first actual use of the bomb was against Hiroshima onAugust 6, a mere three weeks later.  There was not much debate in the US government about whether or not the bomb would be used against Japan.

Over the previous two years, the US had been invading Japanese held territory island by island, and, under the Code of Bushido, Japanese soldiers refused to surrender.  This led to bloody, long battles with US forces, and Truman felt the Japanese army and population would fight even harder on the Japanese home islands.  So some say he decided to drop the bomb to save American lives, which would have been lost in the invasion, and Japanese lives as well.

There is a school of thought that also suggests Truman wanted to scare the Soviet Union.  The Cold War was more or less already underway by this time, and Truman had hinted at the existence of an atomic bomb program when he met with Stalin at Potsdam in 1945.  So some argue he dropped the bomb in order to discourage the Soviets from taking more territory after the war. All it did was lead to an arms race where the USSR developed its own bomb program within four years.

Hiroshima was bombed on August 6, 1945 and Nagasaki was bombed on August 9th. These are the only two atomic attacks that have occurred in history.

By dropping the atomic bomb on Hiroshima and Nagasaki we showed the whole world how technologically advanced we were. We had capabilities that other nations did not have. After we dropped these bombs, World War II ended very quickly. On August 16th, Japan surrended to the allied powers.

The atomic bombings led Japan to adopt the "Three Non-Nuclear Principles." Although it was never adopted into law it stated that Japan will never have nuclear weapons in their country. They came to this conclusion because of the devastation they seen caused by the bombs droped in their country at the end of WWII.

The bomb was actually dropped mainly to demonstrate to the Soviet Union that we had it.  Truman believed very strongly that he had to do something to show Stalin who was boss and this was one way they thought they could do it.  The idea of ending the war was one that was emphasized after the fact to justfiy the horror they'd created .  The casualty estimates for an invasion of the home islands was raised dramatically in the five to ten years after the bombs were dropped, and even people high up in the government in the US and elsewhere knew that the Japanese were in the process of suing for peace but it would take several more weeks.  The invasion of Japan was unlikely at the very outside but again was emphasized after the fact, particularly once we found out that the Russians had already gotten most of the technology and would have a bomb within a few years.

Of course the above posters also have good answers and this should show the fact that history is all about interpretation, opinion, and speculation and not simply a matter of facts and figures as we often think it is.

The dropping of the atomic bombs was motivated for a variety of reasons.  One reason that was most evident was to end the conflict with the Japanese.  The belief was that there was a need to stop the death of U.S. soldiers engaged in battle with the Japanese and the dropping of the bomb was seen as a way to end the conflict, and the death of military personnel, in a quick manner.  A more subterranean reason could be considered when evaluating the relationship between the United States and the Soviet Union.  With the defeat of Hitler, the shared enemy of both nations gone, the distrust between them began to emerge.  Some in the United States believed that the display of the atomic capacity would scare the Soviets into immediate submission, giving the United States singular superpower status.

Some other possibilities, as the length of time between the successful testing of the bomb and our actually dropping it was a mere three weeks, and the decision-making process to do so is a little muddled historically.

First, the Manhattan Project was designing a bomb to be dropped on Germany as soon as we developed it.  However, we were not able to test one until July 16, 1945, and Germany surrendered on May 7th.  The decision to focus on Japan then was a quick one, and with a new President, Harry Truman.

Hiroshima and Nagasaki were not terribly important militarily, but they were two of the only cities not yet bombed, and still mostly intact.  We wanted to see the full effect of the atomic bomb on an undamaged city.  This lends strength to the argument the bomb was dropped to scare the Soviets as well as to convince Japan to surrender.

Another reason, and I think the most compelling, was out of hatred and revenge. Revenge for the Bataan Death March, for Pearl Harbor, for how our prisoners were treated, for the Kamikaze attacks, etc.  There was simply no way our government or military were capable of deciding anything other than using the weapon once we had it.

The US dropped the atomic bombs on Hiroshima and Nagasaki in order to end the war more quickly and without so much bloodshed. The fighting, as the US got closer to Japan was so bloody that it made American planners believe that something like one million American troops would be killed or wounded in an invasion of Japan.

Some historians believe that US policy makers also decided to drop the bombs so as to end the war before the USSR could take part of Japan and hold on to it the way they took part of Korea and made it into what is now North Korea.