Fractions are a confusing way to explain this.  Rather than use fractions,
it would be better to divide 4000 by 6 by long division and look only at the
remainder:
   
   666
6)4000
  36
   40
   36
    40
    36
     4

The 666 quotient tells us how many COMPLETE times the sequence goes through
the cycle of 6,5,4,3,2,1, and the 4 remainder tells us which member of the
cycle is the 4000th digit.

Since the 4th member of the cycle is 3, the answer is 3. 

Edwin