The total area of a certain continent is approximately 3.8 10^16...

Question

The total area of a 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.)

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9.5 10^6 We name the continent’s area in square inches and note the conversion factor. A_in = 3.8 10^16 1 square mile = 4.0 10^9 We then calculate the area in square miles by dividing the total square inches by the conversion factor. A_in4.0 10^9 = 3.8 10^164.0 10^9 We divide the coefficients and subtract the exponents to simplify. 3.8/4.0 10^16-9 = 38/40 10^7 = 2 192 20 10^7 = 19/20 10^7 = 0.95 10^7 We shift the decimal point to match the answer choice format. 0.95 10^7 = 9.5 10^6

Explanation	Calculations	Help
$We name the continent’s area in square inches and note the conversion factor.$	$A_{in} = 3.8 \times 1 0^{16} 1 square mile = 4.0 \times 1 0^{9}$
$We then calculate the area in square miles by dividing the total square inches by the conversion factor.$	$\frac{A _{in}}{4.0 \times 1 0 ^{9}} = \frac{3.8 \times 1 0 ^{16}}{4.0 \times 1 0 ^{9}}$
$We divide the coefficients and subtract the exponents to simplify.$	$\frac{3.8}{4.0} \times 1 0^{16 - 9} = \frac{38}{40} \times 1 0^{7} = \frac{2 \times 19}{2 \times 20} \times 1 0^{7} = \frac{19}{20} \times 1 0^{7} = 0.95 \times 1 0^{7}$
$We shift the decimal point to match the answer choice format.$	$0.95 \times 1 0^{7} = 9.5 \times 1 0^{6}$

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