@CorneliaAdams 9-story is better when describing the building but if you say i live ON the 9th floor of the building then that means you need to walk up the 9 flights of stairs to get to your apartment.
When you are stating how many levels a building has, you usually use stories. "You live in a building with nine stories." If you are talking about a particular level in a building, you usually use floor, not "story". "I live on the ninth floor." If you said, "I live in a 9-floor building." I would assume that it is not an apartment building. If you used "storey" I would assume you are not using native American English.