What fraction is closest to 0.0787?
787/10000. Not only is it closest, it is exactly the same.
Fractions are infinitely dense and this means that between any two fractions there an infinite number of fractions. If any fraction, f, laid claims to being the nearest, there would be infinitely many fractions between 0 and f and so infinitely many fractions which were closer to 0. This means that f could not be the closest. The argument can be used again and again and so there cannot be a fraction closest to 0.
The scale of an inch on the map represents two miles on the surface of the Earth would be CLOSEST to which representative fraction?
22/7 I think is the closest fraction you will get. By definition it is irrational, and cannot be written as fraction of integer numbers. There are a few fractions that are close approximates though. Pi cannot be technically written as a fraction. However, a fraction that is a close approximation of pi is 22/7.