Fairfax County, the Washington area's growth center during most of the 1970s, is now larger than either the "District or Montgomery County and is closing fast on Prince George's County, the Census Bureau's preliminary 1980 population count shows.

With the release yesterday of Fairfax County's figures, it became apparent that the region underwent a dramatic population change in the last decade. Overall, the area's population has remained remarkably stable during the 1970s, with population losses in the older core areas being offset by increases in the new, outer suburbs.

Fairfax County disclosed its 1980 population count was 585,177, a whopping 29 percent increase over its 1970 count of 454,275.

If present trends continue, Fairfax could be the most populous jurisdiction in the region within three years. Prince George's is currently the most populous, but the new census figures show that the suburban Maryland county is losing population, but not as fast as the District.

Fairfax was the only major close-in jurisdiction to show a big population increase during the 1970s. Montgomery gained 8 percent, but there were losses in both Prince George's (3.4 percent) and the District (25 percent).

The new figures mean that if the Washington area's population is to grow beyond the 2.9 million people it had in 1970, all of the increases will have to come in counties in what the government defines as Washington's standard metropolitan statistical area. As previously reported, the fastest growth in the fringe of the area, such as Loudoun County which had a 55 percent increase in population in the past decade.

While population remained stable, there was a 21 percent increase in housing units (from 916,510 to 1.2 million), reflecting the nationwide trend toward smaller families, more single-parent and unmarried households and the phenomenom called "empty nests" -- homes occupied by parents whose children have grown and left.

Fairfax, though, is running somewhat against that trend, primarily because it has a bigger population of younger families than most of the rest of metropolitan Washington. For example, Fairfax's average household size is 2.84 persons, compared to 2.59 persons in Montgomery and 2.72 persons in Prince George's.

Even so, Fairfax also is becoming the home of an increasing number of single-person and single-parent households, as well as empty nests. The size of the average 1970 household was 3.5 persons.

While some jurisdictions -- especially the District -- were stunned to discover they were much smaller than they thought they were, the Census Bureau's preliminary 1980 figures on Fairfax surprised few county officials.

A household survey by county demographers in January put the population at 600,300, about 15,000 more than the new federal count. But Fairfax demographer David W. Sheatsley said the difference will probably shrink to only 10,000 when the preliminary census figures are refined into a final count.

Sheatsley said the figures mean Fairfax has won most of its argument with the state of Virginia and its Taylor Murphy Institute, which has been estimating a lower population for the county. The state, for example, said in 1979 that Fairfax's 1980 population would be 571,200 -- 14,000 less than the new federal figure.

According to Sheatsley, the fast-growning Reston and Burke areas in the western and southern parts of the county accounted for 53 percent of the population increase since 1970.

The area around Burke Centre, south of Fairfax City has a population of 16,477. Ten years ago, the then-rural area had only 765 people. Reston's population jumped from 11,250 to 34,065 over the decade.

Older areas of the county south of Alexandria and inside the Capital Beltway were population losers. Fort Belvoir, a large Army base, also shrank from 5,521 people to 1,272.

When new employment figures are released, it is likely that Metropolitan Washington will be redefined officially to include some outlying areas -- for example, Frederick and Howard counties in Maryland and Stafford in Virginia -- which have been getting an increasing share of suburban growth.

The new Census Bureau figures have been closely watched by local jurisdictions not only because the numbers tell interesting demographic stories. What is possibly more important is the impact the numbers will have on local budgets. Each person is estimated to be worth $200 in various grants of state and federal aid.