![]() There are twelve signs of the zodiac, twelve months in a year, and the Babylonians had twelve hours in a day (although at some point this was changed to 24). Historically, units of time in many civilizations are duodecimal. However, they are considered to come from Proto-Germanic * ainlif and * twalif (respectively one left and two left), both of which were decimal. Germanic languages have special words for 11 and 12, such as eleven and twelve in English, which are often misinterpreted as vestiges of a duodecimal system. Tolkien's Elvish languages use a hybrid decimal-duodecimal system, primarily decimal but with special names for multiples of six. Languages in the Nigerian Middle Belt such as Janji, Gbiri-Niragu (Kahugu), the Nimbia dialect of Gwandara the Chepang language of Nepal and the Mahl language of Minicoy Island in India are known to use duodecimal numerals. Languages using duodecimal number systems are uncommon. For example, 10 means ten, 12 means twelve. Origin In this section, numerals are based on decimal places. ![]() 4.2 Decimal to dozenal digit conversion.4.1 Dozenal to decimal digit conversion.4 Conversion tables to and from decimal.This all makes it a more convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary, octal and hexadecimal systems, although the sexagesimal system (where the reciprocals of all 5-smooth numbers terminate) does better in this respect (but at the cost of an unwieldy multiplication table). In particular, the five most elementary fractions (½, ⅓, ⅔, ¼ and ¾) all have a short terminating representation in duodecimal (0.6, 0.4, 0.8, 0.3 and 0.9, respectively), and twelve is the smallest radix with this feature (since it is the least common multiple of 3 and 4). Of its factors, 2 and 3 are prime, which means the reciprocals of all 3-smooth numbers (such as 2, 3, 4, 6, 8, 9.) have a terminating representation in duodecimal. As a result, duodecimal is sometimes named the number system with the most optimal radix economy. As a result of this increased factorability of the radix and its divisibility by a wide range of the most elemental numbers (whereas ten has only two non-trivial factors: 2 and 5, with neither 3 nor 4), duodecimal representations fit more easily than decimal ones into many common patterns, as evidenced by the higher regularity observable in the duodecimal multiplication table. The number twelve, a 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. Similarly, in duodecimal "100" means "1 gross", "1000" means "1 great gross", and "0.1" means "1 twelfth" (instead of their decimal meanings "1 hundred", "1 thousand", and "1 tenth"). the same number that in decimal is written as "14"). The number twelve (that is, the number written as "12" in the base ten numerical system) is instead written as "10" in duodecimal (meaning "1 dozen and 0 units", instead of "1 ten and 0 units"), whereas the digit string "12" means "1 dozen and 2 units" (i.e. In this system, the number ten may be written as "A", "T" or "X", and the number eleven as "B" or "E" (another common notation, introduced by Sir Isaac Pitman, is to use a rotated "2" for ten and a reversed "3" for eleven). The duodecimal system (also known as base-12 or dozenal) is a positional notation numeral system using twelve as its base.
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