Difference between revisions of "2015 AMC 12A Problems/Problem 15"

(Solution)
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==Solution==
 
==Solution==
The fraction is equivalent to <math>\frac{123456789 \cdot 5^{22}}{10^{26}}.</math> The answer is clearly <math>\textbf{(C)}.</math>
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The fraction is equivalent to <math>\frac{123456789 \cdot 5^{29}}{10^{30}}.</math> The answer is clearly <math>\textbf{(E)}.</math>
  
 
== See Also ==
 
== See Also ==
 
{{AMC12 box|year=2015|ab=A|num-b=14|num-a=16}}
 
{{AMC12 box|year=2015|ab=A|num-b=14|num-a=16}}

Revision as of 03:00, 5 February 2015

Problem

What is the minimum number of digits to the right of the decimal point needed to express the fraction $\frac{123456789}{2^{26}\cdot 5^4}$ 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. ! Extra }, or forgotten $.)

Solution

The fraction is equivalent to $\frac{123456789 \cdot 5^{29}}{10^{30}}.$ The answer is clearly $\textbf{(E)}.$

See Also

2015 AMC 12A (ProblemsAnswer KeyResources)
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
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