The unemployment rate shot up from 9.5 to 9.8 percent last month as 360,000 more Americans found themselves out of work, the Labor Department said yesterday.

There were 10.8 million unemployed people, making the jobless rate the highest in 41 years, since late 1941, when the nation was still shaking off the Great Depression.

The one positive note was that the number of jobs in the economy, which declined 1.1 million over the past year, was unchanged from the month before; the number of Americans at work stayed about the same, at 99.7 million. But the number of people looking for work increased. That was what drove up the unemployment rate.

Robert Ortner, chief economist for the Commerce Department, emphasized that the job total had not fallen, and said the July report was therefore "not as bad as it appears," though he acknowledged that the economy was still not expanding enough to absorb new entrants into the labor force, as it must for the rate to stay steady or decline.

Other economists, however, say the jobless rate may continue to go up somewhat in the months just ahead, and Democrats were quick to cite the new figures as further evidence that Reaganomics is not working.

Jerry Jasinowski, chief economist for the National Association of Manufacturers, said that the July figures showed "the recession has reached bottom," in that the number of jobs has stopped declining.

But he also said that the unemployment rate would probably keep moving up for a few months, would eventually pass 10 percent and probably stay above 9 percent for the "foreseeable future" because the economic recovery will be slow.

A less patient Lane Kirkland, president of the AFL-CIO, said the July rate could be translated into a line of jobless men and women 4,000 miles long, stretching from coast to coast and from Canada to Mexico.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said the increase in unemployment "reinforces the need for immediate action in creating jobs."

He called on President Reagan to support the emergency employment bill pending in the House that sponsors say would put 200,000 people to work on projects such as bridge and road construction.

The report showed that nation's manufacturing sector, which has been on the ropes for several years, continued to lay off workers in July. About 90,000 manufacturing workers lost their jobs in the month, nearly half of them in the machinery industry. The decline in manufacturing employment was offset by increases in service industries.

Ortner noted that the number of people filing their first claims for unemployment compensation in July fell to the lowest level in five months, an indication that layoffs are slowing.

The unemployment rate is the percentage of persons without jobs in the civilian labor force, which is made up of those with jobs and those actively seeking them.

The unemployment rate is based on a monthly survey of about 60,000 households and is adjusted to account for seasonal variations in the economy.

Another July study, based on a monthly survey of nonfarm payrolls, showed that employment remained steady at 89.8 million jobs.

According to the payroll survey, considered more reliable but less inclusive than the household survey, the number of nonfarm jobs has declined by 1.6 million during the last year.

Janet Norwood, commissioner of labor statistics, said that while factory jobs declined in July, the number of hours in the factory workweek increased slightly.

Since April, she testified before the congressional Joint Economic Committee, the average factory workweek has risen 0.3 hours, while the number of factory jobs has declined by 300,000.

The Labor Department reported that the unemployment rate for whites was 8.7 percent in July, compared with 8.4 percent in June.

For blacks it stayed at 18.5 percent, while the unemployment rate for Hispanics rose to 13.9 percent from 13.5 percent.

Teen-age unemployment rose to 24.1 percent from 22.3 percent, while black teen-age unemployment fell to 49.7 percent from 52.6 percent.