Final answer:
President Harry Truman authorized the use of the atomic bomb on Japan to force a surrender and avoid the high casualties of a conventional invasion, following the completion of the Manhattan Project.
Step-by-step explanation:
U.S. President Harry Truman decided to use the atomic bomb on Japan during World War II for several reasons. The primary rationale was that Truman believed Japan would not surrender without a devastating blow and that a conventional invasion would result in heavy Allied casualties, possibly numbering in the hundreds of thousands. Furthermore, American military forces had experienced the fierce resistance of the Japanese forces and saw the atomic bomb as a way to avoid the extended and costly campaign that a full-scale invasion would require. After the Manhattan Project was completed, Truman was informed of the bomb's potential and eventually approved its use, leading to the bombings of Hiroshima and Nagasaki in August 1945.