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- Duodecimal abstract "The duodecimal system (also known as base-12 or dozenal) is a positional notation numeral system using twelve as its base. 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" (2) for ten and a reversed "3" (3) for eleven. 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. the same number that in decimal is written as "14"). 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 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. 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. As a result, duodecimal has been described as the optimal number system. 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. In particular, the five most elementary fractions (1⁄2, 1⁄3, 2⁄3, 1⁄4 and 3⁄4) 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 (because it is the least common multiple of 3 and 4). 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 and a much larger number of symbols to memorize).".
- Duodecimal wikiPageExternalLink dozenal.ae-web.ca.
- Duodecimal wikiPageExternalLink www.dozenal.org.
- Duodecimal wikiPageExternalLink www.dozenalsociety.org.uk.
- Duodecimal wikiPageExternalLink dozenalclock.html.
- Duodecimal wikiPageExternalLink demo.html.
- Duodecimal wikiPageID "8400".
- Duodecimal wikiPageRevisionID "606376441".
- Duodecimal hasPhotoCollection Duodecimal.
- Duodecimal subject Category:Positional_numeral_systems.
- Duodecimal comment "The duodecimal system (also known as base-12 or dozenal) is a positional notation numeral system using twelve as its base. 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" (2) for ten and a reversed "3" (3) for eleven.".
- Duodecimal label "Duodecimal".
- Duodecimal label "Duodezimalsystem".
- Duodecimal label "Dwunastkowy system liczbowy".
- Duodecimal label "Sistema de numeração duodecimal".
- Duodecimal label "Sistema duodecimal".
- Duodecimal label "Système duodécimal".
- Duodecimal label "Twaalftallig stelsel".
- Duodecimal label "Двенадцатеричная система счисления".
- Duodecimal label "نظام عد ثنائي عشر".
- Duodecimal label "十二进制".
- Duodecimal label "十二進法".
- Duodecimal sameAs Dvanáctková_soustava.
- Duodecimal sameAs Duodezimalsystem.
- Duodecimal sameAs Sistema_duodecimal.
- Duodecimal sameAs Zenbaki-sistema_hamabitar.
- Duodecimal sameAs Système_duodécimal.
- Duodecimal sameAs Sistema_numerico_dozzinale.
- Duodecimal sameAs 十二進法.
- Duodecimal sameAs 십이진법.
- Duodecimal sameAs Twaalftallig_stelsel.
- Duodecimal sameAs Dwunastkowy_system_liczbowy.
- Duodecimal sameAs Sistema_de_numeração_duodecimal.
- Duodecimal sameAs m.02bjn.
- Duodecimal sameAs Q212177.
- Duodecimal sameAs Q212177.
- Duodecimal wasDerivedFrom Duodecimal?oldid=606376441.
- Duodecimal isPrimaryTopicOf Duodecimal.