Los Angeles County’s economy showed modest signs of recovery in March as it added nearly 10,000 jobs and the unemployment rate steadied.

The job growth brought total nonfarm employment to 3,780,500, holding the unemployment rate at 12.4 percent even as more people re-entered the labor force looking for work, according to state Employment Development Department.

The unemployment rate remains well above the 10.9 percent recorded in March 2009.

The state’s unemployment rate increased slightly to 12.6 percent in March from 12.5 percent in February. The nation’s unemployment rate remained steady in March at 9.7 percent.

Eight of the county’s 11 major industries added jobs in March. Hotel and food services added 3,200, followed by local school districts, which added 3,000. Professional and business services, manufacturing, construction and financial activities all recorded small increases.

The closely watched year-over-year payroll jobs figures also showed some signs of improvement. The county lost 111,000, or 2.9 percent, of it jobs since March 2009, but that was lower than the 3.5 drop recorded in the 12-month period ending in February.

Manufacturing posted the largest year-over-year loss of 24,500 jobs, followed by construction and the professional and business services sector, which each lost about 23,000 jobs. Government lost 21,600 jobs.

On the positive side, the local motion picture and television industry gained 28,000 jobs over the past year.

Locally, the unemployment rates in the cities of Los Angeles and Long Beach reached 13.5 percent.