The Fairfax City Council lowered the city property tax rate by 10 cents last week as the council adopted a $19.7 million budget for the fiscal year beginning July 1.

The tax cut, from $1.40 to $1.30 for each $100 of assessed value, represents a 40-cent drop in the tax rate over the past two years.

The new budget, which represents a 10.1 percent increase over the current budget of $17.9 million, is $46,000 more than city manager George Hubler recommended. The extra funds have been earmarked to hire four additional police officers.

"We added the four officers to the force for street work," said City Council member Carl J. Hemmer. "Fairfax City has an increasing number of businesses which attracts a type of crime that street patrols help to deter."

The cut in the property tax rate ws approved by a 5-1 vote, with council member William Scott dissenting. He argued that the rate should be droped only 5 cents until the council could determine the exact amount of federal aid the city will receive this year.

But the council majority countered that there was still a surplus in the city treasury as well as the promise of $372,000 in unexpected revenues the city will receive this year.

Even with the lower property tax rate, the average homeowner in Fairfax City will pay more taxes this year because of increases in real estate assessments. In 1978, the average home in Fairfax City was assessed at $63,500.In 1979, the same home was assessed at $73,900. Under the new tax rate, the owner of that home will pay $57 more in taxes this year than last.

The council voted to maintain the personal property tax at the current level of $2.99 per $100 of assessed value and approved lower water and sewage rate for residents who use minimal amounts of water during each three-month billing period.

In the past, the water rate was set at $8.20 for the first 9,000 gallons of water used and 88 cents for every 1,000 additional gallons. The new rate will be $4.68 for up to 5,000 gallons of water and 88 cents for every 1,000 additional gallons. City officials report that 7 percent of residents use 9,000 or less gallons of water per quarter.

The new sewage rate will be $11.23 for up to 5,000 gallons of water. Currently, residents are charged a minimum of $19.68 for 9,000 or less gallons.