Final answer:
President Truman authorized the use of atomic bombs against Japan primarily to save American lives by avoiding a costly invasion, and secondarily to justify the Manhattan Project's expense and possibly influence global power dynamics.
Step-by-step explanation:
The reasons President Truman decided to use the atomic bomb against Japan can be accurately summarized as an effort to end the war swiftly while limiting American casualties. Military advisers had predicted that a conventional invasion of Japan might result in up to 1,000,000 American casualties.
Truman, after becoming president and being briefed about the Manhattan Project, realized the atomic bomb could effectively conclude the war without the high cost of an invasion. Despite understanding the ethical issues, his chief priority was to save American lives and to possibly send a geopolitical message to the Soviet Union.
Other factors such as the desire to justify the expense of the Manhattan Project and possibly influence postwar power dynamics were considered secondary motivations. The atomic bombings of Hiroshima and Nagasaki did result in Japan's surrender, thus bringing an end to World War II.