Unemployment in the District of Columbia fell slightly in August, from 11.8 percent to 11.2 percent, and dipped by four-tenths of 1 percent to 6 percent in the metropolitan area as a whole -- a shift interpreted by some city officials as reflecting a moderate improvement in the economy.

In Maryland, the overall unemployment rate held steady at 8.7 percent during August, although the number of western Marylanders out of work jumped considerably. Montgomery County posted the lowest August unemployment rate in the state, with 4.3 percent, while unemployment fell .2 percent to 6 percent in Prince George's County.

The unemployment rate in Virginia, meanwhile, declined from 7.6 percent in July to 7.3 percent in August. In northern Virginia, the jobless rate fell from 4.6 percent to 4.4 percent.

There were 104,900 unemployed people in the metropolitan area in August, about 6,700 fewer than in July.

Matthew Shannon, acting director of the D.C. Department of Employment Services, said of the city's August figures: "We are pleased to see the moderate improvements and hope that this will signal a trend."

Shannon cautioned, however, that the District's unemployment picture hinges on the general health of the nation's economy and the impact of a new emergency jobs bill signed by President Reagan.

The unemployed ranks in the District shrank by 2,600 between July and August to a total of 37,200 persons, according to city figures. Yet the total number of D.C. residents holding jobs also decreased slightly during that period -- from 297,800 to 296,900, but still 12,000 more jobs than existed a year ago.

Officials attributed the latest decline in the D.C. workforce to high school and college students returning to school from summer jobs or training programs.

Total employment throughout the metropolitan area declined as well -- from 1,637,400 jobs in July to 1,631,500 in August, a decrease of 5,900.

And while the number of jobs available in the area declined by 4,200 between July and August, preliminary estimates show modest gains in wholesale and retail sales, real estate, finance and insurance.

Carolyn Jones, head of the D.C. Office of Job Service, said unemployment has been particularly severe among women.

"Women make up 55 percent of the District population and we have a disproportionate share of female-headed households," Jones said. "The agency will undertake new initiatives this fiscal year to support training and hiring of this group."