One fine fall day, Fred, the famous football player, decided to do a little math activity with his favorite sport. So he put his ball down on one of the goal lines of the 100-yard field. He then moved it forward half the distance — that is, 50 yards — toward the other goal line. Next he moved it half the remaining distance, 25 more yards.
He planned to continue in this manner as long as he could, always advancing the ball half the remaining distance toward the other end. Of course, it should be obvious that sooner or later his moves will be quite small, so small in fact that we could say he was truly “inching along”.
The question now is: on which move of the ball did the distance for the first time become less than one inch?
Bonus: what was the total distance that Fred had moved the ball after that move? Give your answer rounded to the nearest 100th of an inch.
When you get this problem’s two answers, please e-mail me. Be sure to explain “how” you arrived at your conclusions.