Of course, short repetends happen whenever the denominator is a factor of 10^k-1: 1/11 = 9/99 = 0.09 09 09... 1/37 = 27/999 = 0.027 027 027… 1/101 = 99/9999 = 0.0099 0099… 1/41 = 2439/99999 = 0.02439 02439 1/271 = 369/99999 = 0.00369 00369… 1/13 = 76923/999999 = 0.076923 076923… I remember being fascinated by these when I was a kid.
On Mar 17, 2018, at 2:36 PM, James Propp <jamespropp@gmail.com> wrote:
I just figured out for myself a probably well-known trick for deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 = 14/(100-2) = .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857...
Are there other examples where the repetend of the decimal expansion of 1/n in splits into blocks that are related to this sort of fashion?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun