Los Angeles County unemployment inched down a tenth of a point to 9.7 percent in October as the local economy added 48,000 nonfarm jobs since September, according to state figures released Friday.

Government added the most jobs of any economic sector, with a gain of 20,000, followed by business and professional services with 8,000 jobs. Manufacturing was the only sector to lose jobs, shedding 1,800, according to the state Employment Development Department data.

In the greater Valley region, the Antelope Valley had cities with the highest unemployment. Lancaster came in at 13.4 percent, followed by Palmdale at 11.8 percent. Elsewhere, Glendale had 8.2 percent, Burbank had 7.6, and Santa Clarita was at 5.8 percent for the month.

The largest city in the region, Los Angeles, reported unemployment of 10.5 percent.

Overall, the data show the county’s employment picture is improving, said Robert Kleinhenz, chief economist at Los Angeles Economic Development Corp. The county’s 9.7 percent rate in October was significantly lower than the 10.5 percent rate of a year earlier.

“It’s good to see the L.A. County labor market showing gains,” he said on a conference call with media. “It’s good to see those jobs come back.”

Brandi Britton, Los Angeles regional director for Robert Half International, a Menlo Park staffing firm, said there are other signs of confidence in the L.A. job market.

“We’re seeing a lot of people comfortable jumping ship to look for better jobs,” she said. “The companies they leave are now filling the positions, where before they might have left them vacant. So this is creating turnover and it’s definitely a sign of more confidence in the employment market.”

The state agency released numbers for both September and October on Friday due to delays in job reporting stemming from the government shutdown.

The California seasonally adjusted unemployment rate was 8.7 percent in October, the same as the previous month, while the national unemployment rate in October was 7.3 percent, down a tenth of a point.