WASHINGTON (MarketWatch) -- Job openings at U.S. workplaces jumped up to 4.83 million in October, reaching close to the highest level since early 2001, from 4.69 million in September, the U.S. Department of Labor reported Tuesday. Compared with same period in the prior year, October's job openings rose 21%, as private-sector openings increased 23% to 4.42 million, and government positions rose to 413,000 from 393,000. With 9 million unemployed people in October, there were about 1.9 potential job seekers per opening, below September's ratio of two. In October 2013, there were 11.14 million unemployed people -- about 2.8 potential seekers per opening. When the recession began in December 2007, there were about 1.8 potential job seekers per opening. The number of separations, such as quits and layoffs, rose to 4.82 million in October from 4.81 million in September. Meanwhile, the total number of hires declined to 5.06 million from 5.08 million. The level of hires was about 5 million when the recession began.