![]() Languages in the Nigerian Middle Belt such as Janji, Gbiri-Niragu (Gure-Kahugu), Piti, and the Nimbia dialect of Gwandara and the Chepang language of Nepal are known to use duodecimal numerals. Languages using duodecimal number systems are uncommon. This system is still in use in many regions of Asia. In this system, one hand counts repeatedly to 12, while the other displays the number of iterations, until five dozens, i.e. Using the thumb as a pointer, it is possible to count to 12 by touching each finger bone, starting with the farthest bone on the fifth finger, and counting on. Georges Ifrah speculatively traced the origin of the duodecimal system to a system of finger counting based on the knuckle bones of the four larger fingers. ![]() Origin In this section, numerals are in decimal. Sexagesimal (base sixty) does even better in this respect (the reciprocals of all 5-smooth numbers terminate), but at the cost of unwieldy multiplication tables and a much larger number of symbols to memorize. In these respects, duodecimal is considered superior to decimal, which has only 2 and 5 as factors, and other proposed bases like octal or hexadecimal. As a result, duodecimal has been described as the optimal number system. There is also higher regularity observable in the duodecimal multiplication table. All multiples of reciprocals of 3-smooth numbers ( a / 2 b♳ c where a,b,c are integers) have a terminating representation in duodecimal. The number twelve, a superior highly composite number, is the smallest number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range, and the smallest abundant number. The Dozenal Societies of America and Great Britain (organisations promoting the use of duodecimal) use turned digits in their published material: 2 (a turned 2) for ten and 3 (a turned 3) for eleven. Various symbols have been used to stand for ten and eleven in duodecimal notation this page uses A and B, as in hexadecimal, which make a duodecimal count from zero to twelve read 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10. In duodecimal, "100" means twelve squared, "1000" means twelve cubed, and "0.1" means a twelfth. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten. The duodecimal system, also known as base 12 or dozenal, is a positional numeral system using twelve as its base.
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