Serious crime in Fairfax County dropped 9.3 percent in the first half of 1983 compared to the same period last year, continuing a two-year decline in the number of reported crimes in Northern Virginia's largest county, police officials said yesterday.

The decrease follows a trend of declining crime rates reported throughout the metropolitan area and the nation. Alexandria police recorded a 15 percent drop in reported crime in the first six months of 1983, the sharpest decline in five years. Arlington police showed an 8 percent reduction in reported crimes during the same period.

"The public is fed up with crime and is becoming more involved with local police agencies," said Fairfax County Police Chief Carroll D. Buracker. He said growing public awareness about crime prevention and an increase in neighborhood crime watch groups helped reduce the crime rate.

In addition, Buracker said, "Police are taking a more enlightened approach to getting the public involved rather than just saying we need bigger cruisers and more officers and bigger guns."

Reported crimes decreased in Fairfax County in each of seven categories of major crimes except murder, police said. Police reported six murder cases during the first six months of this year compared to three cases last year.

The sharpest decline in reported crime from Jan. 1 to June 30 was rape, according to police statistics. The 34 rapes represent the lowest number of rapes reported in a six-month period since 1975, police said. Reported rapes declined 26 percent this year compared to the first six months of last year, from 46 cases to 34.

Robberies were down 23.6 percent, from 241 cases in 1982 to 184 cases this year. The number of burglaries decreased about 7 percent from 1,882 to 1,743. Larcenies dropped 9.5 percent, from 8,013 to 7,245; motor vehicle thefts were down 6 percent from 605 to 566; and aggravated assaults decreased 4 percent from 164 cases to 157 cases.

Buracker also attributed the decrease to the police department's new career criminal program, which tracks criminals with long felony records, and the department's crime analysis program, which targets areas hard-hit by specific types of crimes.