"Jag bor på sjätte våningen."
Translation:I live on the sixth floor.
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We use both systems and you can never be sure until you've seen what a specific building looks like. The elevator can show either B for street level and 1 for the next level, or B (or 1) for street level and 2 for the next. People of course refer to the floor the same way the elevator in that specific building does.
As per devalanteriel in https://forum.duolingo.com/comment/31695047: Ordinals such as tredje do not normally take the definite article in Swedish. It's more of a stylistic choice, so you may encounter it in e.g. lyrics, poetry, or for dramatic emphasis etc. Depending on the phrase, it may be grammatical, so I just mostly don't want to state a rule which is not always a rule. I do suggest sticking to it as sort of a rule, though. :)