SOLUTION: In the decimal expansion of the rational number 2/13 what is the 200th digit to the right of the decimal point? a) 1 b) 3 c) 5 d) 8

   0.153846... 
13)2.000000...
   1 3
     70
     65
      50
      39
      110
      104
        60
        52
         80
         78
          2  <--starts repeating block of 6 digits 153846


200/6 = 33 1/3

So the decimal will have gone through exactly 33 complete 
blocks of 6 digits each on the 33×6 = 198th digits so the 
199th digit will be the start of a new block and will be 1.
Then the 200th digit will be 5.

Or you can simply say 200 mod 6 = 2, so the 200th digit is
the same as the 2nd digit, or 5

Answer: c) 5

[It has been shown statistically using multiple-choice tests
and exams that the probability is always higher that the correct
answer is choice c).  So any time you must guess, always
guess c).   :)  ]

Edwin