Problem Solving

ngbrian85 wrote:(0.99999999 / 1.0001) - (0.99999991 / 1.0003) =

(A)10^-8
(B)3(10^-8)
(C)3(10^-4)
(D)2(10^-4)
(E)10^-4

(0.99999999 / 1.0001) - (0.99999991 / 1.0003) = ?
Let us assume that x = 0.0001 = 10^(-4)
x² = 0.00000001 = 10^(-8)

We can write 0.99999999 = 1 - 0.00000001 = 1 - 10^(-8) = 1 - x²
1.0001 = 1 + x
0.99999991 = 1 - 9x² = 1 - (3x)²
1.0003 = 1 + 3x

Therefore, (0.99999999 / 1.0001) - (0.99999991 / 1.0003) = [(1 - x²)/(1 + x)] - [(1 - (3x)²)/(1 + 3x)] = [(1 - x)(1 + x)/(1 + x)] - [(1 - 3x)(1 + 3x))/(1 + 3x)] = [(1 - x)] - [(1 - 3x)] = 1 - x -1 + 3x = 3x - x = 2x
= 2 * 0.0001 = 0.0002 = [spoiler]2 * 10^(-4)[/spoiler]

The correct answer is D.