Assuming there are exactly 365 days per year, how many rotations about its axis does the earth make in one year?
As the Earth revolves around the Sun it has to turn slightly more than a complete rotation each day to account for the extra angular distance that it has traveled. Over the course of a year, this will add up to an extra sidereal day over the number of solar days.
Half jokey/ half serious answer:
Exactly one rotation. Assuming the axis in question is the one through the gravitational center of the Earth/Sun system. One rotation around that axis is the definition of a year.
Something like .000000004 rotations around the Milky Way galactic center.
Mama never told me not to play with axes