Upgrading from 3 to 10 is a major jump with several file format changes among other things. Chances are that you will have issues to resolve after conversion. Whether these are simple things to fix or complex depends on the complexity of your database design.
I suggest reading this knowledge base article to start: Click Here
Then download the free trial copy of fmp 10 and try using it to convert a copy of your database. You'll have 30 days to evaluate whether this works fairly smoothly for you or whether you will need to make extensive modifications to the converted database in order to complete the conversion process.
If all else fails, you can export the data from your FMP 3 files into text files and then import them into completely new fmp 10 files.