The war with Japan ended when the United States

The Japanese's navy and airforce were destroyed--The Allied forces bombed their cities and left the country and economy devastated. The final straw was when America captured Okinawa, where the Allies would be able to launch a invasion and take the main islands.

They dropped a dropped an atomic bomb on the Japanese city of Hiroshima.

They formally surrendered on the USS Missouri, August 14, 1945

the U. S. dropped two atomic bombs one on Hiroshima and one on Nagasaki.

Explanation:

The surrender of Imperial Japan was announced by Japanese Emperor Hirohito on August 15 and formally signed on September 2, 1945, bringing the hostilities of World War II to a close. On August 6, 1945, at 8:15 AM local time, the United States detonated an atomic bomb over the Japanese city of Hiroshima. Sixteen hours later, American President Harry S. Truman called again for Japan's surrender, warning them to "expect a rain of ruin from the air, the like of which has never been seen on this earth." Late in the evening of August 8, 1945, in accordance with the Yalta agreements, but in violation of the Soviet-Japanese Neutrality Pact, the Soviet Union declared war on Japan, and soon after midnight on August 9, 1945, the Soviet Union invaded the Imperial Japanese puppet state of Manchukuo. Hours later, the United States dropped a second atomic bomb, this time on the Japanese city of Nagasaki.