Dear Annie: I got laid off from my accounting job in mid-2009 and, since comparable staff positions were scarce back then, I signed on with a temp agency and started doing short-term contract work with a variety of companies in several different industries. I’ve really enjoyed meeting new coworkers every few months, and I believe I’ve not only kept my skills sharp, but also learned quite a lot along the way.

Now that hiring is looking stronger, I’d like to look for a “permanent” job (if anything is permanent anymore), but I’m concerned that interviewers will look askance at six years of temping, including working in 14 different places over that time. Can you advise? — Numbers Guy

Dear Numbers Guy: You’ve got plenty of company. U.S. staffing companies hire more than 14 million temporary and contract employees every year. The industry, among the first to start creating jobs when the recession officially ended, grew by 57% between 2009 and 2014.

Nor does that growth seem to be slowing. Temp employment in the first quarter of this year rose by 5.7% (seasonally adjusted), according to the Bureau of Labor Statistics. About 40% of employers expect to take on temporary or contract workers in 2015, says a CareerBuilder study. While they add more regular full-time staff, “employers are also looking for ways to quickly adapt to market dynamics,” notes Eric Gilpin, president of CareerBuilder’s staffing and recruiting division.

Still, “permanent employment is a top priority for most staffing employees,” says a report from the American Staffing Association, and it’s clearly possible to make that leap. About one in three (35%) contract workers in a recent ASA survey have been offered a job by a client where they had worked on an assignment.

A recently published poll from staffing firm OfficeTeam showed that slightly more than half of hiring managers (51%) see “a long period of consistent temporary assignments” as “comparable to full-time employment.” So your question is really how to win over an interviewer who belongs to the other half.

First, let’s talk about your resume. You mention 14 different assignments in the past six years and, while it’s never a good idea to list that many jobs, it would be an especially big mistake in this instance.

“Your employer the whole time was really the staffing agency,” says Robert Hosking, OfficeTeam’s executive director. “So list that firm on your resume as your employer from 2009 to present.” Then use bullet points, without dates, to describe the work you did on, say, half a dozen projects that are relevant to the job you’re applying for.

It’s almost always smart to write a different resume and cover letter for each job opening you pursue, but it’s especially important to do so now. “Tailor your description of your experience to the position,” says Hosking. “If you’re applying for a job at an insurance company, for instance, only go into detail about the assignments you did in that industry,” including goals you achieved and new skills you may have picked up that are specific to insurance-company accounting.

One unspoken reservation some interviewers may harbor is why you apparently haven’t been among the temps who have been offered a permanent job by any of the companies where you worked. (That’s not necessarily true, by the way: The ASA survey says that, among the 35% of contract workers who received offers, 66% accepted them. The rest said “no, thanks.”)

The best way to address that concern: Give the hiring manager contact information for three or four solid references from among the former peers and bosses you’re sure are fans. Don’t forget to fill them in beforehand on your current hunt for a permanent job. If any of these folks can honestly mention a reason why you weren’t asked to stay on — a hiring freeze, for example, or a restructuring that merged similar functions and cut headcount — then so much the better.

Especially if you sense some skepticism from an interviewer, Hosking recommends turning your having worked in so many places into a plus. “Employers are looking for people who can get up to speed quickly and start contributing right away,” he notes. “So emphasize that working in so many different environments, with new people each time, has made you more adaptable and flexible.”

Go in prepared with a couple of examples, which Hosking says should be easy. “If you’ve worked on five similar projects at five different companies, you’ve learned five new systems in a short period of time,” he points out. After six years, you may take that for granted, but it’s “an ability that any employer would value.” Good luck.

Talkback: Have you ever gone from contract work to a permanent full-time job? What helped you make the move? Leave a comment below.

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