Suppose you have a fraction a/b where 0 < a < b, and a and b are relatively prime integers. The decimal expansion of a/b either terminates or it has an initial non-repeating part followed by a repeating part. How long is the non-repeating part? How long is the period of the repeating part? The answer depends on the prime factorization […]

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Academics : The Endeavour

You can’t subtract 4 from 3 (and stay inside the natural numbers, but you can inside the integers) You can’t divide 3 by 4 (inside the ring of integers, but you can inside its field of fractions, the rational numbers). You can’t tak...

Programming / Windows Development : CodeProject

Class for converting decimals and fractions (allows rounding to a decimal also)

Academics : The Endeavour

Somewhere along the way you may have noticed that the digits in the decimal expansion of multiples of 1/7 are all rotations of the same digits: 1/7 = 0.142857142857… 2/7 = 0.285714285714… 3/7 = 0.428571428571… 4/7 = 0.571428571428… ...

Academics / Mathematics : God Plays Dice

Here's a question. Why is the period of the quotients in the continued fraction of N1/2 "usually" even? For example, if N runs over the ninety non-squares less than 100, then only 20 times does the continued fraction expansion of N1...

Academics : The Endeavour

I posted a couple prime-generating fractions on Google+ this weekend and said that I’d post an explanation later. Here it goes. The decimal expansion of 18966017 / 997002999 is.019 023 029 037 047 059 073 089 107 127 149 … Read more...

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