What are the figured bass or roman numeral inversion numbers for ninth chords?

you are just writing the intervals above the bass, so you can just put a 9 when its in root position.

in inversions, you just put whatever it turned into. like if your 3rd was in the bass, the 9 will become a 7, so you could add 7 to the 6 5 you already needed to write for your 7th chord.

in common practice tonal harmony, these will usually be thought of as non-chord tones that need to resolve, so most of the time, you will see them as suspensions that resolve like "9 - 8" or "7-8"