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Between which two values did Archimedes show that pi lies?

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Portrait of Archimedes by Giuseppe Nogari shows an elderly man with white hair and beard, holding a compass, gazing downward, set against a dark background. — Archimedes Archimedes, oil on canvas by Giuseppe Nogari, 18th century; in the Pushkin Fine Arts Museum, Moscow. Archimedes was an ancient Greek mathematician and inventor.

In his treatise Measurement of the Circle, the Greek mathematician Archimedes demonstrated that the value of pi lies between the following two values:

Lower bound: $3 \frac{10}{71}$
Upper bound: $3 \frac{1}{7}$

Archimedes established these bounds by calculating the perimeters of inscribed and circumscribed regular polygons with 96 sides, utilizing the method of exhaustion to refine his approximation.12