1st. Most elevators when you push '1' take you to the ground floor regardless whether the building has any sub-levels. Sometimes elevators replace the 1 with a G instead just to help some people with the confusion like if it does indeed have sub-levels.
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0th floor would imply that it is 0 floors away from the ground, and 1st would imply that it is 1 floor away.
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I get what you're saying. But the 1st floor is also the "first" floor to cover the ground since it sits right on top of it.
As for room numbering, most buildings that have "rooms" either residences or hotel rooms rarely have any on the first floor/ground floor. Most times the ground floor is reserved for lobby, elevator space and retail uses or some other type of use, conference/meeting space and maintenance. In that case most room numbers would begin on the 2nd floor. This isn't always the case, but with most hotels and residential buildings it seems to be. In that case it would be rare to have any residences with a numbers "100-199". Other types of buildings may have rooms on the first floor where it's not as crucial to have privacy. Cheaper hotels and even some hospitals do this oddly enough.