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07 Feb 2014, 16:19
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the total area of certain continent is approximately 3.8 * 10^16 square inches. which of the following is closest to the area of the continent, in square miles? (1 square mile is approximately 4.0 * 10^9 square inches.)
07 Feb 2014, 16:30
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We are given that a certain continent is \(3.8 \times 10^{16} \text{in}^2\) and that \(1 \text{mi}^2 = 4.0 \times 10^9 \text{in}^2\).
Another way to write that is \(1 = \frac{\text{mi}^2}{4.0 \times 10^9 \text{in}^2\).
So, to figure the area in square miles, we multiply the two together to get: \(3.8 \times 10^{16} \text{in}^2 \times \frac{\text{mi}^2}{4.0 \times 10^9 \text{in}^2}\\
= \frac{3.8 \times 10^{16} \text{mi}^2}{4 \times 10^9}\)
Now, there are two ways to simplify \(\frac{3.8 \times 10^{16} \text{mi}^2}{4 \times 10^9}\)
\((1) \frac{3.8 \times 10^{16} \text{mi}^2}{4 \times 10^9} = \frac{38 \times 10^{15} }{4 \times 10^9}\text{mi}^2 = ( \frac{38}{4} )( \frac{10^{15}}{10^9})\text{mi}^2 = (9.5)(10^{6})\text{mi}^2 = 9.5\times10^6 \text{mi}^2\)
\((2) \frac{3.8 \times 10^{16} \text{mi}^2}{4 \times 10^9} = ( \frac{3.8}{4.0} )( \frac{10^{16}}{10^9})\text{mi}^2 = (.95)(10^{7})\text{mi}^2 = 9.5\times10^6 \text{mi}^2\)
A quick google search tells me the continent in question is North America
Another way to write that is \(1 = \frac{\text{mi}^2}{4.0 \times 10^9 \text{in}^2\).
So, to figure the area in square miles, we multiply the two together to get: \(3.8 \times 10^{16} \text{in}^2 \times \frac{\text{mi}^2}{4.0 \times 10^9 \text{in}^2}\\
= \frac{3.8 \times 10^{16} \text{mi}^2}{4 \times 10^9}\)
Now, there are two ways to simplify \(\frac{3.8 \times 10^{16} \text{mi}^2}{4 \times 10^9}\)
\((1) \frac{3.8 \times 10^{16} \text{mi}^2}{4 \times 10^9} = \frac{38 \times 10^{15} }{4 \times 10^9}\text{mi}^2 = ( \frac{38}{4} )( \frac{10^{15}}{10^9})\text{mi}^2 = (9.5)(10^{6})\text{mi}^2 = 9.5\times10^6 \text{mi}^2\)
\((2) \frac{3.8 \times 10^{16} \text{mi}^2}{4 \times 10^9} = ( \frac{3.8}{4.0} )( \frac{10^{16}}{10^9})\text{mi}^2 = (.95)(10^{7})\text{mi}^2 = 9.5\times10^6 \text{mi}^2\)
A quick google search tells me the continent in question is North America
10 Feb 2014, 02:25
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Luning1
Here is a post on how to change units: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/01 ... nd-ounces/
Given: \((4 * 10^9) in^2 = 1 mi^2\)
\((1) in^2 = \frac{1}{4*10^9} mi^2\)
\((3.8 * 10^{16}) in^2 = \frac{3.8*10^{16}}{4*10^9} mi^2 = 9.5*10^6 mi^2\)
