Answer: B) 194/999
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Explanation:
We can use a calculator to verify this
194/999 = 0.1941941941942
The 2 at the end is because of rounding error. The "194" goes on forever, but the calculator can only display so many digits.
Here are the steps needed to determine the fraction
x = 0.194194...
1000x = 194.194194...
1000x-x = (194.194194...) - (0.194194...)
999x = 194
x = 194/999
Note in the jump from the third step to the fourth step, the decimal expansions cancel out. This is because the string of "194"s match perfectly and subtract to go away. We're left with whole numbers from then on. So this is why I multiplied both sides by 1000 in the second step.
