WASHINGTON (AP) — The number of job postings in the United States rebounded in October from a 3 1/2 year low in September, a sign that businesses are still seeking workers even though hiring has cooled.

Openings rose 5 percent to 7.7 million from 7.4 million in September, the Labor Department said Tuesday. The increase suggests that job gains could pick up in the coming months. Still, the latest figure is down significantly from 8.7 million job postings a year ago.

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Last month, job openings rose sharply in professional and business services, a category that includes engineers, managers, and accountants, as well as in the restaurant and hotel and information technology industries.

The number of people quitting their jobs rose in October, a sign of confidence in the job market. And layoffs tumbled to just 1.6 million — below the lowest figures in the two decades that preceded the 2020 pandemic.

Taken as a whole, Tuesday’s figures suggest that the job market might be stabilizing at a modest level, with hiring moderate but layoffs uncommonly low. The unemployment rate is at a low 4.1 percent, even though job gains slowed sharply in October, according to the monthly jobs report. The slowdown in job growth last month reflected mainly the impact of hurricanes and a strike at Boeing.

“There’s a lot of cause for optimism,” said Cory Stahle, an economist at Indeed, the job listings website. “The fact that job openings ticked up is always an encouraging sign.”

Tuesday’s figures mean there are now 1.1 available jobs for each unemployed worker, a healthy figure. Before the pandemic there were usually more unemployed people than openings.

Still, the latest ratio is down from a peak of roughly two job openings per unemployed person two years ago. Businesses have pulled back from the hiring frenzy that occurred as the economy emerged from the pandemic recession.

Tuesday’s report, known as the Job Openings and Labor Turnover Survey, or JOLTS, showed that overall hiring slowed in October. Total hiring slipped to 5.3 million from 5.6 million, though that decline reflected hurricane-related disruptions.

The JOLTS report is separate from the monthly jobs figures, which will be released Friday. That report is forecast to show a net gain of nearly 210,000 jobs in November, up from an anemic 12,000 in October.

Tuesday’s report also showed that the number of Americans who quit their jobs rebounded in October to 3.4 million, after having reached a four-year low in September. An increase in quitting is a good sign for the economy, because it suggests that people are confident enough to search for new job opportunities.

The Federal Reserve is watching the jobs data closely. Any sign that hiring is sharply weakening could encourage Fed officials to cut their key interest rate more quickly, to try to bolster borrowing and spending and support the economy.