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 
.
See Also
| 2015 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 14 |
Followed by Problem 16 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
