Cez005 wrote:

Which of the following is closest to (1)/(1.001)?

A. 0.997

B. 0.998

C. 0.999

D. 1.000

E. 1.001

We can convert 1.001 to a fraction and we have:

1/[(1001/1000)] = 1000/1001

It is obvious that this number is just a little smaller than 1 (which makes it just a little greater than 0.999), so the answer is either D or C. We must decide which. We will compare the difference between 1 and 1000/1001 to the difference between 1000/1001 and 0.999 = 999/1000.

1 - 1000/1001 = 1000/1000 - 1000/1001

= 1001000/1001000 - 1000000/1001000

= 1000/1001000

= 1/1001

1000/1001 - 999/1000 = 1000000/1001000 - 999999/1001000

= 1/1001000

Since the difference between 1000/1001 and 999/1000 is much smaller than the difference between 1 and 1000/1001, 1000/1001 is closer to 999/1000 = 0.999 than any other choice.

Answer: C

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