University of South Carolina High School Math Contest/1993 Exam/Problem 26
Problem
Let . Then the first nonzero digit in the decimal expansion of
is
![$\mathrm{(A) \ }1 \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ }3 \qquad \mathrm{(D) \ }4 \qquad \mathrm{(E) \ }5$](http://latex.artofproblemsolving.com/6/d/9/6d9996366456c66c07a72d521f4cfc2a611cbee7.png)
Solution
We only need to worry about the decimal expansion of since the
will do nothing to the decimal digits. We have
. Using the extended binomial theorem, we have that
. Now we only have to look at the second term since all the following terms will be too small to affect the first nonzero digit of the decimal expansion. We see that
. The answer is
.