U.S. employers added 96,000 jobs last month, a weak figure that could slow the momentum President Barack Obama hoped to gain from his speech Thursday night to the Democratic National Convention.

The unemployment rate fell to 8.1 percent from 8.3 percent in July. But that was only because more people gave up looking for jobs. People who are out of work are counted as unemployed only if they’re looking for a job.

The government also said Friday that 41,000 fewer jobs were created in July and June than first estimated. The economy has added just 139,000 jobs a month since the start of the year, below 2011’s average of 153,000.

Cash-short governments were a key reason the job market was weaker in June and July than first estimated. Federal, state and local governments cut 39,000 jobs in those months — above the earlier estimate of 18,000. In previous recoveries, governments have typically added jobs, not shed them.

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