OLYMPIA — Washington state’s unemployment rate dropped to 7.8 percent last month, the first time it’s been below 8 percent in nearly four years. The state’s Employment Security Department said today that the fall from October’s 8.2 percent rate was the largest one-month decline in more than three decades. “This is good news for Washington state workers and families,” Gov. Chris Gregoire said in a written statement. “We are clearly heading in the right direction as we slowly emerge from the Great Recession but we cannot rest until every Washingtonian who wants a job has one.” The state saw a net gain of 1,600 jobs in November. Industries that had the most job gains included retail trade, construction, leisure and hospitality, and transportation. Losses were seen in professional and business services, financial activities, wholesale trade and government. Within the government sector, state agencies were down 900 jobs and public higher education saw a decline of 1,000 jobs. But 600 jobs were added in public K-12 schools and local and federal government agencies also saw a combined increase of 500 jobs. “Job growth appeared to slow in November, but the trend of the last three months is very positive,” Joe Elling, chief labor economist for Employment Security, said in a written statement. An estimated 270,000 people in Washington were unemployed and looking for work last month, including nearly 136,000 who claimed unemployment benefits in November. More than 5,300 unemployed workers ran out of unemployment benefits last month. A total of 121,273 people have exhausted their benefits since extended benefits were activated in July 2008. Washington’s jobless rate is still higher than the national rate, which was 7.7 percent last month.