When the temperature of a coin is raised by 79 °f, the coin's diameter increases by 1.90 * 10-5 m. if the original diameter is 1.55 * 10-2 m, find the coefficient of linear expansion?

You should use next formula:

L=L0 (1+αt) ⇒ α = (L-L0-1) / t

but check numbers, because according to this what you wrote in your question, the coin has 1000 times less diameter after the temperature increase.