TITLE: Why is $\frac{987654321}{123456789} = 8.0000000729?!$
QUESTION [97 upvotes]: Many years ago, 
I noticed that $987654321/123456789 = 8.0000000729\ldots$.
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 $10$?

REPLY [2 votes]: I think one should also think about how this is related to 9 being before 10. Notice the two following striking facts:
$12345679*8=98765432$ and $12345679*9=111111111$