Serious crime in Fairfax County rose a fraction of 1 percent in the first nine months of this year compared to 1983, appearing to end three years of steady decline in local crime, county police reported yesterday.

The slight overall increase of three tenths of 1 percent for the seven serious crimes was caused primarily by a 28 percent jump in robberies, 321 compared to 251 in the same nine-month period last year, police reported, and an increase of under 3 percent in the number of larcenies and auto thefts.

However, the number of rapes dropped almost 25 percent, from 61 in the first nine months of 1983 to 46 through September of this year. Aggravated assaults dropped 3 percent and burglaries dropped 8 percent. There were 12 murders in the first nine months, compared to 10 the previous year.

County Police Chief Col. Carroll D. Buracker called the overall percentage increase "so small that when the population growth of 10,000 persons in the last year is considered we are not only holding our own against crime but actually are continuing to make headway."

The county figures, fed into FBI computers, actually show a six tenths of 1 percent decrease in Fairfax crime per 100,000 people for the first nine months of the year, a police spokesman said yesterday.

The rise in robberies, larcenies and car thefts appear to be a natural reflection of the county's growth, especially commercial growth, Buracker said. Police yesterday did not have a breakdown of the robberies.

The chief said he was pleased about the drop in rapes and the continued drop in burglaries, which he attributed to the county's expanding Neighborhood Watch program. Burglaries dropped 8 percent, from 2,590 in 1983 to 2,378 for the January-to-September period.

Larcenies, the most common crime and to many people the least serious, often are the major statistical factor in the seven-crime "index" used by police. The 11,538 larcenies in the nine-month period, up 181 from 1983, represent 75 percent of the crimes listed in the total index of 15,482 crimes. The index was 48 more than last year's, giving the reported three tenths of 1 percent increase in crime.

The police report noted aggravated assaults dropped from 264 in the first nine months of last year, compared to 256 this year. Motor vehicle thefts rose from 901 to 931.