What fraction is closest to 0.0032677165354331?

There are no "closest" fraction because rational numbers are infinitely dense. If for example, you thought that f1 was the closest fraction, then f2 = 0.5*(f1 + 0.0032677165354331) would be closer. And then f3 = 0.5*(f2 + 0.0032677165354331) would be closer still, and so on.