199i 0.99999999 0.99999991_
1.0001 1.0003
180
(A) io-8
(B) 3U0-8)
(0 3(10-4)
(D) 2(10-4)
(E) io-4
Is there an approximation method for this problem?
OG 13 - PS 199
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One approach is to recognize that both 9999.9999 and 9999.9991 can be rewritten as differences of squares.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
First, 0.99999999 = 1 - 0.00000001
= (1 - 0.0001)(1 + 0.0001)
Similarly, 9999.9991 = 1 - 0.00000009
= (1 - 0.0003)(1 + 0.0003)
Original question: 0.99999999/1.0001 - 0.99999991/1.0003
= (1 - 0.0001)(1 + 0.0001)/(1.0001) - (1 - 0.0003)(1 + 0.0003)/(1.0003)
= (1 - 0.0001)(1.0001)/(1.0001) - (1 - 0.0003)(1.0003)/(1.0003)
= (1 - 0.0001) - (1 - 0.0003)
= 1 - 0.0001 - 1 + 0.0003
= 0.0002
= 2 x 10^(-4) = D
Cheers,
Brent