Can a jpeg file be converted into a pdf? If so, what software would be required?
Really just about any Photoshop-like program can do it. Open the jpeg and do a SAVE AS pdf.
Another way is to open the JPEG in your internet browser and to print it as a PDF.
Without an operating system and program listing, these are the most general directions I can give.
You can, but the result will still be only the quality of the JPEG. (I know some people who think converting to a PDF will magically enhance things.) If at all possible, you are better off recreating the PDF from scratch.
You can often recover something from the JPEG with OCR software, so you have something a bit better than an image file to stick into the PDF. OCR software is rarely perfect, however, so you’ll likely want to go back and fix things up by hand; how you do that precisely is software-dependent.
(Of course, this assumes the JPEG has images of text in it to begin with; if it doesn’t, though, why would you want it in PDF form?)
All newer MSFT programs have a “print to PDF” option. If you’re on a MAC, just use "PREVIEW, and save as PDF. Do a “save as” and you have lots of format options to choose from, including PDF.
Or a Mac, if you like to use computers that actually exist. 
The easiest way, for most people, is to load or copy and paste the jpeg into their word processing program. Modern word processing programs generally have a way of then saving the file as a PDF. The exact command will vary according to your word processor.
However, just about any program that can display a jpeg and print it can be used to create a PDF with the help of a PDF writer program, of which several are available for free on line. I use CutePDF Writer. This installs under Windows as if it were a printer driver, so then you “print” the jpeg (or any other file) from the program that is displaying it, but, instead of selecting your real printer in the print dialog box you select CutePDF, which then, instead of actually printing anything, creates a PDF file. (Probably there is similar freeware available for Macs.)
Derleth seems to think you have a JPEG image of some text, and want to recover editable text from it. I am not sure how he gets that from your OP, but if that is correct the issues are rather different (and do, indeed, involve OCR - or CR anyway). I do know of one way it can be done for free, but it is fairly complex to explain (although not really difficult to do), so I won’t bother unless you confirm this is what you actually want.
On a Mac the ability to “Print” to PDF from any app (including Preview, the default image viewer) is built into the OS.
Yep, that’s the way I do it. Open a new document, insert the pic, fiddle with the size and layout if I want something other than the default, then export it as a pdf when I’m done.
I happen to use open office on a linux machine, but as you said, it works on a lot of different word processors these days.
PDF is usually thought of as a vector format that can be displayed at any resolution and which does not need external font resources. However, it can also contain raster images such as JPEGs. Lots of ways are listed upthread, but you’re basically wrapping a JPEG in a PDF wrapper. It won’t make it into a vector graphic.
I often have to convert from jpg to pdf for work. I use PDF24 Creator. Very easy to use and free. Also works for other file formats to convert to pdf as well.
My Canon Scanner software can do this. Really handy if you have to scan a document and email it, without it becoming a 20MB file.