Every transient hotel shall keep posted in a conspicuous place in the office a list of its charges for rooms, with or without meals, in accordance with the plan on which the hotel is operated, giving the exact transient rate, and shall also keep posted in each room the rate for that room, with or without meals, in accordance with its plan as stated above, giving the transient rate per day and week and the rate for each person in the room, as well as such rates for the fractional part of a day. No hotel shall charge a higher rate for a fractional part of a day than for a whole day. As used in this section the term "hotel" shall have the meaning stated in § 45-5-10.