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.
1.000
1x = 0.9999999
9.
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.
1.000
3y = 0.9999999
1.
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.
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