(The NewYork Times) -- “I’ve just returned from a trip overseas where we concluded nearly $350 billion of military and economic development for the United States, creating hundreds of thousands of jobs. It was a very, very successful trip, believe me,” he said Thursday afternoon.

White House officials have also promoted this accomplishment. Lt. Gen. H.R. McMaster, the national security adviser, and Gary D. Cohn, the head of the National Economic Council, wrote Tuesday in The Wall Street Journal that Mr. Trump’s deal-making in Saudi Arabia “will strengthen regional and American security and create American jobs.”

“The visit also included historic economic development deals for the United States, totaling well over half a trillion dollars and the creation of tens of thousands of American jobs,” Sean Spicer, the White House press secretary, said Tuesday.

Mr. Trump himself gave an even more ambitious version of this claim during his trip: “We made and saved billions of dollars and millions of jobs.”

But these assertions of an enormous positive impact on employment rely on fuzzy math and inflated hopes.

The arms deal with Saudi Arabia

The deals include arms sales to Saudi Arabia and more 30 commercial deals with American companies. The White House did not respond to requests for a breakdown, but tallying up publicly announced deals, Mr. Trump’s figures are inflated and premature.

First, the arms sale deal is not final. The $110 billion figure refers to the value of defense capabilities offered to Saudi Arabia, characterized by the State Department and the Defense Security Cooperation Agency as “intended sales.” It remains to be seen how much Saudi Arabia will actually purchase.

The package also includes six sales, totaling just under $24 billion, that were previously offered to the Saudis by the Obama administration. Itemized estimates of intended sales (which include missile defense systems and other military equipment potentially worth billions) are not publicly disclosed, so it’s unclear what the other $86 billion refers to.

“I just don’t see how they get to $110 billion,” said William D. Hartung, the director of the Arms and Security Project at the Center for International Policy, a Washington-based think tank. He estimates that “half of that or less is real and sometime even that falls through.”

That’s because the deals will have to go through a formal arms sales process before they can proceed, said Emma Ashford of the Cato Institute, a libertarian think tank. “I’m extremely skeptical of these White House claims.”

If the past is any indication of the ultimate result, chances are the deal will amount to a fraction of $110 billion. President Barack Obama offered the Saudis more than $115 billion in weapons while he was in office, $57 billion of which became formal sales agreements, according Mr. Hartung’s research.

In a news briefing Tuesday, Mr. Spicer said the commercial deals total $270 billion, but it’s unclear how he gets to this figure. Companies named by him and in the media have publicly announced intended investments totaling just under $120 billion; some have yet to report specific dollar estimates.

Mr. Spicer appears to also be double counting some of these defense contractors involved in the arms deals as part of the $270 billion pool. He listed Lockheed Martin and Raytheon as commercial deals, but the Black Hawk helicopters and defense systems they will provide are also listed under the arms sales.

More important, the vast majority of these announcements were memorandums of understanding or letters of intent — not finalized, formal business contracts.

The number of jobs these deals will create

Mr. Trump’s emphatic declaration of “hundreds of thousands of jobs” is, at this point, tenuous at best given the nature of the various deals and their values. And most new jobs announced by the companies will be in Saudi Arabia, not the United States.

Of the companies listed by Mr. Spicer, Dow Chemical, General Electric and Alcoa have said they will create hundreds to thousands of jobs in the kingdom. But none of their news releases mention jobs in the United States.

Others like Raytheon and Boeing did not give exact estimates. ExxonMobil’s deal, which the company says will create 600 permanent jobs and 6,000 temporary construction jobs in Texas, predated Mr. Trump’s trip by almost a year. Spokesmen for all three companies stipulated that these deals were in the early stages or that it was difficult to be precise about estimates.

Lockheed Martin has said it will sustain 18,000 jobs in the United States, most of which will be existing jobs and is contingent on the deal being finalized, a spokesman for the company said.

Commercial deals aside, the intended arms sales will make more of an impact on the jobs market in the United States than the commercial deals, but it’s too early for anyone to estimate confidently that it will amount to “hundreds of thousands.”

For one, Saudi Arabia has a policy that 50 percent of its military purchases will be local, meaning that defense contractors that are part of the arms sales will face additional pressure to locate jobs in the kingdom.

Job gains resulting from giant arms sales in the past have often fallen short of expectations. In South Africa, a multibillion-dollar sale in the 1990s was projected to generate 65,000 jobs, but ultimately created 28,000. The British government similarly estimated that a 2005 sale of Typhoon aircraft to Saudi Arabia would create 10,000 to 15,000 British jobs, while an independent analysis from York University pinned the number at 5,000.

“The deal will undoubtedly create some American jobs, but there are too many unanswered questions to know how many, and it seems doubtful that it’s as high as the White House is suggesting,” Ms. Ashford said.