OLYMPIA, Wash. - Washington state's unemployment rate dropped to 4. 5 percent last month - the lowest rate for August since 1976, according to a report released Wednesday by the Employment Security Department. The report says the state's economy added 9,100 jobs in August as the unemployment rate dropped from 4. 6 percent in July. “The state data continues to demonstrate the positive trends in its economy,” said Paul Turek, economist for the department.