Fairfax County voters narrowly approved a $39.7 million bond issue yesterday to finance construction of seven new schools in rapidly developing areas of the county and renovation of nine others.

The final count was 20,321 votes for the bonds and 17,295 against; the bonds were supported by about 54 percent of those who voted.

It was the county's second approval of school bonds in a referendum in less than a year. Last June, county voters approved sale of $19.7 in bonds for new school construction.

"What can I say? We're tremendously pleased," said School Board Chairman Rodney Page. "It shows once again that the growth areas are the primary support for bond referendums. The heavy yes votes were in these areas, and most of the no votes, although not all, were in the older areas of the county."

The turnout was light - only 15 percent of the county's 241,000 registered voters went to the polls.

A citizens committee was formed to publicize the need for the bond issue and seek its approval at yesterday's referendum.

The only vocal opposition to the bond issue came from the Fairfax County Taxpayers' Alliance, which maintained that government borrowing through bonds contributes to inflation.

Although school board members hotly debated whether a $39.7 million bond sale would be too large for voters to accept, the board finally decided on the large amount in an effort to break away from a pattern of holding school bond referendums every year.

The board promised that if this bond issue was approved at referendum, there would be no more bond referendums for two years.

Of the $39.7 million total that voters approved. $29.6 million will go for building Mumford park, Great Falls No 2 and Herndon/North Reston elementary schools and South Lakes Intermediate School in the northern part of the county to serve the Reston, Herndon and Great Falls areas. Rolling Valley West and Burke Center elementaries and Chantilly Intermediate School will be built in the Pohick area of Springfield.

Designed to relieve overcrowding at existing schools, these will be filled to capacity upon their opening in the 1979-80 school years school officials said.

Another $9.8 million will pay for renovating nine schools throughout the country. Improvements will include repairs to ceilings, roofs, heating, plumbing and lighting. Also, facilities for the handicapped will be added as required by federal law.

A yet unidentified elementary school will be converted into the North County Educational Center for the Emotionally Disturbed with $293,000 of the proceeds of the bond sale.