The Prince George's County Council approved a fiscal 1984 budget of $550.9 million yesterday that is based on what some council members called a "fragile" foundation of revenues. Those revenues could come in part from such sources as an increase in a tax on business equipment and a new lottery game.

The budget calls for a property tax rate of $2.54 per $100 of valuation, a decrease of 9 cents from this year's rate. The tax rate has declined in all but one year since 1978, when the voters approved TRIM, the property tax limiting measure. Some homeowners may still pay higher tax bills if their assessments increase, however.

The 1984 budget represents an increase of just over 4 percent over this year's budget, but--uniquely in the metropolitan area this year--offers no cost-of-living increases to any of the county's 3,900 employes. Most departments will be funded at or near their levels for the current year, although a few agencies, such as those in charge of police, firefighting, education and programs for the elderly, will receive some increases.

A spokesman for County Executive Parris Glendening, who left on a privately sponsored trip to Europe yesterday, said Glendening would sign the budget, which largely reflects the priorities he set down in his own budget message in March.

In prepared statements read as they cast their votes on the budget, council members said they were pleased that the county was able to avoid the layoffs of 400 employes predicted earlier this year, when the county faced a deficit of $30 million.

Although all the revenue-raising measures the county proposed in the Maryland General Assembly ultimately failed this session, state legislators instead approved a bill establishing a new lottery game that could raise up to $11 million for the county.

Council members also gave preliminary approval earlier this month to their own version of a bill defeated by the assembly that would raise up to $10.5 million by allowing the county to increase its tax on business equipment.

"Even though we're averting layoffs," said William Amonett, "we're doing it with . . . very fragile revenue estimates. We are averting layoffs but we still have some 300 vacant positions that we aren't able to fill. That will affect services."

In the newly approved budget the Board of Education will receive $312.1 million, about $6 million more than the current year but $4 million less than the agency requested. The County Council, along with Glendening, recommended that the board use some of the money to rehire 97 of the 507 teachers fired in the wake of budget difficulties last spring.

The council also approved allocations of $38.5 million for the police department, and $16 million for the fire department.

Council members, who also formally approved budgets for two bicounty agencies yesterday, passed the county budget unanimously CAPTION: Chart, PRINCE GEORGE'S BUDGET HIGHLIGHTS Here are some of the key items in the fiscal 1984 budget adopted yesterday by the Prince George's County Council: Property Taxes--The county tax rate will drop 9 cents from $2.63 to $2.54 per $100 of assessed valuation but property taxes may rise because of increased home assessments. A revised tax on business equipment will increase from $2.63 to $3.57 per $100 of assessed valuation, pending any legal challenges. Expenditures--The general fund for fiscal 1984 will total $550.9 million--$22.6 million more than proposed by County Executive Parris Glendening. The estimated budget last year was $524.7 million but will wind up at about $533.4 million. Revenues--The county expects $7.1 million in "new money" from Lotto, $10.5 million from the increased personal property tax on business equipment, $1.2 million from a rise in transfer and recordation taxes and $3.4 million from a county hospital system lease. Schools--Spending will rise from $306.3 million to $312.1 million. The additional funds will be used to rehire 97 laid-off teachers and prevent the possible layoff of 193 teachers and other school personnel. Transportation--The Department of Public Works and Transportation, which received $14.5 million last year, will get $16.1 million in fiscal 1984--with much of the additional money going to new equipment. Police & Fire--The police department will get $38.5 million, compared with $37.8 million last year. The fire department will get $16 million, up from $15.4 million last year. Volunteer firemen will receive $4.4 million, up from $3.9 million last year.