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Roosevelt's strategic reason was to prove to others that the American Navy was powerful and to improve the navy.

Explanation:

Roosevelt didn't want a break with Japan, as the United States was ill-prepared for war. Most of our battle fleet was concentrated in the Atlantic, and there were only a handful of armored cruisers on duty in the Pacific. In the event of war with Japan, this small contingent that made up the Asiatic Battle Fleet would have to abandon the Philippines for West Coast ports until the United States had strength enough to go on the offensive.

Thus, to impress upon Japan that the US Navy could shift from the Atlantic to the Pacific, Roosevelt ordered the Great White Fleet to sail around the world.

The President also wanted to find out what condition the fleet would be in after such a transit. As he stated before the fleet's departure, "I want all failures, blunders and shortcomings to be made apparent in time of peace and not in time of war."

But, more importantly, Roosevelt felt that a successful cruise of this magnitude would provide the American people with an example of US naval prepardness, strength and range. Such an impression, he hoped, would help him get the desired appropriations for four more battleships.