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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.
"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
For example, 10 2 = 2; 10 3 = 3; 10 16 = 16 10. Note that the last "16" is indicated to be in base 10. The base makes no difference for one-digit numerals. This concept can be demonstrated using a diagram. One object represents one unit. When the number of objects is equal to or greater than the base b, then a group of objects is created with b ...
Exponentiation with base 10 is used in scientific notation to denote large or small numbers. For instance, 299 792 458 m/s (the speed of light in vacuum, in metres per second) can be written as 2.997 924 58 × 10 8 m/s and then approximated as 2.998 × 10 8 m/s. SI prefixes based on powers of 10 are also used to describe small or large quantities.
In base 10, ten different digits 0, ..., 9 are used and the position of a digit is used to signify the power of ten that the digit is to be multiplied with, as in 304 = 3×100 + 0×10 + 4×1 or more precisely 3×10 2 + 0×10 1 + 4×10 0. Zero, which is not needed in the other systems, is of crucial importance here, in order to be able to "skip ...
For example, decimal (base 10) requires ten digits (0 to 9), and binary (base 2) requires only two digits (0 and 1). Bases greater than 10 require more than 10 digits, for instance hexadecimal (base 16) requires 16 digits (usually 0 to 9 and A to F).
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The table shows what number the order of magnitude aim at for base 10 and for base 1 000 000. It can be seen that the order of magnitude is included in the number name in this example, because bi- means 2, tri- means 3, etc. (these make sense in the long scale only), and the suffix -illion tells that the base is 1 000 000.