WASHINGTON (MarketWatch) — A lot of people — some of them very smart — are saying something false about today’s jobs report: That the unemployment rate fell only because lots of part-time jobs were created.

I’ve heard it on Bloomberg News, I’ve heard it from John Silvia, chief economist for Wells Fargo. I’ve heard it from Rob Shapiro, who was an economic adviser to Bill Clinton. And I’ve heard it from many readers of this site. Not to mention that fountain of misinformation, Zero Hedge.

That’s just not so.

According to the Bureau of Labor Statistics, the number of people with full-time jobs increased by 838,000 in September to 115.2 million, while the number of people with part-time jobs declined by 26,000 to 27.7 million.

In other words: All of the gains in employment were due to full-time jobs.

It’s right there in Table A-9.

How did all of those people get it wrong? By looking at separate table (Table A-8) that shows a big spike in the number of people who want a full-time job but who are forced to settle for less than 35 hours of work because of the tepid economy or weak demand at their company.

The BLS explains that the number of people involuntarily working part-time rose, even though the total number of part-timers declined. It’s the total number of part-timers that helps determine the unemployment rate. Read our full coverage of the decline in the unemployment rate to 7.8%.

The rise in involuntary part-time work is surely a sign that the economy remains weak. It’s deplorable that 8.6 million Americans are underemployed.

But their plight does not take away from the strong growth in full-time work. Read our commentary on the jobs report Obama was waiting for.

Will falling jobless rate help Obama?

The idea that most of our new jobs are undesirable part-time jobs is a pervasive myth on the Community Boards and other sites around the Internet.

That was certainly true at the height of the recession, when many people found their hours reduced sharply. By the middle of 2009, the number of part-timers had increased by 2.8 million at the same time that full-time positions fell by 8.9 million.

But since the recovery began in earnest, most of the job growth has been in full-time positions, as the chart above shows.

Compared with a year ago, 2.7 million more Americans are working full time, while the ranks of part-time workers have increased by just 91,000.

— Rex Nutting