Final answer:
The Louisiana Purchase is considered the greatest achievement of Thomas Jefferson's presidency, significantly expanding the United States and enhancing its agricultural capabilities.
Step-by-step explanation:
The greatest single achievement of Thomas Jefferson's presidency was the Louisiana Purchase. In 1803, this landmark acquisition doubled the size of the United States and fulfilled Jefferson's vision of an agrarian republic. It indeed represented one of the most significant real estate transactions in American history, enabling the U.S. to become a major player in agricultural commerce.
Jefferson's presidency was also marked by the successful evasion of major European conflicts, despite challenges such as the Barbary Pirates, and his administration's promotion of limited government and fiscal austerity. His 1804 reelection victory was a landslide largely attributed to his success in expanding the nation through the Louisiana Purchase, despite some constitutional ambiguities and regional concerns regarding the implications for slavery.
Finally, the Revolution of 1800 was another defining moment of Jefferson's legacy, marking the first peaceful transfer of power between political parties in American history, and reinforcing the nation's commitment to a process of political transition free from violence.