Financial troubles will force the Jewish Community Center in Rockville to close its doors for the last nine days of August, usually a low point in activities.

The forced vacation from Aug. 23 to Sept. 1 is one of a number of belt-tightening steps directors of the center are taking to meet what they termed "a shortfall in anticipated funding" for the 1982-83 fiscal year.

A spokesman for the center attributed the financial crunch to inflation and a decline in members.In addition, said Neva Alperin, the allocation from the United Jewish Appeal Federation, which accounts for nearly 18 percent of the center's $3.25 million budget, failed to keep pace with inflation.

The spacious center on Montrose Road provides educational, cultural, religious, recreational and social services seven days a week for the Washington area Jewish community. Currently there are 6,295 members on its rolls, but many activities at the center are open on a fee basis to nonmembers as well.

Activities in the center's branches in the District of Columbia and Northern Virginia will not be affected by the August closing of the Rockville facility, but the budget shortfall will postpone some of the planned program expansion for the D.C. branch.

None of the 113 full- and part-time staff members is expected to be dismissed in the center's cost-cutting efforts, but they will be asked to take over some of the functions once performed by specialized workers, such as teachers and lifeguards, Alperin said. In addition, a four-year plan to increase staff salaries will be delayed.

One-quarter of the center's income comes from members' annual dues, which are being raised from $230 per family to $250, and from $170 to $185 for individuals. Alperin said the center will launch a vigorous membership campaign in the fall. She said the 11 percent membership loss over the past two years was both a reflection of the economy and the fact that "we've gotten a little bit lazy" about recruiting new members.

Beginning in September, various departments of the center will start seeking their own funding, in addition to the overall fund-raising efforts of the center.