COLUMBUS — Unemployment rates dropped slightly in October for both Dayton and Montgomery County, the Ohio Department of Job and Family Services reported Tuesday.

The Dayton rate dropped for the third straight month, to 10.6 percent, down from 10.7 percent in September, 10.9 percent in August and 11.7 percent in July.

The October 2010 rate for the city also was 11.7 percent.

The county rate dipped for a second consecutive month to 9.6 percent, down from 9.7 percent in both September and August.

The county rate was down from 10.5 percent in October 2010.

The October 2011 rate for the Dayton metro area was 9.2 percent, the same as September but down from 10 percent in October 2010.

The metro area includes Montgomery, Miami, Preble and Greene counties.

Across the state, the October rate dropped in 38 of 88 counties. Rates ranged from a low of 5.4 percent in Geauga County east of Cleveland to a high of 15 percent in Pike County in southern Ohio.

Five counties besides Geauga had jobless rates below 7 percent: Mercer, 5.7 percent; Lake and Medina, 5.9 percent; Holmes, 6.2 percent and Delaware, 6.4 percent.

Three counties besides Pike had rates higher than 12 percent: Meigs, 12.6 percent; Clinton, 12.3 percent and Scioto, 12.2 percent.

Ben Johnson, ODJFS spokesman, said that across the state job growth seen earlier in the year has slowed in the summer and fall.

“While we’re headed in the right direction, we’re headed there slowly,” Johnson said.

Among Dayton area counties, Warren County’s 7.6 percent rate was the lowest and Preble County’s 9.8 percent rate was the highest.

Among area cities, Mason’s 6.1 percent rate was the lowest and Trotwood’s 11.3 percent rate was the highest.

Unemployment rates for cities and counties are not seasonally adjusted. The state not-seasonally-adjusted rate for October was 8.4 percent, down from 8.5 percent in September and 9.2 percent in October 2010.

The state seasonally adjusted rate for October was 9 percent, down from 9.1 percent in September and 9.7 percent in October 2010.