Vigesimal
The vigesimal or base20 (basescore) numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten). Vigesimal is derived from the Latin adjective vicesimus.
PlacesEdit
In a vigesimal place 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 20), 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 "A–F". Another less common method skips over the letter "I", in order to avoid confusion between I_{20} as eighteen and 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}.
Converting tableEdit
1  2  3  4  5  6  7  8  9  A  B  C  D  E  F  G  H  I  J  10 

2  4  6  8  A  C  E  G  I  10  12  14  16  18  1A  1C  1E  1G  1I  20 
3  6  9  C  F  I  11  14  17  1A  1D  1G  1J  22  25  28  2B  2E  2H  30 
4  8  C  G  10  14  18  1C  1G  20  24  28  2C  2G  30  34  38  3C  3G  40 
5  A  F  10  15  1A  1F  20  25  2A  2F  30  35  3A  3F  40  45  4A  4F  50 
6  C  I  14  1A  1G  22  28  2E  30  36  3C  3I  44  4A  4G  52  58  5E  60 
7  E  11  18  1F  22  29  2G  33  3A  3H  44  4B  4I  55  5C  5J  66  6D  70 
8  G  14  1C  20  28  2G  34  3C  40  48  4G  54  5C  60  68  6G  74  7C  80 
9  I  17  1G  25  2E  33  3C  41  4A  4J  58  5H  66  6F  74  7D  82  8B  90 
A  10  1A  20  2A  30  3A  40  4A  50  5A  60  6A  70  7A  80  8A  90  9A  A0 
B  12  1D  24  2F  36  3H  48  4J  5A  61  6C  73  7E  85  8G  97  9I  A9  B0 
C  14  1G  28  30  3C  44  4G  58  60  6C  74  7G  88  90  9C  A4  AG  B8  C0 
D  16  1J  2C  35  3I  4B  54  5H  6A  73  7G  89  92  9F  A8  B1  BE  C7  D0 
E  18  22  2G  3A  44  4I  5C  66  70  7E  88  92  9G  AA  B4  BI  CC  D6  E0 
F  1A  25  30  3F  4A  55  60  6F  7A  85  90  9F  AA  B5  C0  CF  DA  E5  F0 
G  1C  28  34  40  4G  5C  68  74  80  8G  9C  A8  B4  C0  CG  DC  E8  F4  G0 
H  1E  2B  38  45  52  5J  6G  7D  8A  97  A4  B1  BI  CF  DC  E9  F6  G3  H0 
I  1G  2E  3C  4A  58  66  74  82  90  9I  AG  BE  CC  DA  E8  F6  G4  H2  I0 
J  1I  2H  3G  4F  5E  6D  7C  8B  9A  A9  B8  C7  D6  E5  F4  G3  H2  I1  J0 
10  20  30  40  50  60  70  80  90  A0  B0  C0  D0  E0  F0  G0  H0  I0  J0  100 
Decimal  Vigesimal  

0  0  
1  1  
2  2  
3  3  
4  4  
5  5  
6  6  
7  7  
8  8  
9  9  
10  A  
11  B  
12  C  
13  D  
14  E  
15  F  
16  G  
17  H  
18  I  J 
19  J  K 
According to this notation:
 20_{20} means forty in decimal = (2 × 20^{1}) + (0 × 20^{0})
 D0_{20} means two hundred and sixty in decimal = (13 × 20^{1}) + (0 × 20^{0})
 100_{20} means four hundred 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, 20 means twenty. Numbers in vigesimal notation use the convention that I means eighteen and J means nineteen.
FractionsEdit
As 20 is divisible by two and five and is adjacent to 21, the product of three and seven, thus covering the first four prime numbers, many vigesimal fractions have simple representations, whether terminating or recurring (although thirds are more complicated than in decimal, repeating two digits instead of one). In decimal, dividing by three twice (ninths) only gives one digit periods (1/9 = 0.1111.... for instance) because 9 is the number below ten. 21, however, the number adjacent to 20 that is divisible by 3, is not divisible by 9. Ninths in vigesimal have sixdigit periods. As 20 has the same prime factors as 10 (two and five), a fraction will terminate in decimal if and only if it terminates in vigesimal.
In decimal Prime factors of the base: 2, 5 Prime factors of one below the base: 3 Prime factors of one above the base: 11 
In vigesimal Prime factors of the base: 2, 5 Prime factors of one below the base: J Prime factors of one above the base: 3, 7  
Fraction  Prime factors of the denominator 
Positional representation  Positional representation  Prime factors of the denominator 
Fraction 
1/2  2  0.5  0.A  2  1/2 
1/3  3  0.3333... = 0.3  0.6D6D... = 0.6D  3  1/3 
1/4  2  0.25  0.5  2  1/4 
1/5  5  0.2  0.4  5  1/5 
1/6  2, 3  0.16  0.36D  2, 3  1/6 
1/7  7  0.142857  0.2H  7  1/7 
1/8  2  0.125  0.2A  2  1/8 
1/9  3  0.1  0.248HFB  3  1/9 
1/10  2, 5  0.1  0.2  2, 5  1/A 
1/11  11  0.09  0.1G759  B  1/B 
1/12  2, 3  0.083  0.1D6  2, 3  1/C 
1/13  13  0.076923  0.1AF7DGI94C63  D  1/D 
1/14  2, 7  0.0714285  0.18B  2, 7  1/E 
1/15  3, 5  0.06  0.16D  3, 5  1/F 
1/16  2  0.0625  0.15  2  1/G 
1/17  17  0.0588235294117647  0.13ABF5HCIG984E27  H  1/H 
1/18  2, 3  0.05  0.1248HFB  2, 3  1/I 
1/19  19  0.052631578947368421  0.1  J  1/J 
1/20  2, 5  0.05  0.1  2, 5  1/10 
Cyclic numbersEdit
The prime factorization of twenty is 2^{2} × 5, so it is not a perfect power. However, its squarefree part, 5, is congruent to 1 (mod 4). Thus, according to Artin's conjecture on primitive roots, vigesimal has infinitely many cyclic primes, but the fraction of primes that are cyclic is not necessarily ~37.395%. An UnrealScript program that computes the lengths of recurring periods of various fractions in a given set of bases found that, of the first 15,456 primes, ~39.344% are cyclic in vigesimal.
Real numbersEdit
Algebraic irrational number  In decimal  In vigesimal 

√2 (the length of the diagonal of a unit square)  1.41421356237309...  1.85DE37JGF09H6... 
√3 (the length of the diagonal of a unit cube)  1.73205080756887...  1.ECG82BDDF5617... 
√5 (the length of the diagonal of a 1 × 2 rectangle)  2.2360679774997...  2.4E8AHAB3JHGIB... 
φ (phi, the golden ratio = 1+√5/2  1.6180339887498...  1.C7458F5BJII95... 
Transcendental irrational number  In decimal  In vigesimal 
π (pi, the ratio of circumference to diameter)  3.14159265358979...  3.2GCEG9GBHJ9D2... 
e (the base of the natural logarithm)  2.7182818284590452...  2.E7651H08B0C95... 
γ (the limiting difference between the harmonic series and the natural logarithm)  0.5772156649015328606...  0.BAHEA2B19BDIBI... 
UseEdit
In many European languages, 20 is used as 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 Open Location Code, used for encoding geographic areas uses a base 20 encoding of coordinates.^{[1]}
AfricaEdit
Vigesimal systems are common in Africa, for example in Yoruba.
Ogún, 20, is the basic numeric block. Ogójì, 40, (Ogúnmeji) = 20 multiplied by 2 (èjì). Ogota, 60, (Ogúnmẹ̀ta) = 20 multiplied by 3 (ẹ̀ta). Ogorin, 80, (Ogúnmẹ̀rin) = 20 multiplied by 4 (ẹ̀rin). Ogorun, 100, (Ogúnmàrún) = 20 multiplied by 5 (àrún).
16 (Ẹẹ́rìndílógún) = 4 less than 20.
17 (Etadinlogun) = 3 less than 20.
18 (Eejidinlogun) = 2 less than 20.
19 (Okandinlogun) = 1 less than 20.
21 (Okanlelogun) = 1 increment on 20.
22 (Eejilelogun) = 2 increment on 20.
23 (Etalelogun) = 3 increment on 20.
24 (Erinlelogun) = 4 increment on 20.
25 (Aarunlelogun) = 5 increment on 20.
AmericasEdit
 Twenty was a base in the Maya and Aztec number systems. The Maya used the following names for the powers of twenty: kal (20), bak (20^{2} = 400), pic (20^{3} = 8,000), calab (20^{4} = 160,000), kinchil (20^{5} = 3,200,000) and alau (20^{6} = 64,000,000). See also Maya numerals and Maya calendar, Mayan languages, Yucatec. The Aztec called them: cempoalli (1 × 20), centzontli (1 × 400), cenxiquipilli (1 × 8,000), cempoalxiquipilli (1 × 20 × 8,000 = 160,000), centzonxiquipilli (1 × 400 × 8,000 = 3,200,000) and cempoaltzonxiquipilli (1 × 20 × 400 × 8,000 = 64,000,000). Note that the ce(n/m) 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, ome (2) × poalli (20) = ompoalli (40), ome (2) × tzontli (400) = ontzontli (800). The li in poalli (and xiquipilli) 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 (instead of *poallitzontlixiquipilli). (See also Nahuatl language.)
 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.^{[2]}
AsiaEdit
 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.^{[3]}
 In Santali, a Munda language of India, "fifty" is expressed by the phrase bār isī gäl, literally "two twenty ten."^{[4]} Likewise, in Didei, another Munda language spoken in India, complex numerals are decimal to 19 and decimalvigesimal to 399.^{[5]}
 The Burushaski number system is base 20. For example, 20 altar, 40 altoaltar (2 times 20), 60 iskialtar (3 times 20) 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” (ten more until two twenties) is 30, “tu hotnep” (two twenties) is 40, “ashikne hotnep” (five twenties) is 100. Subtraction is also heavily used, e.g. “shinepesanpe” (one more until ten) is 9.^{[citation needed]}
 The Chukchi language has a vigesimal numeral system.^{[6]}
OceaniaEdit
There is some evidence of base20 usage in the Māori language of New Zealand as seen in the terms Te Hokowhitu a Tu referring to a war party (literally "the seven 20s of Tu") and Tamahokotahi, referring to a great warrior ("the one man equal to 20").
In EuropeEdit
 Twenty (vingt) 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, quatrevingts, the French word for "80", literally means "fourtwenties"; soixantedix, the word for "70", is literally "sixtyten"; soixantequinze ("75") is literally "sixtyfifteen"; quatrevingtsept ("87") is literally "fourtwentiesseven"; quatrevingtdix ("90") is literally "fourtwentiesten"; and quatrevingtseize ("96") is literally "fourtwentiessixteen". 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 quatrevingtseize" in Parisian French, but it is "mille neuf cent nonantesix" in Belgian French. In Switzerland, "80" can be quatrevingts (Geneva, Neuchâtel, Jura) or huitante (Vaud, Valais, Fribourg); octante is also in use in rural parts of Southern France.^{[citation needed]}
 Twenty (tyve) is used as a base number in the Danish language names of numbers from 50 to 99. For example, tres (short for tresindstyve) 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 quatrevingtseize, 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 (ugent) is used as a base number in the Breton language names of numbers from 40 to 49 and from 60 to 99. For example, daouugent means 2 times 20, i.e. 40, and triwec'h ha pevarugent (literally "threesix and fourtwenty") means 3×6 + 4×20, i.e. 98. However, 30 is tregont and not *dek ha ugent ("ten and twenty"), and 50 is hanterkant ("halfhundred").
 Twenty (ugain) is used as a base number in the Welsh language from numbers up to 50 (hanner cant) and from 60 to 100 (cant), although in the latter part of the 20th century^{[citation needed]} 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 (two upon fifteen upon twoscore). Prior to its withdrawal from circulation in 1970, papur chweugain (note of sixscore) was the nickname for the tenshilling (= 120 pence) note.
 Twenty (fichead) is traditionally used as a base number in Scottish Gaelic, with deich ar fhichead or fichead 's a deich being 30 (ten over twenty, or twenty and ten), dà fhichead 40 (two twenties), dà fhichead 's a deich 50 (two twenty and ten) / lethcheud 50 (half a hundred), trì fichead 60 (three twenties) and so on up to naoidh fichead 180 (nine twenties). Nowadays a decimal system is taught in schools, but the vigesimal system is still used by many, particularly older speakers.
 Twenty (njëzet) is used as a base number in the Albanian language. The word for 40 (dyzet) 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 PreIndoEuropean people of the Balkans to the formation of the PaleoBalkan IndoEuropean tribes and their language.^{[7]}
 Twenty (otsi) is used as a base number in the Georgian language for numbers 30 to 99. For example, 31 (otsdatertmeti) literally means, twentyandeleven. 67 (samotsdashvidi) is said as, “threetwentyandseven”.
 Twenty (tqa) is used as a base number in the Nakh languages.
 Twenty (hogei) is used as a base number in the Basque language for numbers up to 100 (ehun). The words for 40 (berrogei), 60 (hirurogei) and 80 (laurogei) mean "twoscore", "threescore" and "fourscore", respectively. For example, the number 75 is called hirurogeita hamabost, lit. "threescoreand tenfive". The Basque nationalist Sabino Arana proposed a vigesimal digit system to match the spoken language,^{[8]} and, as an alternative, a reform of the spoken language to make it decimal,^{[9]} but both are mostly forgotten.^{[10]}
 Twenty (dwisti or dwujsti) 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 (3×20), 70 by trïkrat dwisti nu dësat (3×20 + 10), 80 by štirikrat dwisti (4×20) and 90 by štirikrat dwisti nu dësat (4×20 + 10).^{[11]}^{[12]}
 In the old British currency system (pre1971), there were 20 shillings (worth 12 pence each) to the pound. 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 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 eightyseven (87) 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 snes.
 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.
Software ApplicationsEdit
Open Location Code uses a wordsafe version of base 20 for its geocodes. The characters in this alphabet were chosen to avoid accidentally forming words. The developers scored all possible sets of 20 letters in 30 different languages for likelihood of forming words, and chose a set that formed as few recognizable words as possible.^{[13]} The alphabet also is intended to reduce typos by avoiding visually similar digits, and is caseinsensitive.
Base 20 digit  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19 

Code digit  2  3  4  5  6  7  8  9  C  F  G  H  J  M  P  Q  R  V  W  X 
Related observationsEdit
 Among multiples of 10, 20 is described in a special way in some languages. For example, the Spanish words treinta (30) and cuarenta (40) consist of "tre(3)+inta (10 times)", "cuar(4)+enta (10 times)", but the word veinte (20) is not presently connected to any word meaning "two" (although historically it is^{[14]}). 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 (hatachi) for 20 years (of age), and for the 20th day of the month (hatsuka).
 In some languages (e.g. English, Slavic languages and German), the names of the twodigit numbers from 11 to 19 consist of one word, but the names of the twodigit numbers from 21 on consist of two words. So for example, the English words eleven (11), twelve (12), thirteen (13) etc., as opposed to twentyone (21), twentytwo (22), twentythree (23), etc. In French, this is true up to 16. In a number of other languages (such as Hebrew), 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 it may in fact be only found in these names of the numbers 1119.
 Cantonese^{[15]} and Wu Chinese frequently use the single unit 廿 (Cantonese yàh, Shanghainese nyae or ne, Mandarin niàn) for twenty, in addition to the fully decimal 二十 (Cantonese yìh sàhp, Shanghainese el sah, Mandarin èr shí) which literally means "two ten". Equivalents exist for 30 and 40 (卅 and 卌 respectively: Mandarin sà and xì), but these are more seldom used. This is a historic remnant of a vigesimal system.^{[citation needed]}
 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 (yi sip) for 20. Other multiples of ten consist of the base number, followed by the word for ten, e.g. สามสิบ (sam sip), lit. three ten, for thirty. The yi of yi sip is different from the number two in other positions, which is สอง (song). 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 (sam sip), litt. three ten, for thirty. The exception is twenty, for which the word ຊາວ (xao) is used. (ซาว sao is also used in the NorthEastern and Northern dialects of Thai, but not in standard Thai.)
 The Kharosthi numeral system behaves like a partial vigesimal system.
Examples in Mesoamerican languagesEdit
Powers of twenty in Yucatec Maya and NahuatlEdit
Powers of twenty in Yucatec Maya and Nahuatl  

Number  English  Maya  Nahuatl (modern orthography)  Classical Nahuatl  Nahuatl root  Aztec pictogram  
1  One  Hun  Se  Ce  Ce  
20  Twenty  K'áal  Sempouali  Cempohualli (Cempoalli)  Pohualli  
400  Four hundred  Bak  Sentsontli  Centzontli  Tzontli  
8,000  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  Sentsonxikipili  Centzonxiquipilli  Tzonxiquipilli  
64,000,000  Sixtyfour million  Alau  Sempoualtzonxikipili  Cempohualtzonxiquipilli  Pohualtzonxiquipilli 
Counting in units of twentyEdit
This table shows the Maya numerals and the number names in Yucatec Maya, Nahuatl in modern orthography and in Classical Nahuatl.
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) 
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 (21 – 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 readingEdit
 Karl Menninger: 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: Macmillan & Co, 1931. Project Gutenberg EBook
NotesEdit
 ^ "google/openlocationcode". GitHub. Retrieved 14 November 2018.
 ^ Bartley, Wm. Clark (January–February 1997). "Making the Old Way Count" (PDF). Sharing Our Pathways. 2 (1): 12–13. Retrieved February 27, 2017.
 ^ van Breugel, Seino. A grammar of Atong. Leiden, Boston: Brill. Chapter 11
 ^ Gvozdanović, Jadranka. Numeral Types and Changes Worldwide (1999), p.223.
 ^ Chatterjee, Suhas. 1963. On Didei nouns, pronouns, numerals, and demonstratives. Chicago: mimeo., 1963. (cf. Munda Bibliography at the University of Hawaii Department of Linguistics)
 ^ Comrie, Bernard. "Typology of numeral systems." Numeral types and changes worldwide. Trends in Linguistics. Studies and monographs 118 (2011).
 ^ Demiraj, Shaban (2006). The origin of the Albanians: linguistically investigated. Tirana: Academy of Sciences of Albania. p. 43. ISBN 9789994381715.
 ^ Artículos publicados en la 1.ª época de "Euzkadi" : revista de Ciencias, Bellas Artes y Letras de Bilbao por AranaGoiri´taŕ Sabin: 1901, Artículos publicados en la 1 época de "Euskadi" : revista de Ciencias, Bellas Artes y Letras de Bilbao por AranaGoiri´ttarr Sabin : 1901, Sabino Arana, 1908, Bilbao, Eléxpuru Hermanos. 102–112
 ^ Artículos ..., Sabino Arana, 112–118
 ^ Efemérides Vascas y Reforma d ela Numeración Euzkérica, Sabino Arana, Biblioteca de la Gran Enciclopedia Vasca, Bilbao, 1969. Extracted from the magazine EuskalErria, 1880 and 1881.
 ^ Fran Ramovš, Karakteristika slovenskega narečja v Reziji in: Časopis za slovenski jezik, književnost in zgodovino, no 4, 1928, pages: 107121 [1]
 ^ Pavle Merku, Ljudje ob teru VI, page: 451
 ^ "Open Location Code: An Open Source Standard for Addresses, Independent of Building Numbers And Street Names". github.com. Google. Retrieved 25 August 2020.
 ^ The diachronic view is like this. Spanish: veinte < Latin: vīgintī, the IE etymology of which (view) connects it to the roots meaning '2' and 10'. (The etymological databases of the Tower of Babel project are referred here.)
 ^ Lau, S. A Practical Cantonese English Dictionary (1977) The Government Printer
Look up vigesimal in Wiktionary, the free dictionary. 