At the doctor's office, there is a scale that measures people's weight. the needle is 20 cm long, and it rotated 100° when frank stepped on it. how far did the needle travel as it rotated

This is asking you how far around that specific portion of the circle did the needle travel. I'm guessing you're in geometry and you're doing circle stuff right now.  This is the arc length. The formula is

which is a combination of the circumference of a circle and its central angle.  Our situation will look like this:

If you leave your answer in terms of pi it would be
or if you multiply it in, then your answer will be 34.9

The following relation is not a function