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For example, in duodecimal, 1 / 2 = 0.6, 1 / 3 = 0.4, 1 / 4 = 0.3 and 1 / 6 = 0.2 all terminate; 1 / 5 = 0. 2497 repeats with period length 4, in contrast with the equivalent decimal expansion of 0.2; 1 / 7 = 0. 186A35 has period 6 in duodecimal, just as it does in decimal. If b is an integer base ...
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.
Decimal: The standard Hindu–Arabic numeral system using base ten. Binary: The base-two numeral system used by computers, with digits 0 and 1. Ternary: The base-three numeral system with 0, 1, and 2 as digits. Quaternary: The base-four numeral system with 0, 1, 2, and 3 as digits.
By {{Convert}} default, the conversion result will be rounded either to precision comparable to that of the input value (the number of digits after the decimal point—or the negative of the number of non-significant zeroes before the point—is increased by one if the conversion is a multiplication by a number between 0.02 and 0.2, remains the ...
Approximation may be needed due to a possibility of non-terminating digits if the reduced fraction's denominator has a prime factor other than any of the base's prime factor(s) to convert to. For example, 0.1 in decimal (1/10) is 0b1/0b1010 in binary, by dividing this in that radix, the result is 0b0.0 0011 (because one of the prime factors of ...
A negative base (or negative radix) may be used to construct a non-standard positional numeral system.Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base b is equal to −r for some natural number r (r ≥ 2).
Most numbers have a unique quater-imaginary representation, but just as 1 has the two representations 1 = 0. 9 in decimal notation, so, because of 0. 0001 2i = 1 / 15 , the number 1 / 5 has the two quater-imaginary representations 0. 0003 2i = 3· 1 / 15 = 1 / 5 = 1 + 3· –4 / 15 = 1. 0300 2i.
The decimal expansion of non-negative real number x will end in zeros (or in nines) if, and only if, x is a rational number whose denominator is of the form 2 n 5 m, where m and n are non-negative integers. Proof: If the decimal expansion of x will end in zeros, or = = = = / for some n, then the denominator of x is of the form 10 n = 2 n 5 n.