This anecdote is described in greater detail in "The Pope of Physics", by Gino Segrè & Bettina Hoerlin (Enrico Fermi's biography told by a nephew of a close col

This anecdote is described in greater detail in "The Pope of Physics", by Gino Segrè & Bettina Hoerlin (Enrico Fermi's biography told by a nephew of a close collaborator of the famous physicist). This fascinating episode is told in the first chapter, if I rember correctly. He also poses the "how many piano tuners are in Chicago" problem, using a similar approximation technique. Great read, totally recommended!