The unemployment rate unexpectedly dipped to 9.7 percent in January, from 10 percent in December, the government reported Friday, buoying hopes that the worst job market in at least a quarter-century is finally improving.

But a different survey in the Labor Department’s report found that the economy lost 20,000 net jobs during the month, muddying the picture and underscoring the formidable struggles still confronting millions of Americans. Yet with the pace of decline slowing, most experts focused on signs that the economy was recovering after the longest recession since the Great Depression.

Manufacturing added 11,000 jobs in January, the first monthly increase since November 2007, while the length of the average workweek rose slightly at factories. The economy added 52,000 temporary workers, and average wages increased modestly, amplifying the view that commercial activity is reawakening after two years of hibernation.

“The economy is continuing to improve,” said John E. Silvia, chief economist at Wells Fargo in Charlotte, N.C. “You don’t have a boom, but you have an economic recovery. It’s a positive sign.”