The tire will rotate about 10 million times.
An automobile tire is slightly less than 2 and half feet in diameter. It's circumference is that times pi with is a bit over 3. So 2.5 * 3 = 7.5 ft as an estimate for how far the tire rolls per revolution.
A mile is a bit over 5000 feet, so call it 700 revolutions per mile.
For the 35000 miles, call it 7 times 5000 miles. Now 7 times 7 is a bit under 50, so call 7 * 700 = 5000. And 5000 times 5000 = 25000000. The nearest order of magnitude is 10 million.
So as an order of magnitude estimate, a automobile tire will rotate about 10 million times during it's life.
