When federal grants to states and localities are cut in Washington, the numbers tend to have an abstract quality. But at the local level, these federal cuts translate into more comprehensible numbers -- and into reductions of services for individuals nationwide.

This is how the $600 million cut in social services grants to the states under Title XX of the Social Security Act from 1981 to 1982 led to reduced services to Richmond's aged, blind and disabled welfare population, according to statistics from federal and local officials.

In fiscal 1981, the national Title XX allocation ceiling was $3 billion, of which Virginia's share was $69.9 million. When Congress cut the 1982 authorization to $2.4 billion at the president's request, Virginia's share dropped to $56.3 million.

As the Urban Institute study of Richmond and other cities pointed out, when federal aid was cut, it was theoretically possible for cities and state governments to raise taxes or find other ways to compensate for federal cuts.

But the cities and states that actually did so were the exceptions, according to the study. Virginia and the city of Richmond did shift funds among programs, but it did not make up for the federal cuts. The late 1970s and early 1980s saw high inflation, taxpayer revolt and then recession. Virginia has alw50 to 400 people receiving services, according to John Twisdale, who administers the programs.

As a result of the cuts, the allocation for the chore and companion program for the city's 1982 fiscal year dropped to $316,392. As a result, officials were forced to cut the rolls sharply -- at one point, to as few as 65 people, Twisdale said.

During the next few years the money in the program barely fluctuated. Today the program totals $371,229 and serves about 150 to 170 people.

For each of the last three years, more than $100,000 of this money came from the federal Community Development Block Grant, a program originally designed for other purposes.

President Reagan's 1987 budget seeks a $500 million reduction in that program, too.