Last August, Carey Rogers, 73 and blind, was admitted to D.C. General Hospital for temporary care until room became available for her in a nursing home. She has been waiting in the hospital ever since.

Levi Fredrick, 99, went to D.C. General Jan. 21 to be treated for a heart ailment. After the treatment, Frederick hoped he would be able to find room in a nursing home. But almost five months later, he remains in the hospital at a cost of about $200 a day.

Rogers and Frederick are among 300 mostly elderly District of Columbia residents who on any given day occupy beds needlessly in the city's 13 hospitals because no nursing home facilities area available.

A group of doctors who recently completed an analysis of unnecessary hospital care in the District said yesterday that in 1977 there were 40,000 days of unneeded hospital care in the city. The group said that the average unnecessary hospital stay was 70 days, while regular patients were in the hospital only 10 days.

For 26,000 of the days of unnecessary care, hospitals were denied Medicare and Medicaid payments amounting to $5,32 million, according to the National Capital Medical Foundation, which held a news conference to discuss the problems.

The foundation, the city's "professional standards review organization" (PSRO), is one of a national network of medical "watchdog" groups created by federal law to monitor hospital stays in an effort to cut costs.

"What concerns us is that consumers often do not realize that as private paying patients they help to make up the hospital's losses in higher rates for hospital rooms," Dr. Norman Fuller, executive director of Washington's PSRO, said.

"We believe that keeping elderly people in a hospital at a cost of $200 to $250 a day rather than in a nursing home for between $35 and $50 a day is a very expensive and inefficient way of caring for the elderly," Fuller said.

Dr. Barrington Barnes, president of the city's PSRO, said that elderly persons usually have only two ways to get out of the hospital. "They either wait sometimes many months until a nursing home bed become available or they simply die waiting," Barnes said.

George Roby, who recently retired as the city's director of social services, said that the need for more nursing home beds became acute in Washington in 1974 after new federal and city regulations forced many nursing homes out of business because they could not comply with the new standards.

Of the approximately 1,400 nursing home beds in the city, 905 are covered by Medicard and Medicare payments, Barnes said.He said that to alleviate the problem of needless hospital care, the city needs between 500 and 1,000 more nursing home beds covered by government payments.

"One problem is that businessmen don't feel that it would be profitable for them to go into the nursing home business in the D.C.," Fuller said. "They will build an office building or a restaurant, but they don't think they can make a profit with a nursing home."

Last year, the city's medical assistance office increased Medicaid and Medicare payments to cover "reasonable costs" of patient care, which averages $250 a day in hospitals and more than $1,000 a month in some nursing homes.

The obvious solution to the nursing home crisis is construction of more nursing homes. But neither the city government nor private developers have so far been able to determine how construction costs can be recovered through the existing fee structure.

Five years ago, a group of doctors built the J. B. Johnson nursing home, a 200-bed structure near 3rd and K streets NE. Before the facility could open, the builders found it would require more than $1 million to bring the building up to city safety code standards. As a result, the structure remains vacant.

Roby said the city may eventually have to let contracts on nursing home care in order to get private developers to build the needed facilities.

Peter B. Coppola, chief of medical assistance, said the Department of Human Resources may have to construct the nursing homes the city needs.