Problem Solving

VJesus12 wrote:A bar below a digit in a decimal indicates an infinitely repeating decimal.

333,333.3 × (10-3-10-5)(10-3-10-5) =

A. 3,333.3
B. 3,330
C. 333.3
D. 330
E. 0

[spoiler]OA=D[/spoiler]

Source: Princeton Review

Note: We are assuming "10-3-10-5" stands for "10^(-3) - 10^(-5)" and also that it has been mistakenly written twice; otherwise the answer we get is not among the answer choices.

Notice that 333,333.3 = 333,333 + 0.3 = 333,333 + 1/3 = 1,000,000/3.

Notice also that 10^(-3) - 10^(-5) = 1/1,000 - 1/100,000 = 100/100,000 - 1/100,000 = 99/100,000.

Then, 333,333.3 x (10^(-3) - 10^(-5)) = 1,000,000/3 x 99/100,000 = 10 x 33 = 330.

Answer: D