2015 AMC 12A Problems/Problem 15
Problem
What is the minimum number of digits to the right of the decimal point needed to express the fraction as a decimal?
$\textbf{(A)}\ 4\qquad\textbf{(B)}\ 22\qquad\textbf{(C)}\ 26\qquad\textbf{(D)}}\ 30\qquad\textbf{(E)}\ 104$ (Error compiling LaTeX. Unknown error_msg)
Solution
We can rewrite the fraction as . Since the last digit of the numerator is odd, a
is added to the right if the numerator is divided by
, and this will continuously happen because
, itself, is odd. Indeed, this happens twenty-two times since we divide by
twenty-two times, so we will need
more digits. Hence, the answer is
.
Alternate Solution
Note that is not a multiple of
or
, and therefore shares no factors with the original denominator. Multiple the numerator and denominator of the fraction by
to give
. This fraction will require
divisions by ten to write as a decimal, and since the original fraction is less than
all of the digits will be to the right of the decimal point. Answer:
See Also
2015 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 14 |
Followed by Problem 16 |
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All AMC 12 Problems and Solutions |