Mercury is about 48,000,000 miles (77,300,000 kilometers) from Earth at its closest approach. With an AU being 149,597,870,691 meters, that's about 0.5167 AU. (Note that due to the changing elliptical evolution of both planets, there's a number of ways to answer this question, but this is the best, in my opinion
Mercury orbits the sun. Earth orbits the sun. The distance between them depends on where they are in their orbits. If both are on the same side of the sun, it's about 48 million miles, if on opposite sides, about 140 million miles.