Question

15% tip to 100 cents why does this make a unit less factor?

Answer 1

15% and the corresponding 0.15 is by necessity unit-less; it's just a multiplier.  If you run up a $1 bill and wish to tip 15%, multiply $1 by 0.15, obtaining $0.15.
Then the total due would be $1 plus $0.15, or $1.15.

Note that $0.15
                -------- = 0.15 is unit-less
                   $1