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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).
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 computer-science practice of writing hexadecimal numerals over 9 with the letters "A-F". Another 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}.
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.
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). As 20 has the same prime factors as 10 (two and five), any fraction that terminates in decimal will terminate in vigesimal, and any fraction that does not terminate in decimal will not terminate in vigesimal either: the converses of these statements are also true.
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).
Vigesimal systems are common in Africa, for example in Yoruba.
Ogún, 20, is the basic numeric block. Ogójì, 40, (Ogún-meji) = 20 multiplied by 2 (èjì). Ogota, 60, (Ogún-mẹ̀ta) = 20 multiplied by 3 (ẹ̀ta). Ogorin, 80, (Ogún-mẹ̀rin) = 20 multiplied by 4 (ẹ̀rin). Ogorun, 100, (Ogún-màrún) = 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.
"Vigesimal" has its roots in the Latin adjective vicesimus (in its first or second declension).
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