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The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base.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.
For comparison, the same number in decimal representation: 1.125 × 2 3 (using decimal representation), or 1.125B3 (still using decimal representation). Some calculators use a mixed representation for binary floating point numbers, where the exponent is displayed as decimal number even in binary mode, so the above becomes 1.001 b × 10 b 3 d or ...
Unless specified by context, numbers without subscript are considered to be decimal. By using a dot to divide the digits into two groups, one can also write fractions in the positional system. For example, the base 2 numeral 10.11 denotes 1×2 1 + 0×2 0 + 1×2 −1 + 1×2 −2 = 2.75. In general, numbers in the base b system are of the form:
In the decimal system, there are 10 digits, 0 through 9, which combine to form numbers. In an octal system, there are only 8 digits, 0 through 7. That is, the value of an octal "10" is the same as a decimal "8", an octal "20" is a decimal "16", and so on.
Twelve is the largest number with a single-syllable name in English.Early Germanic numbers have been theorized to have been non-decimal: evidence includes the unusual phrasing of eleven and twelve, the former use of "hundred" to refer to groups of 120, and the presence of glosses such as "tentywise" or "ten-count" in medieval texts showing that writers could not presume their readers would ...
A real number can be expressed by a finite number of decimal digits only if it is rational and its fractional part has a denominator whose prime factors are 2 or 5 or both, because these are the prime factors of 10, the base of the decimal system. Thus, for example, one half is 0.5, one fifth is 0.2, one-tenth is 0.1, and one fiftieth is 0.02.
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Alternatively, and for greater numbers, one may say for 1 ⁄ 2 "one over two", for 5 ⁄ 8 "five over eight", and so on. This "over" form is also widely used in mathematics. Fractions together with an integer are read as follows: 1 + 1 ⁄ 2 is "one and a half" 6 + 1 ⁄ 4 is "six and a quarter" 7 + 5 ⁄ 8 is "seven and five eighths"