The unemployment rate rose by 0.3 percentage point last month to 7 1/2 percent of the nation's work force as a rising number of adults lost their jobs, the Bureau of Labor Statistics reported yesterday.

Joblessness among white workers jumped nearly half a percentage point between August and September to 6 1/2 percent, a sign that the economic slowdown is becoming more widespread. BLS Commissioner Janet Norwood said "the September labor market indicators show continued weakness in the demand for workers."

Total employment dropped by 675,000 in September to 98.3 million, and the labor force shrank as the number of "discouraged workers" -- who have stopped looking for work -- grew to 1.1 million in the third quarter. There were nearly 8 million people out of work in the month. President Reagan has promised that his economic program will lead to 13 million new jobs, but most private forecasters expect the economy to grow more slowly and so create fewer jobs than the administration is predicting.

The bond market, which has fallen significantly in recent months on fears of a large federal deficit, rose yesterday on the news of the jobless figures. If the economy slows, then the private sector's demand for credit will fall, relieving pressures in financial markets, where tight money has been conflicting with big credit demands from both the public and private sectors.

Evidence of just such economic weakness also came in the latest weekly figures for the nation's money supply. The Federal Reserve reported yesterday that M1-B, the measure of money that includes currency in circulation and checking accounts at financial institutions, fell by $1.9 billion to a seasonally adjusted level of $433.6 billion for the week ended Sept. 23.

The Federal Reserve recently has been trying to boost M1-B growth, which is below its target range, by allowing short-term interest rates to decline. But in a weak economy, the drop in interest rates has not been translated into greater money growth.

Black unemployment climbed to 15.1 percent during the month, up only slightly from the 15.0 percent level in August, but still considerably higher than white joblessness. Norwood commented that "black joblessness has failed to show any improvement over the past year." However the big jump in black and other minority teenage unemployment to 45.7 percent in August was partially reversed last month when the level dropped to 37 1/2 percent after seasonal adjustment.

Those coming onto the unemployment rolls last month either had lost their jobs permanently or had been laid off, perhaps temporarily. There was virtually no increase in unemployment among those who had left their jobs voluntarily or those who were newly entering or reentering the work force, Norwood said.

Adult women suffered the biggest decline in jobs last month. Unemployment among white adult women rose from 5.4 percent to 5.7 percent; and among black women, from 12.8 percent to 13.7 percent. The department said that large numbers of women left the labor force, contributing to a shrinkage of 370,000 during the month. The jobless rate for white adult men went from 5.1 percent in August to 5.3 percent last month.

The rate for all adult men was 6.2 percent in Septermber, up by 0.6 percent from two months earlier but, Norwood said, "still less than the rates which had prevailed at the height of the 1980 recession."

Economists generally have been surprised that unemployment has not risen more this year, as most have been predicting recession. Although the economy did begin to drop in the second quarter of the year, businesses appeared to hold on to their workers despite the declines in production. Analysts believe that unemployment will climb as more and more firms are hit by high interest rates.

The administration's last economic forecast, made in July, was that unemployment would average 7.7 percent in the last quarter of this year, but would start falling in 1982. If this proves too optimistic, then the budget estimates will be thrown out by the need for more spending on unemployment benefits and less revenues from personal taxes