Roger has exactly one of each of the first $22$ states' new U.S. quarters. The quarters were released in the same order that the states joined the union. The graph below shows the number of states that joined the union in each decade. What fraction of Roger's $22$ coins represents states that joined the union during the decade $1780$ through $1789$? Express your answer as a common fraction. (Note: Every space represents $2$ states.)