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Quaternary: The base-four numeral system with 0, 1, 2, and 3 as digits. Hexadecimal: Base 16, widely used by computer system designers and programmers, as it provides a more human-friendly representation of binary-coded values. Octal: Base 8, occasionally used by computer system designers and programmers.
Some real numbers have decimal expansions that eventually get into loops, endlessly repeating a sequence of one or more digits: 1 ⁄ 3 = 0.33333... 1 ⁄ 7 = 0.142857142857... 1318 ⁄ 185 = 7.1243243243... Every time this happens the number is still a rational number (i.e. can alternatively be represented as a ratio of an integer and a ...
Using all numbers and all letters except I and O; the smallest base where 1 / 2 terminates and all of 1 / 2 to 1 / 18 have periods of 4 or shorter. 35: Covers the ten decimal digits and all letters of the English alphabet, apart from not distinguishing 0 from O. 36: Hexatrigesimal [57] [58]
As for rational numbers, ternary offers a convenient way to represent 1 / 3 as same as senary (as opposed to its cumbersome representation as an infinite string of recurring digits in decimal); but a major drawback is that, in turn, ternary does not offer a finite representation for 1 / 2 (nor for 1 / 4 , 1 / 8 ...
10 1 1 3 = 1 × 3 3 + 0 × 3 2 − 1 × 3 1 + 1 × 3 0 = 25. The factorial number system uses a varying radix, giving factorials as place values; they are related to Chinese remainder theorem and residue number system enumerations. This system effectively enumerates permutations.
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. In a hexadecimal system, there are 16 digits, 0 through 9 followed, by convention, with A ...
binary, ternary, octal, decimal, hexadecimal (numbers expressed in base 2, base 3, base 8, base 10, base 16) septuagenarian, octogenarian (a person 70–79 years old, 80–89 years old) centipede , millipede (subgroups of arthropods with around 100 feet, or around 1 000 feet)
An example of a fraction that cannot be represented by a decimal expression (with a finite number of digits) is 1 / 3 , 3 not being a power of 10. More generally, a decimal with n digits after the separator (a point or comma) represents the fraction with denominator 10 n , whose numerator is the integer obtained by removing the separator.