WASHINGTON — The U.S. unemployment rate dropped below 8 percent for the first time since the month President Barack Obama took office, a surprising lift for both the economy and his re-election hopes in the final weeks of the campaign.

The rate, the most-watched measure of the country’s economic health, tumbled to 7.8 percent in September from 8.1 percent in August. It fell because a government survey of households found that 873,000 more people had jobs, the biggest jump since January 2003.

The government’s other monthly survey, of employers, showed they added a modest 114,000 jobs in September, but it also showed job growth in July and August was stronger than first thought.

Obama, eager to shift attention from a disappointing performance at the first presidential debate, said Friday that the report showed the country “has come too far to turn back now.”

His Republican opponent, Mitt Romney, countered: “This is not what a real recovery looks like.”

The drop brought the jobless rate back to where it was when Obama was sworn in, in January 2009, and snapped a 43-month streak in which unemployment was 8 percent or higher — a run Romney had been emphasizing.

The October jobs report comes out Nov. 2, four days before the election, so Friday’s report provided one of the final snapshots of the economy as undecided voters make up their minds.

The government calculates the unemployment rate by calling 60,000 households and asking whether the adults have jobs, and whether those who don’t are looking for work.

Those who do not have jobs and are looking are counted as unemployed. Those who aren’t looking are not considered part of the work force and aren’t counted as unemployed.

A separate monthly survey seeks information from 140,000 companies and government agencies that together employ about one in three nonfarm workers in the United States.

That survey found that the economy added 114,000 jobs in September, the fewest since June. Most of the job growth came in service businesses such as health care and restaurants.

The Labor Department raised its job-creation figures by a total of 86,000 jobs for July and August. The July figure was revised from 141,000 to 181,000, and the August figure from 96,000 to 142,000.

Taken together, the two surveys suggest the job situation in the United States is better than was thought.

Economist Joel Naroff, president of Naroff Economic Advisors, called the strong employment reports “a shocker” that showed the job market was sturdier than most economists had thought.

Financial markets seemed less impressed. The Dow Jones industrial average climbed as much as 86 points in early trading but drifted lower for most of the rest of the day. It finished up 34 points at 13,610.

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