What's 3 reasons truman and the us military had for using nuclear weapons to end ww2?

By August, 1945, Japan had lost World War II.  Japan and the United States both knew it.  How long would it be, however, before Japan surrendered?  Japan was split between surrender or fighting to the end.  They chose to fight.

In mid-July, President Harry S Truman was notified of the successful test of the atomic bomb, what he called “the most terrible bomb in the history of the world.”  Thousands of hours of research and development as well as billions of dollars had contributed to its production.  This was no theoretical research project.  It was created to destroy and kill on a massive scale.  As president, it was Harry Truman’s decision if the weapon would be used with the goal to end the war.  “It is an awful responsibility that has come to us,” the president wrote.

President Truman had four options:  1) continue conventional bombing of Japanese cities; 2) invade Japan; 3) demonstrate the bomb on an unpopulated island; or, 4) drop the bomb on an inhabited Japanese city.

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after defeating german forces in north africa allied leaders turned their attention to "italy," since this was the location that made the most geographic sense before invading northern europe via france.