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Open question: what is a round number, for you personally? (self.programming)

submitted 1 year ago by verstra to c/programming

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[–] UlrikHD 6 points 1 year ago

A round number is a number that is the product of a considerable number of comparatively small factors (Hardy 1999, p. 48). Round numbers are very rare. As Hardy (1999, p. 48) notes, "Half the numbers are divisible by 2, one-third by 3, one-sixth by both 2 and 3, and so on. Surely, then we may expect most numbers to have a large number of factors. But the facts seem to show the opposite."

A positive integer n is sometimes said to be round (or "square root-smooth") if it has no prime factors greater than sqrt(n). The first few such numbers are 1, 4, 8, 9, 12, 16, 18, 24, 25, 27, 30, 32, ... (OEIS A048098). Using this definition, an asymptotic formula for the number of round integers less than or equal to a positive real number x is given by N(x)∼(1-ln2)x+O(x/lnx)

(Hildebrand).

https://mathworld.wolfram.com/RoundNumber.html

Alternatively, a number rounded off to a given precision in whatever numeral system you are using. E.g. ten in decimal may be round if you are dealing with small numbers in the decimal system, but it wouldn't be particularly round if you were dealing with large numbers or hexadecimal.