Vigesimal

Places

Converting table

Fractions

Cyclic numbers

Real numbers

Use

• The Open Location Code, used for encoding geographic areas uses a base 20 encoding of coordinates.

  Africa

Americas

• Twenty was a base in the Maya and Aztec number systems. The Maya used the following names for the powers of twenty: kal, bak, pic, calab, kinchil and alau. See also Maya numerals and Maya calendar, Mayan languages, Yucatec. The Aztec called them: cempoalli, centzontli, cenxiquipilli, cempoalxiquipilli, centzonxiquipilli and cempoaltzonxiquipilli. Note that the ce prefix at the beginning means "one" and is replaced with the corresponding number to get the names of other multiples of the power. For example, ome × poalli = ompoalli, ome × tzontli = ontzontli. The -li in poalli and the -tli in tzontli are grammatical noun suffixes that are appended only at the end of the word; thus poalli, tzontli and xiquipilli compound together as poaltzonxiquipilli.
• The Tlingit people use base 20.
• The Kaktovik Inupiaq numerals uses a base 20 system. In 1994, Students from Kaktovik, Alaska, came up with the Kaktovik Inupiaq numerals in 1994. Before the numerals had been developed, the Inuit names had been falling out of favor.

  Asia

• Dzongkha, the national language of Bhutan, has a full vigesimal system, with numerals for the powers of 20, 400, 8,000 and 160,000.
• Atong, a language spoken in the South Garo Hills of Meghalaya state, Northeast India, and adjacent areas in Bangladesh, has a full vigesimal system that is nowadays considered archaic.
• In Santali, a Munda language of India, "fifty" is expressed by the phrase bār isī gäl, literally "two twenty ten." Likewise, in Didei, another Munda language spoken in India, complex numerals are decimal to 19 and decimal-vigesimal to 399.
• The Burushaski number system is base 20. For example, 20 altar, 40 alto-altar, 60 iski-altar etc.
• In East Asia, the Ainu language also uses a counting system that is based around the number 20. “hotnep” is 20, “wanpe etu hotnep” is 30, “tu hotnep” is 40, “ashikne hotnep” is 100. Subtraction is also heavily used, e.g. “shinepesanpe” is 9.
• The Chukchi language has a vigesimal numeral system.

  Oceania

In Europe

Etymology

Examples

• Twenty is used as a base number in the French language names of numbers from 70 to 99, except in the French of Belgium, Switzerland, the Democratic Republic of the Congo, Rwanda, the Aosta Valley and the Channel Islands. For example, quatre-vingts, the French word for "80", literally means "four-twenties"; soixante-dix, the word for "70", is literally "sixty-ten"; soixante-quinze is literally "sixty-fifteen"; quatre-vingt-sept is literally "four-twenties-seven"; quatre-vingt-dix is literally "four-twenties-ten"; and quatre-vingt-seize is literally "four-twenties-sixteen". However, in the French of Belgium, Switzerland, 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. Therefore, the year 1996 is "mille neuf cent quatre-vingt-seize" in Parisian French, but it is "mille neuf cent nonante-six" in Belgian French. In Switzerland, "80" can be quatre-vingts or huitante ; octante is also in use in rural parts of Southern France.
• Twenty is used as a base number in the Danish language names of numbers from 50 to 99. For example, tres means 3 times 20, i.e. 60. However, Danish numerals are not vigesimal since it is only the names of some of the tens that are etymologically formed in a vigesimal way. In contrast with e.g. French quatre-vingt-seize, the units only go from zero to nine between each ten which is a defining trait of a decimal system. For details, see Danish numerals.
• Twenty is used as a base number in the Breton language names of numbers from 40 to 49 and from 60 to 99. For example, daou-ugent means 2 times 20, i.e. 40, and triwec'h ha pevar-ugent means 3×6 + 4×20, i.e. 98. However, 30 is tregont and not *dek ha ugent, and 50 is hanter-kant.
• Twenty is used as a base number in the Welsh language from numbers up to 50 and from 60 to 100, although in the latter part of the 20th century a decimal counting system has come to be preferred. However, the vigesimal system exclusively is used for ordinal numbers. Deugain means 2 times 20 i.e. 40, trigain means 3 times 20 i.e. 60, etc. Dau ar bymtheg ar ddeugain means 57. Prior to its withdrawal from circulation in 1970, papur chweugain was the nickname for the ten-shilling note.
• Twenty is traditionally used as a base number in Scottish Gaelic, with deich ar fhichead or fichead 's a deich being 30, dà fhichead 40, dà fhichead 's a deich 50 / leth-cheud 50, trì fichead 60 and so on up to naoidh fichead 180. Nowadays a decimal system is taught in schools, but the vigesimal system is still used by many, particularly older speakers.
• Twenty is used as a base number in the Albanian language. The word for 40 means two times 20. The Arbëreshë in Italy may use 'trizetë' for 60. Formerly, 'katërzetë' was also used for 80. Today Cham Albanians in Greece use all zet numbers. Basically, 20 means 1 zet, 40 means 2 zet, 60 means 3 zet and 80 means 4 zet. Albanian is the only language in the Balkans which has retained elements of the vigesimal numeral system side by side with decimal system. The existence of the two systems in Albanian reflect the contribution of Pre-Indo-European people of the Balkans to the formation of the Paleo-Balkan Indo-European tribes and their language.
• Twenty is used as a base number in the Georgian language for numbers 30 to 99. For example, 31 literally means, twenty-and-eleven. 67 is said as, “three-twenty-and-seven”.
• Twenty is used as a base number in the Nakh languages.
• Twenty is used as a base number in the Basque language for numbers up to 100. The words for 40, 60 and 80 mean "two-score", "three-score" and "four-score", respectively. For example, the number 75 is called hirurogeita hamabost, lit. "three-score-and ten-five". The Basque nationalist Sabino Arana 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 is used as a base number in the Resian dialect of the Slovenian language in Italy's Resia Valley. 60 is expressed by trïkrat dwisti, 70 by trïkrat dwisti nu dësat, 80 by štirikrat dwisti and 90 by štirikrat dwisti nu dësat.
• In the old British currency system, there were 20 shillings to the pound. Under the decimal system introduced in 1971, the shilling coins still in circulation were re-valued at 5 pence.
• In the imperial weight system there are twenty hundredweight in a ton.
• In English, counting by the score has been used historically, as in the famous opening of the Gettysburg Address "Four score and seven years ago…", meaning eighty-seven years ago, referring to the signing of the Declaration of Independence that happened in. In the Authorised Version of the Bible the term score is used over 130 times although only when prefixed by a number greater than one while a single "score" is always expressed as twenty. The use of the term score to signify multiples of twenty has fallen into disuse in modern English.
• Other languages have terms similar to the old English score, for example Danish and Norwegian .
• In regions where traces of the Brythonic Celtic languages have survived in dialect, sheep enumeration systems that are vigesimal are recalled to the present day. See Yan Tan Tethera.

  Related observations

• Among multiples of 10, 20 is described in a special way in some languages. For example, the Spanish words treinta and cuarenta consist of "tre+inta ", "cuar+enta ", but the word veinte is not presently connected to any word meaning "two". Similarly, in Semitic languages 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. The Japanese language has a special word for 20 years, and for the 20th day of the month.
• In some languages, the names of the two-digit numbers from 11 to 19 consist of one word, but the names of the two-digit numbers from 21 on consist of two words. So for example, the English words eleven, twelve, thirteen etc., as opposed to twenty-one, twenty-two, twenty-three, etc. In French, this is true up to 16. In a number of other languages, the names of the numbers from 11-19 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 it may in fact be only found in these names of the numbers 11-19.
• Cantonese and Wu Chinese frequently use the single unit 廿 for twenty, in addition to the fully decimal 二十 which literally means "two ten". Equivalents exist for 30 and 40, but these are more seldom used. This is a historic remnant of a vigesimal system.
• Although Khmer numerals have represented a decimal positional notation system since at least the 7th century, Old Khmer, or Angkorian Khmer, also possessed separate symbols for the numbers 10, 20, and 100. Each multiple of 20 or 100 would require an additional stroke over the character, so the number 47 was constructed using the 20 symbol with an additional upper stroke, followed by the symbol for number 7. This suggests that spoken Angkorian Khmer used a vigesimal system.
• Thai uses the term ยี่สิบ for 20. Other multiples of ten consist of the base number, followed by the word for ten, e.g. สามสิบ, lit. three ten, for thirty. The yi of yi sip is different from the number two in other positions, which is สอง. Nevertheless, yi sip is a loan word from Chinese.
• Lao similarly forms multiples of ten by putting the base number in front of the word ten, so ສາມສິບ, litt. three ten, for thirty. The exception is twenty, for which the word ຊາວ is used.
• The Kharosthi numeral system behaves like a partial vigesimal system.

  Examples in Mesoamerican languages

Powers of twenty in Yucatec Maya and Nahuatl

Counting in units of twenty