That the economy added just 96,000 jobs in August will be hotly debated by both sides in the remaining weeks of the presidential campaign, but one thing is almost certain: The number is wrong.

Only once in the past three decades has the government not revised its estimate of how many jobs were created in a given month. It usually takes many weeks, and sometimes years, before economists settle on the most accurate figure.

That’s not to say that the The Number is a mere mirage. Even as a rough cut, it’s a pretty persuasive gauge of the economy’s health and a crucial input into the prognosis of what lies ahead.

But in recent years, the jobs figure has taken on almost iconic status. Especially since the financial crisis rocked the U.S. economy, politicians and traders — and the general public — have come to anxiously await the monthly announcement of The Number. It has been treated with the respect due scientific truth and deference accorded to religious writ. And as the presidential campaign has entered its final season, the power of the jobs number has only grown despite its questionable pedigree.

Over the past three years, the monthly employment report has understated how many jobs were created by as much as 99,000 and overstated it by as much as 86,000.

At precisely this time last year, Obama learned the lesson the hard way. It was Thursday, Sept. 1, and the president’s senior economic team had just heard the details of the August jobs report. The jobs number, made available to a few government officials ahead of the public release the next morning, was a scary one.

Gene Sperling, the director of the National Economic Council, and Katharine G. Abraham, a member of the Council of Economic Advisers, headed to the Oval Office. There, they told Obama how many jobs were created in August: zero.

The next day, Obama was called “President Zero” by his critics. It was a painful coda to a difficult summer when the nation flirted with a default on the government’s debt. Sperling and other advisers used the news to successfully make the case for boosting the president’s jobs plan — to be unveiled in Congress just a few days later — by $75 billion.

But the number was wrong. After the government revised its data three more times, it concluded that 84,000 jobs were created in August 2011.

That wasn’t a great number by any means. The economy needs at least 120,000 jobs per month just to keep up with population growth. But it also meant that much of the political fallout in the following days was based on the wrong number.

Friday’s report of 96,000 jobs added in August will be used the same way, fairly or not, to judge Obama’s record. In October, when the first revision of the August number is made available, a jobs report for September will be announced, and that will move to the center of the political debate.

“The initial number is important, but the data the initial number is based on are incomplete, so the number will be revised as soon as next month, and will be revised with much more complete information after the election,” Tara M. Sinclair, an economics professor at George Washington University, said in an e-mail.

The number of jobs created is not the only measure of employment. The unemployment rate fell from 8.3 percent to 8.1 percent in August, the government said Friday, but this, too, can be misleading.

The unemployment rate measures what percentage of people in the labor force lack jobs. But in August, the number of people in the labor force — that is, people working or looking for work — declined by 368,000. It was the departure of discouraged job-seekers that caused the jobless rate to fall.

“Obviously, we’re hoping for much higher numbers [of workers] at some point to bring the unemployment rate down,” Sinclair said.

The Bureau of Labor Statistics, a unit of the Labor Department that compiles the employment data, comes up with the jobs estimate based on a survey of thousands of businesses and government employers. As responses to the survey come in, the bureau updates its estimates.

The bureau acknowledges that the initial jobs figure has a wide margin of error: 100,000 jobs. (That means that 90 percent of the time, the true figure lies somewhere between 100,000 more than the initial figure and 100,000 less than the initial figure. Ten percent of the time, the actual number is off by even more.)

In practice, government economists have tended to revise initial jobs data over the past three years by about 40,000 jobs.

Often, the initial report has played to Obama’s political disadvantage. Early in his term, in the depths of the recession, the bureau tended to understate how many jobs were being lost each month. So when the jobs numbers were being reported, it didn’t seem as if Obama had inherited such a bad situation — even though it felt that way to many Americans because so many people were, in fact, losing their jobs.

In February 2009, weeks after Obama took office, for example, the bureau reported that 539,000 jobs had been lost the previous month. Later revisions showed that 692,000 jobs actually had been lost.

As the economy has recovered, the data have tended to low-ball growth in the labor market. In the first three months of this year, the government reported that 243,000, 227,000 and 120,000 jobs were created, respectively. Later revisions put the numbers at 275,000, 259,000, and 143,000 — a cumulative difference of 87,000 more jobs.

But most recently, the numbers have overshot. Revisions for June and July suggest that 50,000 fewer jobs than earlier estimated were created.

Revisions to employment data are not new, but they appear to be growing smaller, perhaps due to improved statistical methods.