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A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating.
[2] [3] These complementary sequences are generated between multiples of prime reciprocals that add to 1. More specifically, a factor n {\displaystyle n} in the numerator of the reciprocal of a prime number p {\displaystyle p} will shift the decimal places of its decimal expansion accordingly,
Cyclic numbers can be constructed by the following procedure: Let b be the number base (10 for decimal) Let p be a prime that does not divide b. Let t = 0. Let r = 1. Let n = 0. loop: Let t = t + 1 Let x = r ⋅ b Let d = int(x / p) Let r = x mod p Let n = n ⋅ b + d If r ≠ 1 then repeat the loop. if t = p − 1 then n is a cyclic number.
The real-number Euclidean algorithm differs from its integer counterpart in two respects. First, the remainders r k are real numbers, although the quotients q k are integers as before. Second, the algorithm is not guaranteed to end in a finite number N of steps. If it does, the fraction a/b is a rational number, i.e., the ratio of two integers
Octal (base 8) is a numeral system with eight as the base.. In the decimal system, each place is a power of ten.For example: = + In the octal system, each place is a power of eight.
Another way of expressing fractions was originally limited to weight measures, specifically fractions of the mina (π πΎ ma-na): π šuššana "one-third" (literarlly "two-sixths"), π šanabi "two-thirds" (the former two words are of Akkadian origins), π gigΜusila or π²ππ la 2 gigΜ 4 u "five-sixths" (literally "ten shekels ...