A FLOATING HOTEL ON THE GREAT BARRIER REEF is scheduled to be put in place early next month. The Four Seasons Barrier Reef Resort, billed as the world's first such facility, will employ a mooring system similar to that used for supertankers. The 200-room hotel and conference center, built by Sembawang Shipyward in Singapore for Barrier Reef Holdings Limited of Australia, will be positioned 44 miles off Townsville, Australia. WOMEN BUSINESS TRAVELERS will account for half of the traveling population by the year 2000, according to a Purdue University faculty member who follows trends in travel and tourism. Assistant professor Alastair Morrison also notes that the travel industry is making hotels and restaurants more comfortable and secure for women. SEATING FOR SMOKERS on US airlines has shrunk over the last four years from 36 to 33 percent of the seats available in first class and from 30 to 25 percent of the seats in coach class, according to estimates from Airline Passenger Services. SPEEDIER CHECKOUT IS OFFERED by the Hotel Inter-Continental in New York. Guests can punch buttons attached to the television set in their room to check out, if using a credit card, or to read telephone messages. Spectradyne, Inc. builds the device that interfaces with the hotel computer to make these services available.