The Fairfax County Board of Supervisors has approved a pared-down design competition for the proposed Fairfax Center, planned as the county's new governmental headquarters and a possible home for local cultural events.

To save an estimated $225,000, the supervisors rejected an international open competition -- the first choice of the citizens' committee which drew up the master plan for the center -- and instead approved a national invitational competition. The national competition would cost about $342,962, according to the master plan committee, while the international competition would have cost $571,272.

Approval of a design competition is one of several major steps the supervisors have taken to shif the county seat from Fairfax City, where it has been for more than 175 years, to a larger site in the county itself.

The center would be built on a 138-acre county-owned site near Rte. 50 and I-66 just west of Fairfax City. The 50/66 area, which includes about 2,400 acres, is slated to become a major retail-industrial-residential complex even larger than Tysons Corner by the end of the decade.

But the change still must be approved by county voters in a bond referendum, which has not been scheduled by the supervisors but probably will be set for November 1982. The referendum would cover only the costs of the governmental complex, expected to be about $72 million for more than double the space in the county's Massey Building in Fairfax City. Funds for any related cultural facilities are expected to come from private sources, according to the master plan committee.

Monday's vote on the design competition was 7 to 2, with chairman John F. Herrity and supervisor Audrey Moore (D-Annandale) voting against the scaled-down competition.

Herrity, in casting his vote, reiterated his opposition to the entire proposal for a new governmental center.

"Large governmental centers are not the wave of the future," Herrity said. "The trend is toward decentralizing government."

In other action, the supervisors approved the creation of 18 new voting precincts, the abolishment of one and modification of 42 others.

New precincts are Forestville (formerly part of Great Falls), Clearview (formerly part of Herndon No. 1), Shouse (formerly part of Kenmore), Sunrise Valley (formerly part of South Lakes), Vale (formerly part of Thompsons), Sully (formerly part of Chantilly, Leehigh (formerly part of Newgate), West Woodburn (formerly part of Woodburn), Robinson (formerly part of Laurel), Long Branch (formerly part of Oak Hill), Fairview, Terra Centre, Burke, White Oaks and Cherry Run (all formerly part of Burke), Irving (formerly part of West Springfield), Saratoga (formerly part of Valley) and South Woodyard (formerly part of Woodyard).

West Springfield was abolished, and part of it will be in the new Irving percinct and another part in the new Saratoga precinct.

Some of the changes were made in principle and will have to be ratified formally by the supervisors.

Voters will be notified by mail in August of all the changes, including the alterations in the 42 other precincts.

Electoral board secretary Millard C. Rappleyea Sr. said the changes are contigent on final approval of the recent changes in state Senate and House districts, which have been challenged in federal court.

The redrawn precincts will not be affected immediately by the redrawing of supervisor districts, which is expected to take place in the fall. If redrawing of the supervisor districts requires shifts in the boundaries of precincts, those changes will not be made until after the Nov. 3 general election.

The supervisors also scheduled a public hearing for July 13 on a proposal that would require smoke detectors in all existing and new multi-family buildings containing four or more apartments and in hotels, motels, rooming houses and other lodging that can accommodate at least four persons.