Property tax bills sent to Alexandria homeowners later this month will reflect the first rise in the tax rate in more than 10 years, a step taken by the City Council Monday night to finance the new $147 million operating budget for fiscal 1984.

Even with the new rate of $1.41 per $100 assessed value, the average homeowners tax bill will not increase this year as much as in past years because assessments have stagnated amid the downturn of the area's property markets.

Under the new rates, which will be retroactive to Jan. 1, the owner of a typical house assessed at $100,000 will pay $1,410 in taxes this calendar year. That is about 4 percent higher than the 1982 bill. In past years, bills have increased about 8 percent per year.

The council passed the new budget, an 8 percent rise over approved spending for this year, after a late-night session in which members added money for day care, legal services and job placement for ex-convicts and voted to reduce city contributions to firefighter and police pension plans by $500,000.

City officials generally characterized the budget as a "hold the line" spending plan, blaming most of the rise on inflation and other uncontrollable factors. "We're not cutting any services," said Councilman Donald Casey. "We're not making any major expansions." The council also approved a 3 percent raise for city workers.

The budget also provides full funding for the Alexandria school board's $50 million request, though $400,000 was cut with the board's approval because of savings in the school bus program and in personnel costs.

The school budget is a 3 percent increase over this year's spending. School superintendent Robert W. Peebles praised the council for granting the full request and said the budget would not force any belt-tightening that will affect students and classrooms.

The council also added $375,000 to the capital budget for fiscal 1984, which begins July 1, to increase the capacity of the Seminary Road/Beauregard Street intersection and $300,000 for improvements near the unopened King Street Metro station such as crosswalks and placing utility wires underground.

The 1984 capital budget, which also was given final approval, totals almost $19 million. That is 50 percent higher than this year's, an increase due largely to major new capital projects such as the city's new jail and police complex, the renovation of City Hall, bridge work and improvement of the Metro station area.

The council rejected a $96 per household trash collection fee that City Manager Douglas Harman had proposed, opting instead to raise the current $1.37 property tax rate four cents instead of the two cents Harman recommended.

Despite objections from the Chamber of Commerce and restaurateurs, the council voted to raise the meal tax from 1 percent to 3 percent and the hotel tax from 4 percent to 5 percent. The increases are designed to shift some of the tax burden away from property owners and are expected to generate $2 million per year.

The tax rate on personal property such as automobiles and boats was lowered from $5.20 per $100 assessed value to $5.10.

Council members rejected repeated requests to cut spending from council member Carlyle Ring, the only council member to vote against adoption of the budget.

Ring asked that 29 police and firefighter management jobs be eliminated through attrition and transfers. While rejecting the proposal, the council instructed Harman to report back in the fall on personnel issues. The $500,000 reduction in contributions for the police and firefighter pension plans followed a council study of the plans. It concluded that disability retirement provisions were being abused. Police and firefighters oppose the findings and have said they may challenge the cuts in court.