GMAT Practice Question: The total area of a certain continent is approximately 3.8 \times 10^{16}...
Question
The total area of a certain continent is approximately 3.8 \times 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 \times 10^{9} square inches.)
- 6.7 \times 10^{5}
- 2.0 \times 10^{6}
- 9.5 \times 10^{6}
- 1.1 \times 10^{7}
- 9.5 \times 10^{8}
Topics: conversions, word problems, approximations
Solution
Step 1
We name the continent’s area in square inches and note the conversion factor.
A_{\text{in}} = 3.8 \times 10^{16} 1 \text{ square mile} = 4.0 \times 10^{9}
Step 2
We then calculate the area in square miles by dividing the total square inches by the conversion factor.
\frac{A_{\text{in}}}{4.0 \times 10^{9}} = \frac{3.8 \times 10^{16}}{4.0 \times 10^{9}}
Step 3
We divide the coefficients and subtract the exponents to simplify.
\frac{3.8}{4.0} \times 10^{16-9} = \frac{38}{40} \times 10^{7} = \frac{\cancel{2} \times 19}{\cancel{2} \times 20} \times 10^{7} = \frac{19}{20} \times 10^{7} = 0.95 \times 10^{7}
Step 4
We shift the decimal point to match the answer choice format.
0.95 \times 10^{7} = 9.5 \times 10^{6}
Answer
9.5 \times 10^{6}
