If a/b rounded to the nearest trillionth is 0.008012018027, where a and b are positive integers, what is the smallest possible value a+b?

0.008012018027=16/1997

16 + 1,997 =2,013

Could you explain how you arrived at this solution???

CPhill: I have programmed my computer (in Java) to convert decimals to fractions and vise versa, up to about 50 digits long. It does it instantaneously.

16/1997 is the 5th convergent in it's continued fraction expansion.