The demand for workers that had been running white-hot for much of the past year is now starting to cool off, offering the latest sign that the labor market is moving back toward normal.

Job openings fell in October to 10.3 million, new Labor Department data showed on Wednesday, bringing them back to roughly the level where they stood in August. That marks a significant drop both from the peak in March, when job openings reached nearly 11.9 million, and from September, when available positions had unexpectedly jumped to 10.7 million.