I often change pictures from jpg to gif and vice versa and never seem to lose any colour quality. I do it using Microsoft Paint. Give it a try. Of course, if you create a new gif file you will still have your jpg saved also.
Try experimenting. Copy the file then try renaming it, but don't forget to put .gif .jpg .tif etc.at the end of the name or the PC may not open it. I understand that every time you open a jpg file it can lose a little of its quality, something to do with a 'lossie' format but I'm not expert enough to explain it.