How many times around the earth equals 1 billion miles?

You need to remember that the earth is not a perfect sphere, so it depends where you measure it from (at the equator it's about 24,900 miles).

Round that to 25,000 miles.

(1,000,000,000 mi ) / (25,000 mi ) = (1,000,000 / 25 ) = 40,000 times.