On August 15th, 1945, Japan announced that it was surrendering. They signed the official surrender on September 2nd, 1945.

I was in my early 'teens at the time, and my parents, my sisters, and I were taking a trip from Seattle to Vancouver, B.C. on August 15th. We heard the news on the car radio, and when we pulled into downtown Vancouver, people were literally dancing in the streets!   

Using the A-bomb undoubtedly shortened the war by several months, with hundreds of thousands of lives saved, both Japanese and American.

AND—actually using the A-bomb made people think pretty cautiously about using it in future conflicts. A nuclear World War III, especially with ICBMs and H-bombs would have been short, would have resulted in the deaths of many millions, and would quite probably have left us with the kind of bleak world that has often been depicted in science fiction movies….

Don Firth