(1.00001)(0.99999) - (1.00002)(0.99998) =
a. 0
b. 10^-10
c. 3(10^-10)
d. 10^-5
e. 3(10^-5)
1.00001 = 1+10ˉ�
.99999 = 1-10ˉ�
1.00002 = 1+2(10ˉ�)
.99998 = 1-2(10ˉ�)
Thus:
(1.00001)(0.99999) - (1.00002)(0.99998)
= (1+10ˉ�)(1-10ˉ�) - (1 + 2*10ˉ�)(1 - 2*10ˉ�)
[Note the difference of two squares: (x+y)(x-y) = x²-y²]
= (1 - 10ˉ¹�) - (1 - 4*10ˉ¹�)
= 3*10ˉ¹�
The correct answer is
C.
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