The nation’s unemployment rate dropped sharply to 7.8 percent in September, its lowest level since the month President Obama took office, the Labor Department said Friday.

While employers added only a modest 114,000 jobs last month, the jobless rate declined from 8.1 percent in August. The unemployment rate fell because more people were working, not because discouraged job seekers stopped looking, the numbers showed.

Adding to the positive news, job gains were revised upward by 40,000 for July (to 181,000) and by 46,000 for August (to 142,000), casting a slightly rosier light on what had been perceived as a summer slump.

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