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Concept
Vigesimal
Summary
A vigesimal (vɪˈdʒɛsɪməl) or base-20 (base-score) 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, meaning 'twentieth'.
In a vigesimal place system, twenty individual numerals (or digit symbols) are used, ten more than in the decimal system. One modern method of finding the extra needed symbols is to write ten as the letter (the 20 means base ), to write nineteen as , 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 less common method skips over the letter "I", in order to avoid confusion between I20 as eighteen and one, so that the number eighteen is written as J20, and nineteen is written as K20. The number twenty is written as .
According to this notation:
is equivalent to forty in decimal = (2 × 201) + (0 × 200)
is equivalent to two hundred and sixty in decimal = (13 × 201) + (0 × 200)
is equivalent to four hundred in decimal = (1 × 202) + (0 × 201) + (0 × 200).
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.
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 six-digit 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.
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