Problem Solving

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

What is the Easiest way to solve this

OA D

AkiB 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

Alternate approach:
The answer choices imply that 1.0001 must divide easily into 0.99999999 and that 1.0003 must divide easily into 0.99999991.

x = 0.99999999/1.0001.
1.0001x = 0.99999999.
Notice the values in red.
For the product on the left to yield 0.99999999 -- a value with a rightmost digit of 9 -- the rightmost digit of x must be 9.

y = 0.99999991/1.0003.
1.0003y = 0.99999991.
Notice the values in red.
For the product on the left to yield 0.99999991 -- a value with a rightmost digit of 1 -- the rightmost digit of y must be 7.

Thus:
x-y = (value with a rightmost digit of 9) - (value with a rightmost digit of 7) = (value with a rightmost digit of 2).

Only one answer choice includes a digit of 2:
D: 2(10^-4) = 0.0002.

The correct answer is D.