Quote: What is -10.6666666666666667 in a fraction?
what you're really interested in is what does 0.6666666666666666666 etc. convert to
the trick to this (and it is a trick) is to consider the difference between itself and 10 times itself i.e.
6.666666666666666... - 0.6666666666666666... = 6
so let x = 0.666666666666666666...
10x - x = 6
9x = 6
x = 6/9 = 2/3
suppose you had 0.12121212121212.......
you can consider the difference of 100 times itself and itself
you get
99x = 12
x = 12/99 = 4/33
similarly with repeating patterns of length K, just consider the difference of 10
K times itself and itself.
+6251 
