GMAT Word Problems: Which of the following expresses…

State X has 77 acres designated as wilderness, which is 0.0003 percent of its total acreage. Which of the following expresses the total acreage of State X ?

A. $3 (1 0^{4}) (77)$
B. $3 (1 0^{6}) (77)$
C. $\frac{( 1 0 ^{2} ) ( 77 )}{3}$
D. $\frac{( 1 0 ^{4} ) ( 77 )}{3}$
E. $\frac{( 1 0 ^{6} ) ( 77 )}{3}$

word problemspercentagesconversions

Explanation	Calculations	Help
$We first choose a variable for the total acreage of State X.$	$T = total acreage of State X$
$We translate the statement "77 acres designated as wilderness, which is 0.0003 percent of its total acreage" into an equation.$	$77 = \frac{0.0003}{100} \times T$
$We isolate the total acreage by dividing both sides by the percentage coefficient.$	$T = \frac{77}{\frac{0.0003}{100}}$
$We simplify the percentage fraction in the denominator to scientific notation.$	$\frac{0.0003}{100} = 0.000003 0.000003 = 3 \times 1 0^{- 6}$
$We then simplify and express the total acreage in scientific notation.$	$T = \frac{77}{3 \times 1 0 ^{- 6}} = \frac{77}{3} \times 1 0^{6}$

((10^6)(77))/3 (E)

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