词条 | Long and short scales | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
释义 |
The long and short scales are two of several large-number naming systems for integer powers of ten that use the same words with different meanings. The long scale is based on powers of one million, whereas the short scale is based on powers of one thousand. For whole numbers less than a thousand million (< 109) the two scales are identical. From a thousand million up (≥ 109) the two scales diverge, using the same words for different numbers, which can cause misunderstanding. Short scaleEvery new term greater than million is one thousand times as large as the previous term. Thus, billion means a thousand millions (109), trillion means a thousand billions (1012), and so on. Thus, an n-illion equals 103n + 3.[1][2] Long scaleEvery new term greater than million is one million times as large as the previous term. Thus, billion means a million millions (1012), trillion means a million billions (1018), and so on. Thus, an n-illion equals 106n.[1][2] UseCountries where the long scale is currently used include most countries in continental Europe and most that are French-speaking, Spanish-speaking[1] (except Spanish-speakers born into an English-speaking culture, e.g. Puerto Rico, because of its influence from English-speaking United States) and Portuguese-speaking countries, except Brazil. The short scale is now used in most English-speaking and Arabic-speaking countries, in Brazil, in the former Soviet Union and several other countries. Number names are rendered in the language of the country, but are similar everywhere 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 example the Indian numbering system.[2][3] For most of the 19th and 20th centuries, the United Kingdom largely used the long scale,[4][5] whereas the United States used the short scale,[4] so that the two systems were often referred to as British and American in the English language. After several decades of increasing informal British usage of the short scale, in 1974 the government of the UK adopted it,[6] and it is used for all official purposes.[7][8][9][10][11] With very few exceptions,{{explain|date=January 2017}}[12] the British usage and American usage are now identical. The first recorded use of the terms short scale ({{lang-fr|échelle courte}}) and long scale ({{lang-fr|échelle longue}}) was by the French mathematician Geneviève Guitel in 1975.[2][3] To avoid confusion resulting from the coexistence of short and long term in any language, the SI recommends using the Metric prefix, which keeps the same meaning regardless of the country and the language. Long and short scales remain in de facto use for counting money.{{explain|reason=I think this is trying to say that for counting money, /million/ and /billion/ are still used (despite the long-scale/short-scale issue) instead of SI prefixes, but I'm not sure|date=March 2019}} ComparisonThe 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, 1. 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 12×144 = 1728.[13] 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 (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.[14][15][16][17][18] HistoryThe 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 (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 the 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.[13]
As large numbers in natural sciences are usually represented by metric prefixes, scientific notation or otherwise, the most commonplace occurrence of large numbers represented by long or short scale terms is in finance. The following table includes some historic examples related to hyper-inflation and other financial incidents.
Current usageShort scale usersEnglish-speaking106, one million; 109, one billion; 1012, one trillion; etc. Most English-language countries and regions use the short scale with 109 being billion. For example:{{#tag:ref|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[12] and the official status of the short scale in anglophone countries other than the UK and US is sometimes obscure.{{citation needed|date=January 2013}}|group="shortscale note"}} {{div col|colwidth=27em}}{{ASM}} {{AIA}} {{ATG}} {{AUS}} {{#tag:ref|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.[43] 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"}}[43] {{BHS}} {{BRB}} {{BLZ}} (English-speaking) {{BMU}} {{BWA}} (English-speaking) {{VGB}} {{CMR}} (English-speaking) {{CYM}} {{COK}} {{DMA}} {{ERI}} {{ETH}} {{FLK}} {{FJI}} {{GMB}} {{GHA}} (English-speaking) {{GIB}} {{GRD}} {{GUM}} {{GGY}} {{GUY}} (English-speaking) {{HKG}} (English-speaking) {{IRL}} (English-speaking, {{lang-ga|billiún}}, trilliún) {{IMN}} {{JAM}} {{JEY}} {{KEN}} (English-speaking) {{KIR}} {{LSO}} {{LBR}} {{MWI}} (English-speaking) {{MYS}} (English-speaking; {{lang-ms|bilion}} billion, trilion trillion) {{MLT}} (English-speaking; {{lang-mt|biljun}}, triljun) {{MHL}} {{FSM}} {{MSR}} {{NRU}} {{NZ}} (English-speaking) {{NGA}} (English-speaking) {{NIU}} {{NFK}} {{MNP}} {{PLW}} {{PNG}} (English-speaking) {{PHI}} (English-speaking) {{#tag:ref|Filipino usage: Some short-scale words have been adopted into Filipino. |group="shortscale note"}} {{PCN}} {{RWA}} {{SHN}} {{KNA}} {{LCA}} {{VCT}} {{WSM}} {{SLE}} {{SGP}} (English-speaking) {{SLB}} {{SGS}} {{SSD}} (English-speaking) {{SWZ}} {{TZA}} (English-speaking) {{TKL}} {{TON}} {{TTO}} {{TCA}} {{TUV}} {{UGA}} (English-speaking) {{UK}} (see Wales below) {{#tag:ref|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.[6][7][8][9]{{paragraph break}} Before the widespread use of billion for 109, UK usage generally referred to thousand million rather than milliard.[10] 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. |group="shortscale note"}}[6][7][8][9][10] {{USA}} {{#tag:ref|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.[44][45] |group="shortscale note"}}[44][45] {{VIR}} {{ZMB}} (English-speaking) {{ZIM}} (English-speaking)[38][39][40]{{div col end}} Arabic-speaking106, {{lang|ar|مَلْيُوْن|rtl=yes}} malyoon; 109, {{lang|ar|مِلْيَار|rtl=yes}} milyar; 1012, {{lang|ar|تِرِلْيُوْن|rtl=yes}} trilyoon; etc. Most Arabic-language countries and regions use the short scale with 109 being {{lang|ar|مليار|rtl=yes}} milyar, except for a few countries like Saudi Arabia and the UAE which use the world بليون billion for 109. For example:{{#tag:ref|Arabic language countries: Most Arabic-language countries use: 106, {{lang|ar|میليون|rtl=yes}} million; 109, {{lang|ar|میليار|rtl=yes}} milyar; 1012, {{lang|ar|تريليون|rtl=yes}} trilyon; etc.[46][47] |group="shortscale note"}}[46][47] {{div col|colwidth=27em}}{{DZA}} {{BHR}} {{TCD}} {{COM}} {{DJI}} {{EGY}} {{ERI}} {{IRQ}} {{JOR}} {{KWT}} {{LBN}} {{LBY}} {{MRT}} {{MAR}} {{OMN}} {{flag|Palestine}} {{QAT}} {{SAU}} {{SOM}} {{SDN}} {{SYR}} {{TUN}} {{ARE}} {{ESH}} {{YEM}}{{div col end}} Other short scale106, one million; 109, one milliard or one billion; 1012, one trillion; etc. Other countries also use a word similar to trillion to mean 1012, etc. Whilst 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 {{div col|colwidth=27em}}{{AFG}} (Dari: میلیارد milyard or بیلیون billion, تریلیون trillion, Pashto: میلیارد milyard, بیلیون billion, تریلیون trillion) {{ALB}} (miliard, trilion)[48] {{ARM}} (միլիարդ miliard, տրիլիոն trilion) {{AZE}} (milyard, trilyon) {{BLR}} (мільярд milyard, трыльён trilyon) {{BRA}} (Brazilian Portuguese: bilhão, trilhão) {{BRN}} ({{lang-ms|bilion}}, trilion) {{BUL}} (милиард miliard, трилион trilion) {{MYA}} (Burmese: {{my|ဘီလျံ}}, {{IPA-my|bìljàɴ|IPA}}; {{my|ထရီလျံ}}, {{IPA-my|tʰəɹìljàɴ|}})[49] {{CYP}} (Greek: δισεκατομμύριο disekatommyrio, τρισεκατομμύριο trisekatommyrio, {{lang-tr|milyar}}, {{lang|tr|trilyon}}) {{EST}} (miljard or biljon{{#tag:ref|Estonian usage: Biljon is used due to English influences and is less common than miljard.|group="shortscale note" }}, triljon)[50][51][52] {{GEO}} (მილიარდი miliardi, ტრილიონი trilioni) {{INA}} (miliar, triliun) {{#tag:ref|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.[53]|group="shortscale note"}}[53] {{ISR}} (Hebrew: מיליארד milyard, טריליון trilyon) {{KAZ}} (Kazakh: миллиард milliard, триллион trillion) {{KGZ}} (Kyrgyz: миллиард milliard, триллион trillion) {{LVA}} (miljards, triljons) {{LTU}} (milijardas, trilijonas) {{MDA}} (Romanian:[54] miliard, trilion; Russian: миллиард milliard, триллион trillion) {{RUS}} (миллиард milliard, триллион trillion) {{TJK}} (Tajik: миллиард milliard, триллион trillion) {{TUR}} (milyar, trilyon) {{TKM}} (Turkmen: ; Russian: миллиард milliard, триллион trillion) {{UKR}} (мільярд mil'yard, трильйон tryl'yon) {{UZB}} (Uzbek: ; Russian: миллиард milliard, триллион trillion) {{WAL}} (biliwn, triliwn) In some contexts a paraphrase is needed to resolve ambiguity, as the lenitive of both miliwn and biliwn is the same: filiwn.{{div col end}} Long scale usersThe 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 Albania, Greece, Romania,[54] 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. Spanish-speaking106, millón; 109, mil millones or millardo; 1012, billón; etc. Most Spanish-language countries and regions use the long scale, for example:{{#tag:ref|Spanish language countries: Spanish-speaking countries sometimes use millardo (milliard)[55] for 109, but mil millones (thousand millions) is used more frequently. The word billón 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 "billón" to mean "one thousand millions", controversial from the start, was denounced by the Royal Spanish Academy as recently as 2010,[56] 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).[57]|group="longscale note"}}[55][56] {{div col|colwidth=27em}}{{ARG}} {{BOL}} {{CHI}} {{COL}} {{CRC}} {{CUB}} {{DOM}} {{ECU}} {{SLV}} {{GNQ}} {{GUA}} (millardo) {{HON}} (millardo) {{MEX}} (mil millones or millardo) {{NIC}} (mil millones or millardo) {{PAN}} (mil millones or millardo) {{PRY}} {{PER}} (mil millones) {{ESP}} (millardo or typ. mil millones) {{URU}} {{VEN}}{{div col end}} French-speaking106, million; 109, milliard; 1012, billion; etc. Most French-language countries and regions use the long scale with 109 = milliard, for example:{{#TAG:REF|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.[37][58][59] However the 9th edition of the dictionary of the Académie française describes billion as an outdated synonym of milliard, and says that the new meaning of 1012 was decreed in 1961, but never caught on.[60] |group="longscale note"}}[58][59] {{div col|colwidth=27em}}{{BEL}} {{BEN}} {{BFA}} {{CAF}} {{COD}} {{COG}} {{FRA}} {{PYF}} {{ATF}} {{GAB}} {{GIN}} {{HTI}} {{CIV}} (Côte d'Ivoire) {{MLI}} {{MON}} {{NCL}} {{NER}} {{BLM}} {{SEN}} {{TGO}} {{WLF}}{{div col end}} Portuguese-speaking106, 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 with 109 = mil de milhões or milhar de milhões, for example: {{div col|colwidth=27em}}{{AGO}} {{CPV}} {{ETM}} {{GNB}} {{MAC}} {{MOZ}} {{POR}} {{STP}}{{div col end}} Dutch-speaking106, miljoen; 109, miljard; 1012, biljoen; Most Dutch-language countries and regions use the long scale with 109 = miljard, for example:[61][62] {{div col|colwidth=27em}}{{ABW}} {{BEL}} {{CUW}} {{NLD}} {{SXM}} {{SUR}}{{div col end}} German-speaking106, Million; 109, Milliarde; 1012, Billion; 1015, Billiarde; etc. German-language countries and regions use the long scale with 109 = Milliarde, for example: {{AUT}} (Austrian German: Milliarde, Billion) {{BEL}} (German: Milliarde, Billion) {{DEU}} (Milliarde, Billion)[14][15] {{LIE}} (German: Milliarde, Billion) Other long scale106, one million; 109, one milliard or one thousand million; 1012, one billion; etc. Some examples of long scale use, and the words used for 109 and 1012, are {{div col|colwidth=27em}}{{AND}} ({{lang-ca|miliard}} or typ. {{lang|ca|mil milions}}, {{lang|ca|bilió}}) {{BEL}} (Belgian French: milliard, billion; Flemish: miljard, biljoen; {{lang-de|Milliarde}}, {{lang|de|Billion}}) {{BIH}} ({{lang-bs|milijarda}}, {{lang|bs|bilion}}; {{lang-hr|milijarda}}, {{lang|hr|bilijun}}, {{lang-sr|милијарда}} {{lang|sr-Latn|milijarda}}, {{lang|sr|билион}} {{lang|sr-Latn|bilion}}) {{CRO}} (milijarda, bilijun) {{CZE}} (miliarda, bilion) {{DEN}} (milliard, billion) {{flagicon image|Flag of Esperanto.svg}} Esperanto (miliardo, duiliono) {{#TAG:REF|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.[63] 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{{E|6X}} long scale convention. Miliardo is an unambiguous term for 109, and generally the suffix -iliardo, for values 1{{E|6X+3}}, for example triliardo = 1021 and so forth. |group="longscale note"}}[63] {{FRO}} (Danish: milliard, billion) {{FIN}} ({{lang-fi|miljardi}}, {{lang|fi|biljoona}}; Swedish: {{lang|sv|miljard}}, {{lang|sv|biljon}}) {{GRL}} (milliardi, billioni) {{HUN}} (milliárd, billió or ezermilliárd) {{ISL}} (milljarður, billjón) {{IRN}} (Persian: میلیارد milyard, بیلیون billion, تریلیون trillion) {{citation needed|date=November 2013}} {{ITA}} (miliardo, bilione) {{#tag:ref|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.[18] {{LUX}} (French: milliard, billion; German: Milliarde, Billion; {{lang-lb|milliard}}, {{lang|lb|billioun}}) {{MDG}} (French: milliard, billion; {{lang-mg|miliara}}, arivo miliara ) {{MNE}} (Montenegrin: milijarda, bilion) {{NMK}} (милијарда milijarda, билион bilion) {{NOR}} (Bokmål: milliard, billion; Nynorsk: milliard, billion) {{POL}} (miliard, bilion) {{ROM}}[65] (miliard, bilion). See also [66] for ambiguities above 1012). {{SMR}} (Italian: miliardo, bilione) {{SRB}} (милијарда milijarda, билион bilion) {{SVK}} (miliarda, bilión) {{SLO}} (milijarda, bilijon) {{SWE}} (miljard, biljon) {{CHE}} (French: milliard, billion; German: Milliarde, Billion; Italian: miliardo, bilione, Romansh: milliarda, billiun[67] ) {{VAT}} (Italian: miliardo, bilione){{div col end}} Using bothSome 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.
Using neitherThe following countries use naming systems for large numbers that are not etymologically related to the short and long scales:
The long and short scales are both present on most continents, with usage dependent on the language used. Examples include:
Notes on current usageShort scale1. ^Authoritative RAE dictionary: billón 2. ^1 2 3 4 {{Cite book |last= Guitel |first= Geneviève |authorlink= Geneviève Guitel |title= Histoire comparée des numérations écrites |publisher= Flammarion |year= 1975 |location= Paris |pages= 51–52 |language= French |isbn= 978-2-08-211104-1}} 3. ^1 2 3 4 {{Cite book |last= Guitel |first= Geneviève |authorlink= Geneviève Guitel |title= Histoire comparée des numérations écrites |publisher= Flammarion |year= 1975 |location= Paris |pages= 566–574 |chapter= "Les grands nombres en numération parlée (État actuel de la question)", i.e. "The large numbers in oral numeration (Present state of the question)" |language= French |isbn= 978-2-08-211104-1}} 4. ^1 2 3 {{Cite book |last= Fowler |first= H. W. |authorlink= Henry Watson Fowler |coauthors= |title= A Dictionary of Modern English Usage |publisher= Oxford University Press |year= 1926 |location= Great Britain |pages= 52–53 |url= https://books.google.com/?id=hrtIDakUpA4C&pg=PT169&dq=billion |doi= |id= |isbn= 978-0-19-860506-5}} 5. ^{{cite book |url= https://books.google.com/ngrams/graph?content=billion%2Cthousand+million%2Cmilliard&year_start=1808&year_end=1967&corpus=18&smoothing=3&share= |title= British-English usage of 'Billion vs Thousand million vs Milliard' |last= |first= |date= |website= Google Books ngram viewer |publisher= Google Inc |accessdate= 26 April 2014}} 6. ^1 2 3 {{cite web |title= "BILLION" (DEFINITION) — HC Deb 20 December 1974 vol 883 cc711W–712W |work= Hansard Written Answers |publisher= Hansard |date= 20 December 1972 |url= http://hansard.millbanksystems.com/written_answers/1974/dec/20/billion-definition#S5CV0883P0_19741220_CWA_439 |accessdate= 2 April 2009}} 7. ^1 2 3 {{Cite news |last= O'Donnell |first= Frank |coauthors= |title= Britain's £1 trillion debt mountain — How many zeros is that? |newspaper= The Scotsman |location= |pages= |publisher= |date= 30 July 2004 |url= http://news.scotsman.com/latestnews/Britains-1-trillion-debt-mountain.2550147.jp |accessdate= 31 January 2008}} 8. ^1 2 {{Cite news |publisher= BBC |title= BBC News: Who wants to be a trillionaire? |date= 7 May 2007 |url= http://news.bbc.co.uk/1/hi/programmes/more_or_less/6625545.stm |accessdate= 11 May 2010}} 9. ^1 2 {{Cite mailing list |last= Comrie |first= Bernard |authorlink= Bernard Comrie |title= billion:summary |mailinglist= Linguist List |date= 24 March 1996 |url= http://www.linguistlist.org/issues/7/7-451.html |accessdate= 24 July 2011}} 10. ^1 2 {{cite web |last= |first= |authorlink= |coauthors= |title= Oxford Dictionaries: How many is a billion? |work= |publisher= Oxford University Press |date= |url= https://en.oxforddictionaries.com/explore/how-many-is-a-billion/ |doi= |accessdate= 7 May 2018}} 11. ^{{cite web |last= |first= |authorlink= |coauthors= |title= Oxford Dictionaries: Billion |work= |publisher= Oxford University Press |date= |url= http://oxforddictionaries.com/definition/billion |doi= |accessdate= 24 July 2011}} 12. ^1 {{Cite book |last= Nielsen |first= Ron |coauthors= |title= The Little Green Handbook |publisher= Macmillan Publishers |series= |volume= |edition= |year= 2006 |location= |page= 290 |url= |doi= |id= |isbn= 978-0-312-42581-4 |mr= |zbl= |jfm=}} 13. ^1 2 3 4 5 6 7 8 {{Cite book |last= Smith |first= David Eugene |authorlink= David Eugene Smith |coauthors= |title= History of Mathematics |publisher= Courier Dover Publications |series= |volume= II |edition= |orig-year= first published 1925 |date= 1953 |location= |pages= 84–86 |url= https://books.google.com/?id=uTytJGnTf1kC&pg=PA84 |doi= |id= |isbn= 978-0-486-20430-7 |mr= |zbl= |jfm=}} 14. ^1 2 {{cite web|last=|first=|authorlink=|coauthors=|title=Wortschatz-Lexikon: Milliarde|work=|publisher=Universität Leipzig: Wortschatz-Lexikon|language=German|date=|url=http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Milliarde|doi=|accessdate=19 August 2011|deadurl=yes|archiveurl=https://web.archive.org/web/20110927052529/http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Milliarde|archivedate=27 September 2011|df=dmy-all}} 15. ^1 2 {{cite web|last=|first=|authorlink=|coauthors=|title=Wortschatz-Lexikon: Billion|work=|publisher=Universität Leipzig: Wortschatz-Lexikon|language=German|date=|url=http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Billion|doi=|accessdate=19 August 2011|deadurl=yes|archiveurl=https://web.archive.org/web/20110807144431/http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Billion|archivedate=7 August 2011|df=dmy-all}} 16. ^1 {{cite web|last=|first=|authorlink=|coauthors=|title=Wortschatz-Lexikon: Billiarde|work=|publisher=Universität Leipzig: Wortschatz-Lexikon|language=German|date=|url=http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Billiarde|doi=|accessdate=28 July 2011|deadurl=yes|archiveurl=https://web.archive.org/web/20110927052446/http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Billiarde|archivedate=27 September 2011|df=dmy-all}} 17. ^1 {{cite web|last=|first=|authorlink=|coauthors=|title=Wortschatz-Lexikon: Trilliarde|work=|publisher=Universität Leipzig: Wortschatz-Lexikon|language=German|date=|url=http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Trilliarde|doi=|accessdate=28 July 2011|deadurl=yes|archiveurl=https://web.archive.org/web/20110927052502/http://wortschatz.uni-leipzig.de/cgi-bin/wort_www.exe?site=1&Wort=Trilliarde|archivedate=27 September 2011|df=dmy-all}} 18. ^1 2 3 4 5 {{cite web |last= |first= |authorlink= |coauthors= |title= Direttiva CEE / CEEA / CE 1994 n. 55, p.12 |language= Italian |work= |publisher= Italian Government |date= 21 November 1994 |url= http://www.frareg.com/news/legislazione/ambiente/direttiva_1994_55_CE.pdf |doi= |accessdate= 24 July 2011}} 19. ^{{Cite journal |last= Adam |first= Jehan |authorlink= Jehan Adam |title= Traicté en arismetique pour la practique par gectouers... (MS 3143) |publisher= Bibliothèque Sainte-Geneviève |place= Paris |year= 1475 |language= Middle French |postscript=}} 20. ^{{cite web |url= http://www-bsg.univ-paris1.fr/ExposVirtuelles/exposvirtuellesreserves/sciences/savants2.htm |title= HOMMES DE SCIENCE, LIVRES DE SAVANTS A LA BIBLIOTHÈQUE SAINTE-GENEVIÈVE, Livres de savants II |author= |year= 2005 |work= Traicté en arismetique pour la practique par gectouers… |publisher= Bibliothèque Sainte-Geneviève |accessdate= 25 October 2014 |language= French}} 21. ^{{Cite journal |last= Thorndike |first= Lynn |authorlink= Lynn Thorndike |coauthors= |title= The Arithmetic of Jehan Adam, 1475 A.D |journal= The American Mathematical Monthly |volume= 1926 |issue= January |page= 24 |publisher= Mathematical Association of America |location= |date= |url= |jstor= 2298533 |doi= |id= |mr= |zbl= |jfm=}} 22. ^1 {{Cite journal |last= Chuquet |first= Nicolas |authorlink= Nicolas Chuquet |coauthors= |title= Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien |journal= Bulletino di Bibliographia e di Storia delle Scienze matematische e fisische |volume= XIII |issue= 1880 |pages= 593–594 |publisher= Aristide Marre |location= Bologna |date= 1880 |orig-year= written 1484 |language= Middle French |url= http://www.miakinen.net/vrac/nombres#lettres_zillions |jstor= |issn= 1123-5209 |doi= |id= |mr= |zbl= |jfm= |accessdate= 17 July 2011}} 23. ^{{cite web |last= Chuquet |first= Nicolas |authorlink= Nicolas Chuquet |coauthors= |title= Le Triparty en la Science des Nombres par Maistre Nicolas Chuquet Parisien |work= |publisher= www.miakinen.net |language= Middle French |url= http://www.miakinen.net/vrac/nombres#lettres_zillions |doi= |accessdate= 1 March 2008 |date= 1880 |orig-year= written 1484}} 24. ^{{Cite journal |last= Flegg |first= Graham |coauthors= |title= Tracing the origins of One, Two, Three. |journal= New Scientist |volume= 72 |issue= 1032 |page= 747 |publisher= Reed Business Information |location= |date= 23–30 December 1976 |url= https://books.google.com/?id=obHSBCxiJ1YC&pg=PA747 |jstor= |issn= 0262-4079 |doi= |id= |mr= |zbl= |jfm= |accessdate= 17 July 2011}} 25. ^1 {{Cite book |last= Budaeus |first= Guilielmus |authorlink= Guillaume Budé |coauthors= |title= De Asse et partibus eius Libri quinque |publisher= |series= |volume= |edition= |year= 1516 |location= |pages= folio 93 |language= Latin |url= |doi= |id= |isbn= |mr= |zbl= |jfm=}} 26. ^{{cite book |last=Littré |first=Émile |date=1873–1874 |title=Dictionnaire de la langue française |url=http://www.littre.org/definition/billion |location=Paris, France |publisher=L. Hachette |page=347|quote=Ce n'est qu'au milieu du XVIIe siècle qu'il fut réglé que les tranches, au lieu d'être de six en six chiffres, seraient de trois en trois chiffres ; ce qui revint à diviser par 1000 l'ancien billion, l'ancien trillion, etc. [It was only in the middle of the 17th century that it was settled that the slices, instead of being from six to six digits, would be from three to three digits; which resulted in dividing by 1000 the old billion, the old trillion, and so on.]}} 27. ^{{Cite journal |last= Houck |first= |year= 1676 |title= Arithmetic |publisher= |publication-place= Netherlands |page= 2 |url= |accessdate= |postscript= {{inconsistent citations}}}} 28. ^{{cite book |author= |title=Dictionnaire de l'académie françoise |url=https://books.google.com/books?id=0oM-AAAAcAAJ&pg=PA1&dq=Dictionnaire+de+l'Académie+Française&hl=en&sa=X&ved=0ahUKEwiYtsT218fQAhVS92MKHQ6ODaEQ6AEIIzAB#v=onepage&q=billion&f=false |location=Paris, France |publisher=Institut de France |page=177 |date=1762 |edition= 4th}} 29. ^{{cite book |author= |title=Dictionnaire de l'Académie française |url=http://portail.atilf.fr/cgi-bin/dico1look.pl?strippedhw=billion&dicoid=ACAD1835&headword=&dicoid=ACAD1835 |location=Paris, France |page=189 |date=1835 | edition= 6th}} 30. ^{{cite book |author= |title=Dictionnaire de l'Académie française |url=https://books.google.com/books?id=P2whAQAAMAAJ&pg=PR23&dq=Dictionnaire+de+l'Académie+Française&hl=en&sa=X&ved=0ahUKEwjDtNfA08fQAhVP0GMKHWJWAgAQ6AEIGjAA#v=onepage&q=billion&f=false |location=Paris, France |publisher=Institut de France |page=182 |date=1877 |edition= 7th}} 31. ^{{cite book |author= |title=Dictionnaire de l'Académie française |url=http://portail.atilf.fr/cgi-bin/dico1look.pl?strippedhw=billion&headword=&docyear=ALL&dicoid=ACAD1932&articletype=1 |location=Paris, France |publisher=Institut de France |page=144 |date=1932–1935|edition= 8th}} 32. ^1 {{cite web |last= |first= |authorlink= |coauthors= |title= Resolution 6 of the 9th meeting of the CGPM (1948) |work= |publisher= BIPM |date= |url= http://www.bipm.org/en/CGPM/db/9/6/ |doi= |accessdate= 7 August 2011}} 33. ^{{cite web |last= |first= |authorlink= |coauthors= |title= Resolution 6 of the 10th meeting of the CGPM (1954) |work= |publisher= BIPM |date= |url= http://www.bipm.org/en/CGPM/db/10/6/ |doi= |accessdate= 23 June 2012}} 34. ^1 {{cite web |last= |first= |authorlink= |coauthors= |title= Resolution 12 of the 11th meeting of the CGPM (1960) |work= |publisher= BIPM |date= |url= http://www.bipm.org/jsp/en/ViewCGPMResolution.jsp?CGPM=11&RES=12 |doi= |accessdate= 28 July 2011}} 35. ^{{Cite book |last= |first= |authorlink= |coauthors= |title= The International System of Units (SI) |publisher= BIPM |series= |volume= |edition= 8 |date= May 2006 |location= |pages= 134 / 5.3.7 Stating values of dimensionless quantities, or quantities of dimension one |url= http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf |doi= |id= |isbn= 92-822-2213-6 |mr= |zbl= |jfm= |format= PDF}} 36. ^{{cite book |last= Thompson |first= Ambler |last2= Taylor |first2= Barry N. |date= March 30, 2008 |title= Guide for the Use of the International System of Units (SI), NIST SP - 811 |url= https://www.nist.gov/manuscript-publication-search.cfm?pub_id=200349 |location= US |publisher= National Institute of Standards and Technology |page= 21 |isbn= |accessdate= September 13, 2014}} 37. ^1 {{Cite journal|last=|first=|authorlink=|coauthors=|title=Décret 61-501|journal=Journal Officiel|volume=|issue=|pages=4587 note 3a, and erratum on page 7572|publisher=French Government|location=|date=11 August 1961|language=French|url=http://www.ensmp.net/pdf/1961/decr-61-0501.pdf|jstor=|issn=|doi=|id=|mr=|zbl=|jfm=|accessdate=31 January 2008|format=PDF|orig-year=commissioned 3 May 1961 published 20 May 1961|deadurl=yes|archiveurl=https://web.archive.org/web/20100120005624/http://www.ensmp.net/pdf/1961/decr-61-0501.pdf|archivedate=20 January 2010|df=dmy-all}} 38. ^1 {{cite news |last= |first= |authorlink= |coauthors= |title= BBC News: Zimbabweans play the zero game |work= |publisher= BBC |date= 23 July 2008 |url= http://news.bbc.co.uk/1/hi/world/africa/7516874.stm |doi= |accessdate= 13 July 2012}} 39. ^1 {{cite news |last= |first= |authorlink= |coauthors= |title= BBC News: Zimbabwe rolls out Z$100tr note |work= |publisher= BBC |date= 16 January 2009 |url= http://news.bbc.co.uk/1/hi/7832601.stm |doi= |accessdate= 24 July 2010}} 40. ^1 {{cite news |last= |first= |authorlink= |coauthors= |title= BBC News: Zimbabwe abandons its currency |work= |publisher= BBC |date= 29 January 2009 |url= http://news.bbc.co.uk/1/hi/7859033.stm |doi= |accessdate= 13 July 2012}} 41. ^{{cite web |url= http://www.treasurydirect.gov/NP/BPDLogin?application=np |title= The Debt to the Penny and Who Holds It |last1= |first1= |last2= |first2= |date= |website= www.treasurydirect.gov |publisher= US Government |accessdate= 27 October 2013}} 42. ^{{cite web |url= http://demonocracy.info/ |title= Economic infographics |last1= |first1= |last2= |first2= |date= |website= demonocracy.info |publisher= BTC |accessdate= 27 October 2013}} 43. ^1 {{cite web |last= |first= |authorlink= |coauthors= |title= RBA: Definition of billion |work= |publisher= Reserve Bank of Australia |date= |url= http://www.rba.gov.au/glossary/index.html?search=billion |doi= |accessdate= 22 August 2011}} 44. ^1 {{cite web |last= |first= |authorlink= |coauthors= |title= Cambridge Dictionaries Online: billion |work= American Dictionary |publisher= Cambridge University Press |date= |url= http://dictionaries.cambridge.org/define.asp?key=billion*1+0&dict=A |doi= |accessdate= 21 August 2011}} 45. ^1 {{cite web |last= |first= |authorlink= |coauthors= |title= Cambridge Dictionaries Online: trillion |work= American Dictionary |publisher= Cambridge University Press |date= |url= http://dictionaries.cambridge.org/define.asp?key=trillion*1+0&dict=A |doi= |accessdate= 21 August 2011}} 46. ^1 {{cite web |last= |first= |authorlink= |coauthors= |title= Al Jazem English-Arabic online dictionary: Billion |work= Al Jazem English-Arabic online dictionary |publisher= Encyclopædia Britannica |date= |url= http://www.aljazem.com/en/billion |doi= |accessdate= 6 June 2012}} 47. ^1 {{cite web |last= |first= |authorlink= |coauthors= |title= Al Jazem English-Arabic online dictionary:Trillion |work= Al Jazem English-Arabic online dictionary |publisher= Encyclopædia Britannica |date= |url= http://www.aljazem.com/en/trillion |doi= |accessdate= 6 June 2012}} 48. ^{{cite web |last= Qeli |first= Albi |coauthors= |title= An English-Albanian Dictionary |work= |publisher= Albi Qeli, MD |date= |url= http://www.argjiro.net/fjalor/index.php |doi= |accessdate= 6 June 2012}} 49. ^{{Cite journal |last= |first= |authorlink= |coauthors= |title= Britain to Reduce $4 billion from Defence |journal= Bi-Weekly Eleven |volume= 3 |issue= 30 |page= |publisher= |location= Yangon |date= 15 October 2010 |language= Burmese |url= |jstor= |issn= |doi= |id= |mr= |zbl= |jfm=}} 50. ^{{cite web |last= |first= |authorlink= |coauthors= |title= Eesti õigekeelsussõnaraamat ÕS 2006: miljard |work= |publisher= Institute of the Estonian Language (Eesti Keele Instituut) |year= 2006 |url= http://www.eki.ee/dict/qs/index.cgi?Q=miljard&F=M |language= Estonian |doi= |accessdate= 13 August 2011}} 51. ^{{cite web |last= |first= |authorlink= |coauthors= |title= Eesti õigekeelsussõnaraamat ÕS 2013: biljon |work= |publisher= Institute of the Estonian Language (Eesti Keele Instituut) |year= 2013 |url= http://www.eki.ee/dict/qs/index.cgi?Q=biljon&F=M |language= Estonian |doi= |accessdate= 25 June 2017}} 52. ^{{cite web |last= |first= |authorlink= |coauthors= |title= Eesti õigekeelsussõnaraamat ÕS 2006: triljon |work= |publisher= Institute of the Estonian Language (Eesti Keele Instituut) |year= 2006 |url= http://www.eki.ee/dict/qs/index.cgi?Q=triljon&F=M |language= Estonian |doi= |accessdate= 13 August 2011}} 53. ^1 Robson S. O. (Stuart O.), Singgih Wibisono, Yacinta Kurniasih. Javanese English dictionary Tuttle Publishing: 2002, {{ISBN|0-7946-0000-X}}, 821 pages 54. ^1 {{citation|title=May We Introduce the Romanian Language to You?|first1=Mioara|last1=Avram|first2=Marius|last2=Sala|publisher=Editura Fundatiei Culturale Române|year=2000|isbn=9789735772246|page=151|quote=the numeral miliard "billion"}} 55. ^1 {{cite web |last= |first= |authorlink= |coauthors= |title= Diccionario Panhispánico de Dudas: millardo |work= |publisher= Real Academia Española |language= Spanish |date= |url= http://buscon.rae.es/dpdI/SrvltConsulta?lema=millardo |doi= |accessdate= 19 August 2011}} 56. ^1 {{cite web |last= |first= |authorlink= |coauthors= |title= Diccionario Panhispánico de Dudas: billon |work= |publisher= Real Academia Española |language= Spanish |date= |url= http://buscon.rae.es/dpdI/SrvltConsulta?lema=billon |doi= |accessdate= 24 July 2010}} 57. ^{{cite web |last= |first= |authorlink= |coauthors= |title= Diccionario de la lengua española |work= |publisher= Real Academia Española |language= Spanish |date= |url= http://dle.rae.es/?id=5WQzD1r |doi= |accessdate= 2 July 2018}} 58. ^1 {{cite web|last=|first=|authorlink=|coauthors=|title=French Larousse: milliard|work=|publisher=Éditions Larousse|date=|url=http://www.larousse.com/en/dictionaries/french/milliard|language=French|doi=|accessdate=19 August 2011|deadurl=yes|archiveurl=https://web.archive.org/web/20120318130447/http://www.larousse.com/en/dictionaries/french/milliard|archivedate=18 March 2012|df=dmy-all}} 59. ^1 {{cite web|last=|first=|authorlink=|coauthors=|title=French Larousse: billion|work=|publisher=Éditions Larousse|date=|url=http://www.larousse.com/en/dictionaries/french/billion|language=French|doi=|accessdate=19 August 2011|deadurl=yes|archiveurl=https://web.archive.org/web/20120318130500/http://www.larousse.com/en/dictionaries/french/billion|archivedate=18 March 2012|df=dmy-all}} 60. ^{{cite web |last= |first= |authorlink= |coauthors= |title= Definition of 'Billion' in the 9th edition of the Dictionnaire de l'Académie française. |work= |publisher= Académie française |year= 1992 |url= http://atilf.atilf.fr/dendien/scripts/generic/cherche.exe?15;s=802200930;; |doi= |accessdate= 17 January 2016 |quote=BILLION (les deux l se prononcent sans mouillure) n. m. XVe siècle, byllion, « un million de millions » ; XVIe siècle, « mille millions ». Altération arbitraire de l'initiale de million, d'après la particule latine bi-, « deux fois ». Rare. Mille millions. Syn. vieilli de Milliard. Selon un décret de 1961, le mot Billion a reçu une nouvelle valeur, à savoir un million de millions (1012), qui n'est pas entrée dans l'usage. This translates into English as : BILLION (the two Ls are pronounced without palatalisation) masculine noun. Spelled byllion in the 15th century when it meant a million millions; in the 16th century it meant a thousand millions. It is an arbitrary alteration of the start of million by inserting the Latin prefix bi-, meaning twice. Now rarely used. It means a thousand millions. It is an outdated synonym of Milliard. According to a decree of 1961, the word Billion received a new value, to wit a million millions (1012), which has not come into common usage.}} 61. ^{{cite web |last= |first= |authorlink= |coauthors= |title= De Geïntegreerde Taal-Bank: miljard |work= |publisher= Instituut voor Nederlandse Lexicologie |date= |url= http://www.wnt.inl.nl/iWDB/search?actie=article&wdb=WFT&id=63043&lemmodern=miljard |language= Dutch |doi= |accessdate= 19 August 2011}} 62. ^{{cite web |last= |first= |authorlink= |coauthors= |title= De Geïntegreerde Taal-Bank: biljoen |work= |publisher= Instituut voor Nederlandse Lexicologie |date= |url= http://gtb.inl.nl/iWDB/search?actie=article&wdb=WFT&id=8253&lemmodern=biljoen |language= Dutch |doi= |accessdate= 19 August 2011}} 63. ^1 {{cite web |last= Wennergren |first= Bertilo |authorlink= Bertilo Wennergren |coauthors= |title= Plena Manlibro de Esperanta Gramatiko |work= |publisher= |language= Esperanto |date= 8 March 2008 |url= http://bertilow.com/pmeg/ |doi= |accessdate= 15 September 2010}} 64. ^1 {{cite web|last=|first=|authorlink=|coauthors=|title=Italian-English Larousse: bilione|work=|publisher=Éditions Larousse|date=|url=http://www.larousse.com/en/dictionaries/italian-english/bilione/5726|doi=|accessdate=21 August 2011|deadurl=yes|archiveurl=https://web.archive.org/web/20120318130613/http://www.larousse.com/en/dictionaries/italian-english/bilione/5726|archivedate=18 March 2012|df=dmy-all}} 65. ^{{citation|title=Dicționarul explicativ al limbii române (ediția a II-a revăzută și adăugită)|last=Institutul de Lingvistică „Iorgu Iordan - Alexandru Rosetti” al Academiei Române|publisher=Editura Univers Enciclopedic Gold|year=2012}} 66. ^{{cite web |title=Scara numerică |trans-title= numerical scale |language=Romanian |url=http://dexonline.ro/articol/Scara_numeric%C4%83 |work=dexonline.ro |date=2016 |accessdate=3 May 2016}} 67. ^{{cite web |last= |first= |authorlink= |coauthors= |title= Switzerland: Words and Phrases |work= |publisher= TRAMsoft Gmbh |date= 29 August 2009 |url= http://www.about.ch/culture/languages/words_n_phrases.html#numbers |doi= |accessdate= 15 August 2011}} 68. ^{{cite web |last= |first= |authorlink= |coauthors= |title= Canadian government standards website |work= |publisher= Canadian Government |year= 2010 |url= http://btb.termiumplus.gc.ca/tpv2alpha/alpha-eng.html?lang=eng&i=&index=frt&__index=frt&srchtxt=billion&comencsrch.x=12&comencsrch.y=10 |doi= |accessdate= 15 September 2010}} 69. ^{{cite web|url=http://www.granddictionnaire.com/ficheOqlf.aspx?Id_Fiche=8872290 |title=billion |publisher=Granddictionnaire.com |date=2013-05-13 |accessdate=2018-04-24}} 70. ^{{cite web |url= http://152.111.1.88/argief/berigte/beeld/2008/02/20/B1/14/01milbiltril.html |title= Taalkommissie se reaksie op biljoen, triljoen |language= Afrikaans |publisher= Naspers: Media24 |accessdate= 16 July 2014 |deadurl= yes |archiveurl= https://web.archive.org/web/20140714224334/http://152.111.1.88/argief/berigte/beeld/2008/02/20/B1/14/01milbiltril.html |archivedate= 14 July 2014 |df= dmy-all }} 71. ^{{cite web |url=http://152.111.1.87/argief/berigte/dieburger/2009/07/13/SK/9/BBfpistorAWS.html |title=‘Groen boek’: mooiste, beste, gebruikersvriendelikste |language=Afrikaans |publisher=Naspers:Media24 |accessdate=16 July 2014 |deadurl=yes |archiveurl=https://web.archive.org/web/20140714134302/http://152.111.1.87/argief/berigte/dieburger/2009/07/13/SK/9/BBfpistorAWS.html |archivedate=14 July 2014 |df=dmy-all }} 72. ^{{Cite book |last= Gupta |first= S.V. |title= Units of measurement: past, present and future : international system of units |publisher= Springer |series= |volume= |edition= |year= 2010 |location= |pages= 12 (Section 1.2.8 Numeration) |url= https://books.google.com/books?id=pHiKycrLmEQC&dq=crore%20lakh%20arab&pg=PA12 |doi= |id= |isbn= 3642007384 |mr= |zbl= |jfm= |accessdate= 22 August 2011}} 73. ^{{cite web |last= Foundalis |first= Harry |authorlink= |coauthors= |title= Greek Numbers and Numerals (Ancient and Modern) |work= |publisher= |date= |url= http://www.foundalis.com/lan/grknum.htm |doi= |accessdate= 20 May 2007}} 74. ^{{cite web |last= |first= |authorlink= |vauthors= |title= BBC: GCSE Bitesize — The origins of the universe |work= |publisher= BBC |date= |url= http://www.bbc.co.uk/schools/gcsebitesize/science/edexcel/space/theoriginsoftheuniverserev1.shtml |doi= |accessdate= 28 July 2011}} Long scaleBoth long and short scaleNeither long nor short scaleAlternative approachesUnambiguous ways of identifying large numbers include:
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ReferencesExternal links
3 : Numerals|Numeral systems|Articles with images not understandable by color blind users |
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