Many years ago,
I noticed that 987654321/123456789=8.0000000729….
I sent it in to Martin Gardner at Scientific American
and he published it in his column!!!
My life has gone downhill since then:)
My questions are:
Why is this so?
What happens beyond the “729“?
What happens in bases other than 10?
In base n the numerator is p=nn−1−nn−1−1(n−1)2 and the denominator is q=n(nn−1−1)(n−1)2−1.
Note that p=(n−2)q+n−1 and for the quotient we get
Indeed for n=10 this is