SOLUTION: The decimal expansion of (1/2)^100 has what digit for its third nonzero digit from the right?

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Question 252377: The decimal expansion of (1/2)^100 has what digit for its third nonzero digit from
the right?
Found 2 solutions by richwmiller, Alan3354:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
1/1267650600228229401496703205376=
7.888609052210118054117285652827862296732064351090230047702789306640625 x 10^-31

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
0.5 to any power (or 5) produces the same 4 digits on the right once it becomes greater than the 4th power.
Exp...last 4
0......1
1......0005
2......0025
3......0125
4......0625 now it repeats
5......3125
6......5625
7......8125
8......0625
9......3125
etc.
The last 4 of the 100th power is the same as the 4th, 8th, 12th, etc, = 0625