SOLUTION: if 1/17=0.0588235294117647...., determine the 614th digit of the decimal expansion.

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Question 933190: if 1/17=0.0588235294117647...., determine the 614th digit of the decimal expansion.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if 1%2F17=0.0588235294117647...., determine the 614th digit of the decimal expansion.
0.0588235294117647- here you got 16-digit-cycle, means you just add next cycle to first one like this
0.0588235294117647+0588235294117647... and repeat until you got decimal 614 digits to see which one is it...:-)
or do it this way:
614%2F16=38+%2B6%2F16=38%28full_cycles%29%2B%283%2F8%29%28of_39th_cycle%29 ..
since cycle has 16 digits,%283%2F8%2916=6 digits; so, we add 058823 from 39th full cycle,last one is digit we need and it is 3
so, the 614th digit of the decimal expansion 3