Difference between revisions of "1986 AJHSME Problems/Problem 20"
5849206328x (talk | contribs) (New page: ==Problem== The value of the expression <math>\frac{(304)^5}{(29.7)(399)^4}</math> is closest to <math>\text{(A)}\ .003 \qquad \text{(B)}\ .03 \qquad \text{(C)}\ .3 \qquad \text{(D)}\ 3 ...) |
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==Solution== | ==Solution== | ||
| − | {{ | + | <cmath> \frac{(304)^5}{(29.7)(399)^4} \simeq \frac{300^5}{30\cdot400^4} = \frac{3^5 \cdot 10^{10}}{3\cdot 4^4 \cdot 10^9} = \frac{3^4\cdot 10}{4^4} = \frac{810}{256}</cmath> |
| + | which is obviously closest to <math>\boxed{3}</math>. | ||
| + | |||
| + | (The original expression is approximately equal to <math>3.44921198</math>.) | ||
==See Also== | ==See Also== | ||
[[1986 AJHSME Problems]] | [[1986 AJHSME Problems]] | ||
Revision as of 19:36, 25 January 2009
Problem
The value of the expression 
is closest to
Solution
![\[\frac{(304)^5}{(29.7)(399)^4} \simeq \frac{300^5}{30\cdot400^4} = \frac{3^5 \cdot 10^{10}}{3\cdot 4^4 \cdot 10^9} = \frac{3^4\cdot 10}{4^4} = \frac{810}{256}\]](http://latex.artofproblemsolving.com/5/f/9/5f92c6816bd9b09d142bd6007cce567f1f47335e.png)
which is obviously closest to 
.
(The original expression is approximately equal to 
.)
