Vigesimal
Encyclopedia
The vigesimal or base 20 numeral system is based on twenty (in the same way in which the ordinary decimal numeral system
is based on ten).
system, twenty individual numerals (or digit symbols) are used, ten more than in the usual decimal system. One modern method of finding the extra needed symbols is to write ten
as the letter A_{20} (the _{20} means base), to write nineteen
as J_{20}, and the numbers between with the corresponding letters of the alphabet. This is similar to the common computerscience
practice of writing hexadecimal
numerals over 9 with the letters "AF". Another method skips over the letter "I", in order to avoid confusion between I_{20} as eighteen
and 1 (one), so that the number eighteen is written as J_{20}, and nineteen is written as K_{20}. The number twenty is written as 10_{20}.
According to this notation:
In the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example, 10 means ten
, 20 means twenty
.
s, especially in Europe
, 20
is a base, at least with respect to the linguistic structure of the names of certain numbers (though a thoroughgoing consistent vigesimal system, based on the powers 20, 400, 8000 etc., is not generally used).
, the vigesimal system in Europe is of Basque
(Vasconic) origin and spread from Vasconic languages
to other European tongues, such as many Celtic languages
, French and Danish.
According to Menninger, the vigesimal system originated with the Normans and spread through them to Western Europe, the evidence being that Celtic languages
often use vigesimal counting systems. Others believe that this theory is unlikely, however.
and the number names
in Yucatec Maya, Nahuatl
in modern orthography and in Classical Nahuatl
.
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
is based on ten).
Places
In a vigesimal placeNumerical digit
A digit is a symbol used in combinations to represent numbers in positional numeral systems. The name "digit" comes from the fact that the 10 digits of the hands correspond to the 10 symbols of the common base 10 number system, i.e...
system, twenty individual numerals (or digit symbols) are used, ten more than in the usual decimal system. One modern method of finding the extra needed symbols is to write ten
10 (number)
10 is an even natural number following 9 and preceding 11.In mathematics:Ten is a composite number, its proper divisors being , and...
as the letter A_{20} (the _{20} means base), to write nineteen
19 (number)
19 is the natural number following 18 and preceding 20. It is a prime number.In English speech, the numbers 19 and 90 are often confused. When carefully enunciated, they differ in which syllable is stressed: 19 vs 90...
as J_{20}, and the numbers between with the corresponding letters of the alphabet. This is similar to the common computerscience
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
practice of writing hexadecimal
Hexadecimal
In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...
numerals over 9 with the letters "AF". Another method skips over the letter "I", in order to avoid confusion between I_{20} as eighteen
18 (number)
18 is the natural number following 17 and preceding 19.In speech, the numbers 18 and 80 are sometimes confused. When carefully enunciated, they differ in which syllable is stressed: 18 vs 80 . However, in dates such as 1864, or when contrasting numbers in the teens, such as 17, 18, 19, the stress...
and 1 (one), so that the number eighteen is written as J_{20}, and nineteen is written as K_{20}. The number twenty is written as 10_{20}.
According to this notation:
 20_{20} means forty40 (number)40 is the natural number following 39 and preceding 41.Despite being related to the word "four" , 40 is spelled "forty", and not "fourty"...
in decimal {= (2 × 20^{1}) + (0 × 20^{0})}  DA_{20} means two hundred [and] seventy270 (number)270 is the natural number following 269 and preceding 271.In mathematics:*270 is a harmonic divisor number*270 is the fourth number that is divisible by its average integer divisor...
in decimal {= (13 × 20^{1}) + (10 × 20^{0}}  100_{20} means four hundred400 (number)400 is the natural number following 399 and preceding 401.  Mathematical properties :400 is the square of 20.A circle is divided into 400 grads, which is equal to 360 degrees and 2π radians...
in decimal {= (1 × 20^{2}) + (0 × 20^{1}) + (0 × 20^{0})}.
In the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example, 10 means ten
10 (number)
10 is an even natural number following 9 and preceding 11.In mathematics:Ten is a composite number, its proper divisors being , and...
, 20 means twenty
20 (number)
20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.In mathematics:*20 is the basis for vigesimal number systems....
.
Use
In many languageLanguage
Language may refer either to the specifically human capacity for acquiring and using complex systems of communication, or to a specific instance of such a system of complex communication...
s, especially in Europe
Europe
Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...
, 20
20 (number)
20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.In mathematics:*20 is the basis for vigesimal number systems....
is a base, at least with respect to the linguistic structure of the names of certain numbers (though a thoroughgoing consistent vigesimal system, based on the powers 20, 400, 8000 etc., is not generally used).
Asia and America
 DzongkhaDzongkha numeralsDzongkha, the national language of Bhutan, has two numeral systems, one vigesimal , and a modern decimal system. The vigesimal system remains in robust use. Ten is an auxiliary base: the teens are formed with ten and the numerals 1–9.Vigesimal:...
, the national language of BhutanBhutanBhutan , officially the Kingdom of Bhutan, is a landlocked state in South Asia, located at the eastern end of the Himalayas and bordered to the south, east and west by the Republic of India and to the north by the People's Republic of China...
, has a full vigesimal system, with numerals for the powers of twenty 20, 400, 8000, and 160,000.  In SantaliSantali languageSanthali is a language in the Santhali subfamily of AustroAsiatic, related to Ho and Mundari. It is spoken by about six million people in India, Bangladesh, Nepal, and Bhutan . Most of its speakers live in India, in the states of Jharkhand, Assam, Bihar, Orissa, Tripura, and West Bengal. It has...
, a Munda languageMunda languagesAnderson :Gregory Anderson's 1999 proposal is as follows. Individual languages are highlighted in italics.*North Munda **Korku**Kherwarian***Santhali***Mundari*South Munda **Kharia–Juang***Juang***Kharia...
of IndiaIndiaIndia , officially the Republic of India , is a country in South Asia. It is the seventhlargest country by geographical area, the secondmost populous country with over 1.2 billion people, and the most populous democracy in the world...
, "fifty" is expressed by the phrase bār isī gäl, literally "two twenty ten." Likewise, in DideiGataq languageThe Gataq language, also known as is a language spoken by the Didayi people of India.Classification:The Gataq language belongs to the South Munda subgroup of the Munda branch of the AustroAsiatic language family...
, another Munda language spoken in India, complex numerals are decimal to 19 and decimalvigesimal to 399.  In East AsiaEast AsiaEast Asia or Eastern Asia is a subregion of Asia that can be defined in either geographical or cultural terms...
, the Ainu languageAinu languageAinu is one of the Ainu languages, spoken by members of the Ainu ethnic group on the northern Japanese island of Hokkaidō....
also uses a counting system that is based around the number 20. “” is 20, “” (ten more until two twenties) is 3030 (number)30 is the natural number following 29 and preceding 31.In mathematics:30 is the sum of the first four squares, which makes it a square pyramidal number.It is a primorial and is the smallest Giuga number....
, “” (two twenties) is 40, “” (five twenties) is 100100 (number)100 is the natural number following 99 and preceding 101.In mathematics:One hundred is the square of 10...
. Subtraction is also heavily used, e.g. “” (one more until ten) is 9.  Twenty was a base in the MayaMaya civilizationThe Maya is a Mesoamerican civilization, noted for the only known fully developed written language of the preColumbian Americas, as well as for its art, architecture, and mathematical and astronomical systems. Initially established during the PreClassic period The Maya is a Mesoamerican...
number systems. The Maya used the following names for the powers of twenty: (20), (20^{2} = 400), (20^{3} = 8,000), (20^{4} = 160,000), (20^{5} = 3,200,000) and (20^{6} = 64,000,000). See also Maya numeralsMaya numeralsMaya Numerals were a vigesimal numeral system used by the PreColumbian Maya civilization.The numerals are made up of three symbols; zero , one and five...
and Maya calendarMaya calendarThe Maya calendar is a system of calendars and almanacs used in the Maya civilization of preColumbian Mesoamerica, and in many modern Maya communities in highland Guatemala. and in Chiapas....
, Mayan languagesMayan languagesThe Mayan languages form a language family spoken in Mesoamerica and northern Central America. Mayan languages are spoken by at least 6 million indigenous Maya, primarily in Guatemala, Mexico, Belize and Honduras...
, Yucatec. The Aztec called them: (1 × 20), (1 × 400), (1 × 8,000), (1 × 20 × 8,000 = 160,000), (1 × 400 × 8,000 = 3,200,000) and (1 × 20 × 400 × 8,000 = 64,000,000). Note that the prefix at the beginning means "one" (as in "one hundred" and "one thousand") and is replaced with the corresponding number to get the names of other multiples of the power. For example, (2) × (20) = (40), (2) × (400) = (800). Note also that the in (and ) and the in are grammatical noun suffixes that are appended only at the end of the word; thus , and compound together as (instead of *). (See also Nahuatl language.)  The Tlingit people use base 20.
In Europe
According to German linguist Theo VennemannTheo Vennemann
Theo Vennemann is a German linguist known best for his work on historical linguistics, especially for his disputed theories of a Vasconic substratum and an Atlantic superstratum of European languages. He also suggests that the High German consonant shift was already completed in the early 1st...
, the vigesimal system in Europe is of Basque
Basque language
Basque is the ancestral language of the Basque people, who inhabit the Basque Country, a region spanning an area in northeastern Spain and southwestern France. It is spoken by 25.7% of Basques in all territories...
(Vasconic) origin and spread from Vasconic languages
Vasconic languages
The Vasconic substratum theory is a proposal that many western European languages contain remnants of an old language family of Vasconic languages, of which Basque is the only surviving member. The proposal was made by the German linguist Theo Vennemann, but has been rejected by other linguists...
to other European tongues, such as many Celtic languages
Celtic languages
The Celtic languages are descended from ProtoCeltic, or "Common Celtic"; a branch of the greater IndoEuropean language family...
, French and Danish.
According to Menninger, the vigesimal system originated with the Normans and spread through them to Western Europe, the evidence being that Celtic languages
Celtic languages
The Celtic languages are descended from ProtoCeltic, or "Common Celtic"; a branch of the greater IndoEuropean language family...
often use vigesimal counting systems. Others believe that this theory is unlikely, however.
 Twenty () is used as a base number in the French languageFrench languageFrench is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Secondlanguage speakers of French are distributed throughout many parts...
names of numbers from 70 to 99, except in the French of BelgiumBelgiumBelgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...
, SwitzerlandSwitzerlandSwitzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
, the Democratic Republic of the CongoDemocratic Republic of the CongoThe Democratic Republic of the Congo is a state located in Central Africa. It is the second largest country in Africa by area and the eleventh largest in the world...
, RwandaRwandaRwanda or , officially the Republic of Rwanda , is a country in central and eastern Africa with a population of approximately 11.4 million . Rwanda is located a few degrees south of the Equator, and is bordered by Uganda, Tanzania, Burundi and the Democratic Republic of the Congo...
, the Aosta Valley and the Channel IslandsChannel IslandsThe Channel Islands are an archipelago of British Crown Dependencies in the English Channel, off the French coast of Normandy. They include two separate bailiwicks: the Bailiwick of Guernsey and the Bailiwick of Jersey...
. For example, , the French word for 8080 (number)80 is the natural number following 79 and preceding 81. In mathematics :The sum of Euler's totient function φ over the first sixteen integers is 80....
, literally means "four twenties", soixantedix, the word for 7070 (number)70 is the natural number following 69 and preceding 71.In mathematics:Its factorization makes it a sphenic number. 70 is a Pell number and a generalized heptagonal number, one of only two numbers to be both. Also, it is the seventh pentagonal number and the fourth 13gonal number, as well as the...
, is literally "sixtyten", (7575 (number)75 is the natural number following 74 and preceding 76.In mathematics:As the sum of the first five pentagonal numbers, seventyfive is a pentagonal pyramidal number. It is also an enneagonal number....
) is literally "sixtyfifteen", quatrevingtsept (8787 (number)87 is the natural number following 86 and preceding 88.In mathematics:Eightyseven is the twentysixth distinct semiprime and the eighth of the form . The aliquot sum of 87 is 33 within the aliquot sequence 86 being the eighteenth composite number in the 3aliquot tree.Eightyseven is the sum of...
) is literally "fourtwentiesseven", quatrevingtdix (9090 (number)90 is the natural number preceded by 89 and followed by 91. In mathematics :*Because 90 is the sum of its unitary divisors , it is a unitary perfect number, and because it is equal to the sum of a subset of its divisors, it is a semiperfect number. 90 is a pronic number. But it is also a...
) is literally "fourtwentiesten", and quatrevingtseize (9696 (number)96 is the natural number following 95 and preceding 97.In mathematics:Ninetysix is an octagonal number, a refactorable number and an untouchable number. Since it is a multiple of 6, it is a semiperfect number...
) is literally "fourtwentiessixteen". However, in the French of Belgium, the Democratic Republic of the Congo, Rwanda, the Aosta Valley, and the Channel Islands, the numbers 70 and 90 generally have the names septante and nonante. So, the year 1996 is "mille neuf cent quatrevingtseize" in Parisian French, but it is "mille neuf cent nonantesix" in e.g. Belgian French. In Switzerland, 80 can be quatrevingts (Geneva, Neuchâtel, Jura) or huitante (Vaud, Valais, Fribourg); in the past octante was also in use.  Twenty () is used as a base number in the Danish languageDanish languageDanish is a North Germanic language spoken by around six million people, principally in the country of Denmark. It is also spoken by 50,000 Germans of Danish ethnicity in the northern parts of SchleswigHolstein, Germany, where it holds the status of minority language...
names of numbers from 50 to 99. For example, (short for ) means 3 times 20, i.e. 6060 (number)60 is the natural number following 59 and preceding 61. Being three times twenty, 60 is called "three score" in some older literature.In mathematics:...
. For details, see Danish numerals.  Twenty () is used as a base number in the Breton languageBreton languageBreton is a Celtic language spoken in Brittany , France. Breton is a Brythonic language, descended from the Celtic British language brought from Great Britain to Armorica by migrating Britons during the Early Middle Ages. Like the other Brythonic languages, Welsh and Cornish, it is classified as...
names of numbers from 40 to 49 and from 60 to 99. For example, means 2 times 20, i.e. 4040 (number)40 is the natural number following 39 and preceding 41.Despite being related to the word "four" , 40 is spelled "forty", and not "fourty"...
, and (literally "threesix and fourtwenty") means 3×6 + 4×20, i.e. 98. However, 30 is and not * ("ten and twenty"), and 50 is ("halfhundred").  Twenty () is used as a base number in the Welsh languageWelsh languageWelsh is a member of the Brythonic branch of the Celtic languages spoken natively in Wales, by some along the Welsh border in England, and in Y Wladfa...
, although in the latter part of the twentieth century a decimal counting system has come to be preferred (particularly in the South), with the vigesimal system becoming 'traditional' and more popular in North Welsh. means 2 times 20 i.e. 40, means 3 times 20 i.e. 60. Prior to the currency decimalisation in 1971, (6 times 20 paper) was the nickname for the 10 shilling (= 120120 (number)120 is the natural number following 119 and preceding 121. 120 was known as "the great hundred", especially prior to the year 1700, from the Teutonic Hundert which equalled 120. The number 100, now known commonly as "one hundred" was then known as "the small hundred". It is also known as...
pence) note. A vigesimal system (Yan Tan TetheraYan Tan TetheraYan Tan Tethera is a sheep counting rhyme traditionally used by shepherds in Northern England. Until the Industrial Revolution, the use of traditional number systems was common among shepherds, especially in the dales of the Lake District. The Yan Tan Tethera system was also used for counting...
) for counting sheep has also been recorded in areas of Britain that today are no longer Celticspeaking.  Twenty () is used in an older counting system in Irish Gaelic, though most people nowadays use a decimal system, and this is what is taught in schools. Thirty is (originally fiche agus deich), literally twenty and ten. Forty is , literally two twenties (retained in the decimal system as daichead). is sixty (three twenties) and is eighty (literally four twenties).
 Scottish Gaelic traditionally uses a vigesimal system similar to that of traditional Irish, with () being the word for twenty, being 30 (ten over twenty), 40 (two twenties), 50 (two twenty and ten), 60 (three twenties) and so on up to 180 (nine twenties). A decimal system is now taught in schools.
 Twenty () is used as a base number in the Albanian languageAlbanian languageAlbanian is an IndoEuropean language spoken by approximately 7.6 million people, primarily in Albania and Kosovo but also in other areas of the Balkans in which there is an Albanian population, including western Macedonia, southern Montenegro, southern Serbia and northwestern Greece...
. The word for 40 () means two times 20.  Twenty () is used as a base number in the Georgian languageGeorgian languageGeorgian is the native language of the Georgians and the official language of Georgia, a country in the Caucasus.Georgian is the primary language of about 4 million people in Georgia itself, and of another 500,000 abroad...
. For example, 3131 (number)31 is the natural number following 30 and preceding 32. In mathematics :Thirtyone is the third Mersenne prime as well as the fourth primorial prime, and together with twentynine, another primorial prime, it comprises a twin prime. As a Mersenne prime, 31 is related to the perfect number 496,...
() literally means, twentyandeleven. 6767 (number)67 is the natural number following 66 and preceding 68. It is an odd number.In mathematics:Sixtyseven is the 19th prime number , an irregular prime, a lucky prime, the sum of five consecutive primes , and a Heegner number.Since 18! + 1 is divisible by 67 but 67 is not one more than a multiple of...
() is said as, “threetwentyandseven”.  Twenty () is used as a base number in the Nakh languagesNakh languagesThe Nakh languages are a small family of languages spoken chiefly by the Nakh peoples, in Russia , in Georgia, and in the Chechen diaspora ....
.  Twenty () is used as a base number in the Basque languageBasque languageBasque is the ancestral language of the Basque people, who inhabit the Basque Country, a region spanning an area in northeastern Spain and southwestern France. It is spoken by 25.7% of Basques in all territories...
for numbers up to 100 (). The words for 40 (), 60 () and 80 () mean "twoscore", "threescore" and "fourscore", respectively. The number 75 is called , lit. "threescoreand tenfive". The Basque nationalist Sabino AranaSabino AranaSabino Arana Goiri, selfstyled as Arana ta Goiri'taŕ Sabin, , was a Spanish and Basque writer. He was the founder of the Basque Nationalist Party and father of Basque nationalism....
proposed a vigesimal digit system to match the spoken language, and, as an alternative, a reform of the spoken language to make it decimal, but both are mostly forgotten.  Twenty (dwisti) is used as a base number in the Resian dialectResian dialectThe Resian dialect is a distinct dialect of Slovene spoken in the Resia Valley, Province of Udine, Italy, close to the border with Slovenia...
of the Slovenian languageSlovenian languageSlovene or Slovenian is a South Slavic language spoken by approximately 2.5 million speakers worldwide, the majority of whom live in Slovenia. It is the first language of about 1.85 million people and is one of the 23 official and working languages of the European Union...
in ItalyItalyItaly , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in SouthCentral Europe. To the north it borders France, Switzerland, Austria and...
's Resia Valley. 60 is expressed by trïkart dwisti (3×20), 70 by trïkart dwisti nu dësat (3x20 + 10), 80 by štirikrat dwisti (4×20) and 90 by štirikrat dwisti nu dësat (4×20 + 10).  In the old BritishUnited KingdomThe United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
currency system (pre1971), there were 20 shillingShillingThe shilling is a unit of currency used in some current and former British Commonwealth countries. The word shilling comes from scilling, an accounting term that dates back to AngloSaxon times where it was deemed to be the value of a cow in Kent or a sheep elsewhere. The word is thought to derive...
s (worth 12 pence each) to the poundPound sterlingThe pound sterling , commonly called the pound, is the official currency of the United Kingdom, its Crown Dependencies and the British Overseas Territories of South Georgia and the South Sandwich Islands, British Antarctic Territory and Tristan da Cunha. It is subdivided into 100 pence...
. Under the decimal system introduced in 1971 (1 pound equals 100 new pence instead of 240 pence in the old system), the shilling coins still in circulation were revalued at 5 pence (no more were minted and the shilling coin was demonetised in 1990).  In the imperial weight system there are twenty hundredweightHundredweightThe hundredweight or centum weight is a unit of mass defined in terms of the pound . The definition used in Britain differs from that used in North America. The two are distinguished by the terms long hundredweight and short hundredweight:* The long hundredweight is defined as 112 lb, which...
in a tonTonThe ton is a unit of measure. It has a long history and has acquired a number of meanings and uses over the years. It is used principally as a unit of weight, and as a unit of volume. It can also be used as a measure of energy, for truck classification, or as a colloquial term.It is derived from...
.  In EnglishEnglish languageEnglish is a West Germanic language that arose in the AngloSaxon kingdoms of England and spread into what was to become southeast Scotland under the influence of the Anglian medieval kingdom of Northumbria...
, counting by the score has been used historically, as in the famous opening of the Gettysburg AddressGettysburg AddressThe Gettysburg Address is a speech by U.S. President Abraham Lincoln and is one of the most wellknown speeches in United States history. It was delivered by Lincoln during the American Civil War, on the afternoon of Thursday, November 19, 1863, at the dedication of the Soldiers' National Cemetery...
"Four score and seven years ago…", meaning eightyseven (8787 (number)87 is the natural number following 86 and preceding 88.In mathematics:Eightyseven is the twentysixth distinct semiprime and the eighth of the form . The aliquot sum of 87 is 33 within the aliquot sequence 86 being the eighteenth composite number in the 3aliquot tree.Eightyseven is the sum of...
) years ago. This method has fallen into disuse, however.
Related observations
 Among multipleMultiple (mathematics)In mathematics, a multiple is the product of any quantity and an integer. In other words, for the quantities a and b, we say that b is a multiple of a if b = na for some integer n , which is called the multiplier or coefficient. If a is not zero, this is equivalent to saying that b/a is an integer...
s of 1010 (number)10 is an even natural number following 9 and preceding 11.In mathematics:Ten is a composite number, its proper divisors being , and...
, 20 is described in a special way in some languages. For example, the SpanishSpanish languageSpanish , also known as Castilian , is a Romance language in the IberoRomance group that evolved from several languages and dialects in centralnorthern Iberia around the 9th century and gradually spread with the expansion of the Kingdom of Castile into central and southern Iberia during the...
words (3030 (number)30 is the natural number following 29 and preceding 31.In mathematics:30 is the sum of the first four squares, which makes it a square pyramidal number.It is a primorial and is the smallest Giuga number....
) and (40) consist of " (10 times)", " (10 times)", but the word (2020 (number)20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.In mathematics:*20 is the basis for vigesimal number systems....
) is not presently connected to any word meaning "two" (although historically it is). Similarly, in Semitic languagesSemitic languagesThe Semitic languages are a group of related languages whose living representatives are spoken by more than 270 million people across much of the Middle East, North Africa and the Horn of Africa...
such as Arabic and Hebrew, the numbers 30, 40 ... 90 are expressed by morphologically plural forms of the words for the numbers 3, 4 ... 9, but the number 20 is expressed by a morphologically plural form of the word for 10.  In some languages (e.g. English, Slavic languagesSlavic languagesThe Slavic languages , a group of closely related languages of the Slavic peoples and a subgroup of IndoEuropean languages, have speakers in most of Eastern Europe, in much of the Balkans, in parts of Central Europe, and in the northern part of Asia.Branches:Scholars traditionally divide Slavic...
), the names of the twodigit numbers from 1111 (number)11 is the natural number following 10 and preceding 12.Eleven is the first number which cannot be counted with a human's eight fingers and two thumbs additively. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a singlemorpheme name...
to 1919 (number)19 is the natural number following 18 and preceding 20. It is a prime number.In English speech, the numbers 19 and 90 are often confused. When carefully enunciated, they differ in which syllable is stressed: 19 vs 90...
consist of one word, but the names of the twodigit numbers from 2121 (number)21 is the natural number following 20 and preceding 22.In mathematics:Twentyone is the fifth discrete Semiprime and the second in the family. With 22 it forms the second discrete Semiprime pair...
on consist of two words. So for example, the English words eleven (1111 (number)11 is the natural number following 10 and preceding 12.Eleven is the first number which cannot be counted with a human's eight fingers and two thumbs additively. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a singlemorpheme name...
), twelve (1212 (number)12 is the natural number following 11 and preceding 13.The word "twelve" is the largest number with a singlemorpheme name in English. Etymology suggests that "twelve" arises from the Germanic compound twalif "twoleftover", so a literal translation would yield "two remaining [after having ten...
), thirteen (1313 (number)13 is the natural number after 12 and before 14. It is the smallest number with eight letters in its name spelled out in English. It is also the first of the teens – the numbers 13 through 19 – the ages of teenagers....
) etc., as opposed to twentyone (2121 (number)21 is the natural number following 20 and preceding 22.In mathematics:Twentyone is the fifth discrete Semiprime and the second in the family. With 22 it forms the second discrete Semiprime pair...
), twentytwo (2222 (number)22 is the natural number following 21 and preceding 23. In mathematics :Twentytwo is an even composite number, its proper divisors being 1, 2 and 11....
), twentythree (2323 (number)23 is the natural number following 22 and preceding 24. In mathematics :Twentythree is the ninth prime number, the smallest odd prime that is not a twin prime. Twentythree is also the fifth factorial prime, the third Woodall prime...
), etc. In French, this is true up to 16. In a number of other languages (such as HebrewHebrew languageHebrew is a Semitic language of the Afroasiatic language family. Culturally, is it considered by Jews and other religious groups as the language of the Jewish people, though other Jewish languages had originated among diaspora Jews, and the Hebrew language is also used by nonJewish groups, such...
), the names of the numbers from 1119 contain two words, but one of these words is a special "teen" form which is different from the ordinary form of the word for the number 10, and may in fact be only found in these names of the numbers 1119.  Cantonese and Wu Chinese frequently use the single unit (Cantonese yàh, ShanghaineseShanghaineseShanghainese , or the Shanghai language , is a dialect of Wu Chinese spoken in the city of Shanghai and the surrounding region. It is classified as part of the SinoTibetan family of languages. Shanghainese, like other Wu dialects, is largely not mutually intelligible with other Chinese varieties...
nyae or ne, Mandarin niàn) for twenty, in addition to the fully decimal (Cantonese yìh sàhp, Shanghainese el sah, Mandarin èr shí) which literally means "two ten". However, this system is never used in larger numbers. It is more an abbreviation than any indication of a base 20 system.  The term vicesimal (from the Latin vicesimus) is sometimes used.
 The Kharosthi numeral system behaves like a partial vigesimal system.
Powers of twenty in Yucatec Maya and Nahuatl
Powers of Twenty in Yucatec Maya and Nahuatl  

Number  English  Maya  Nahuatl Nahuatl Nahuatl is thought to mean "a good, clear sound" This language name has several spellings, among them náhuatl , Naoatl, Nauatl, Nahuatl, Nawatl. In a back formation from the name of the language, the ethnic group of Nahuatl speakers are called Nahua... (modern orthography)  Classical Nahuatl Classical Nahuatl Classical Nahuatl is a term used to describe the variants of the Nahuatl language that were spoken in the Valley of Mexico — and central Mexico as a lingua franca — at the time of the 16thcentury Spanish conquest of Mexico...  Nahuatl root  Aztec pictogram  
1  One  Hun  Se  Ce  Ce  
20  Twenty 20 (number) 20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.In mathematics:*20 is the basis for vigesimal number systems.... 
K'áal  Sempouali  Cempohualli (Cempoalli)  Pohualli  
400  Four hundred  Bak  Sentzontli  Centzontli  Tzontli  
8000  Eight thousand  Pic  Senxikipili  Cenxiquipilli  Xiquipilli  
160.000  One hundred sixty thousand  Calab  Sempoualxikipili  Cempohualxiquipilli  Pohualxiquipilli  
3.200.000  Three million two hundred thousand  Kinchil  Sentzonxikipili  Centzonxiquipilli  Tzonxiquipilli  
64.000.000  Sixtyfour million  Alau  Sempoualtzonxikipili  Cempohualtzonxiquipilli  Pohualtzonxiquipilli 
Counting in units of twenty
This table shows the Maya numeralsMaya numerals
Maya Numerals were a vigesimal numeral system used by the PreColumbian Maya civilization.The numerals are made up of three symbols; zero , one and five...
and the number names
Number names
In linguistics, number names are specific words in a natural language that represent numbers.In writing, numerals are symbols also representing numbers...
in Yucatec Maya, Nahuatl
Nahuatl
Nahuatl is thought to mean "a good, clear sound" This language name has several spellings, among them náhuatl , Naoatl, Nauatl, Nahuatl, Nawatl. In a back formation from the name of the language, the ethnic group of Nahuatl speakers are called Nahua...
in modern orthography and in Classical Nahuatl
Classical Nahuatl
Classical Nahuatl is a term used to describe the variants of the Nahuatl language that were spoken in the Valley of Mexico — and central Mexico as a lingua franca — at the time of the 16thcentury Spanish conquest of Mexico...
.
From one to ten (1  10)  

1 (one)  2 (two)  3 (three)  4 (four)  5 (five)  6 (six)  7 (seven)  8 (eight)  9 (nine)  10 (ten) 10 (number) 10 is an even natural number following 9 and preceding 11.In mathematics:Ten is a composite number, its proper divisors being , and... 
Hun  Ka'ah  Óox  Kan  Ho'  Wak  Uk  Waxak  Bolon  Lahun 
Se  Ome  Yeyi  Naui  Makuili  Chikuasen  Chikome  Chikueyi  Chiknaui  Majtlaktli 
Ce  Ome  Yei  Nahui  Macuilli  Chicuace  Chicome  Chicuei  Chicnahui  Matlactli 
From eleven to twenty (11  20)  
11  12  13  14  15  16  17  18  19  20 


Buluk  Lahka'a  Óox lahun  Kan lahun  Ho' lahun  Wak lahun  Uk lahun  Waxak lahun  Bolon lahun  Hun k'áal 
Majtlaktli onse  Majtlaktli omome  Majtlaktli omeyi  Majtlaktli onnaui  Kaxtoli  Kaxtoli onse  Kaxtoli omome  Kaxtoli omeyi  Kaxtoli onnaui  Sempouali 
Matlactli huan ce  Matlactli huan ome  Matlactli huan yei  Matlactli huan nahui  Caxtolli  Caxtolli huan ce  Caxtolli huan ome  Caxtolli huan yei  Caxtolli huan nahui  Cempohualli 
From twentyone to thirty (11  30)  
21  22  23  24  25  26  27  28  29  30 










Hump'éel katak hun k'áal  Ka'ah katak hun k'áal  Óox katak hun k'áal  Kan katak hun k'áal  Ho' katak hun k'áal  Wak katak hun k'áal  Uk katak hun k'áal  Waxak katak hun k'áal  Bolon katak hun k'áal  Lahun katak hun k'áal 
Sempouali onse  Sempouali omome  Sempouali omeyi  Sempouali onnaui  Sempouali ommakuili  Sempouali onchikuasen  Sempouali onchikome  Sempouali onchikueyi  Sempouali onchiknaui  Sempouali ommajtlaktli 
Cempohualli huan ce  Cempohualli huan ome  Cempohualli huan yei  Cempohualli huan nahui  Cempohualli huan macuilli  Cempohualli huan chicuace  Cempohualli huan chicome  Cempohualli huan chicuei  Cempohualli huan chicnahui  Cempohualli huan matlactli 
From thirtyone to forty (31  40)  
31  32  33  34  35  36  37  38  39  40 










Buluk katak hun k'áal  Lahka'a katak hun k'áal  Óox lahun katak hun k'áal  Kan lahun katak hun k'áal  Ho' lahun katak hun k'áal  Wak lahun katak hun k'áal  Uk lahun katak hun k'áal  Waxak lahun katak hun k'áal  Bolon lahun katak hun k'áal  Ka' k'áal 
Sempouali ommajtlaktli onse  Sempouali ommajtlaktli omome  Sempouali ommajtlaktli omeyi  Sempouali ommajtlaktli onnaui  Sempouali onkaxtoli  Sempouali onkaxtoli onse  Sempouali onkaxtoli omome  Sempouali onkaxtoli omeyi  Sempouali onkaxtoli onnaui  Ompouali 
Cempohualli huan matlactli huan ce  Cempohualli huan matlactli huan ome  Cempohualli huan matlactli huan yei  Cempohualli huan matlactli huan nahui  Cempohualli huan caxtolli  Cempohualli huan caxtolli huan ce  Cempohualli huan caxtolli huan ome  Cempohualli huan caxtolli huan yei  Cempohualli huan caxtolli huan nahui  Ompohualli 
From twenty to two hundred in steps of twenty (20  200)  
20  40  60  80  100  120  140  160  180  200 










Hun k'áal  Ka' k'áal  Óox k'áal  Kan k'áal  Ho' k'áal  Wak k'áal  Uk k'áal  Waxak k'áal  Bolon k'áal  Lahun k'áal 
Sempouali  Ompouali  Yepouali  Naupouali  Makuilpouali  Chikuasempouali  Chikompouali  Chikuepouali  Chiknaupouali  Majtlakpouali 
Cempohualli  Ompohualli  Yeipohualli  Nauhpohualli  Macuilpohualli  Chicuacepohualli  Chicomepohualli  Chicueipohualli  Chicnahuipohualli  Matlacpohualli 
From two hundred twenty to four hundred in steps of twenty (220  400)  
220  240  260  280  300  320  340  360  380  400 










Buluk k'áal  Lahka'a k'áal  Óox lahun k'áal  Kan lahun k'áal  Ho' lahun k'áal  Wak lahun k'áal  Uk lahun k'áal  Waxak lahun k'áal  Bolon lahun k'áal  Hun bak 
Majtlaktli onse pouali  Majtlaktli omome pouali  Majtlaktli omeyi pouali  Majtlaktli onnaui pouali  Kaxtolpouali  Kaxtolli onse pouali  Kaxtolli omome pouali  Kaxtolli omeyi pouali  Kaxtolli onnaui pouali  Sentsontli 
Matlactli huan ce pohualli  Matlactli huan ome pohualli  Matlactli huan yei pohualli  Matlactli huan nahui pohualli  Caxtolpohualli  Caxtolli huan ce pohualli  Caxtolli huan ome pohualli  Caxtolli huan yei pohualli  Caxtolli huan nahui pohualli  Centzontli 
Further reading
 Karl MenningerKarl Menninger (mathematics)Karl Menninger was a German teacher of and writer about mathematics. His major work was Zahlwort und Ziffer , about nonacademic mathematics in much of the world...
: Number words and number symbols: a cultural history of numbers; translated by Paul Broneer from the revised German edition. Cambridge, Mass.: M.I.T. Press, 1969 (also available in paperback: New York: Dover, 1992 ISBN 0486270963)  Levi Leonard Conant: The Number Concept: Its Origin and Development; New York, New York: MacMillon & Co, 1931. Project Gutenberg EBook