Specifically, he determined that pi was less than 3 1/7 but greater than 3 10/71. In the decimal notation we use today, this translates to 3.1429 to 3.1408. That's pretty close to the known value ...

Archimedes determined the upper and lower range of pi by finding the perimeters of ... Values are shown in decimal notation rather than the fractions that Archimedes used.