• BBC News article: "Is trillion the new billion?"
• Live-Counter.com: How to visualize large numbers:"