The nation's unemployment rate continued to hover around 6 percent in September, a level it has been stuck at nearly all year.

The Labor Department yesterday reported that the official unemployment rate moved up slightly, from 5.9 percent in August to 6 percent last month and that the number of persons with jobs climbed by 287,000.

There was a big decline in the number of persons at work in July, however, and the September level is little changed from June. Last month 94.86 million Americans were at work; in June 94.82 million persons had jobs.

Although the unemployment rate has been stuck at about 6 percent for many months, it is well below the 6.8 percent rate that prevailed a year ago.

Over the last year the administration has had more success than anticipated in putting people back to work, but has had great difficulty in controlling inflation.

Thursday the Labor Department reported that wholesale prices, which foreshadow prices consumers eventually pay at retail, surged 0.9 percent, or at an annual rate of 11.4 percent.

Administration analysts had hoped that a decline in food prices in July and August would continue and help moderate inflation across the economy. But food prices shot up 1.7 percent in September, almost erasing "the July and August declines," according to Janet Norwood, acting commissioner of labor statistics.

While 94.86 million persons had jobs last month, about 6 million were out of work and seeking employment, roughly the same number as in August.

The employment situation for most major groups in the economy was little changed in September, except for teenagers.

The teenage unemployment rate rose from 15.6 percent to 16.6 percent.

The Labor Department said the teenage unemployment rate jumped because "an unusually large number of specially created summer jobs ended" at the same time the school year started.

A survey of employer payrolls, showed virtually no increase in employment between August and September.

The only industry that showed a significant decline in employment according to the payroll survey was state and local governments.

Labor Department analysts said most of the 85,000 jobs lost in state and local governments were in education, a reflection of cutbacks due to declining student enrollments and Proposition 13-like tax reductions.

After remaining around 7 percent for a good part of last year, employment began to climb and joblessness began to fall beginning in October 1977. Unemployment declined nearly a full percentage point by February, when it again levelled off. "Historically in expansions unemployment declines, then hits a plateau for a while and declines again. The fact that unemployment has been stuck around 6-percent for more than six months does not imply that this is as low as the unemployment rate can get," one government analyst said.

Many economists, however, think that it will be hard to get the unemployment rate much below 5.5 percent without a sharp increase in pecial programs aimed at people who are hard to employ.

Officially the Labor Department claims that umemployment can be reduced to about 4.75 percent before creating severe inflationary pressures.

The unemployment rate is the without work but actively seeking a job. The labor force is simply the sum of those with jobs and those seeking them.

The umemployment rate for adult men was 4.1 percent last month. While the unemployment rate for adult women was 6 percent. Black workers had an unemployment rate of 11.2 percent, while 5.3 percent of white workers were unemployed.