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Geoff,
A wonderful gift and talking piece. I think everyone has a fascination with pi.
22/7 is accurate to 3 digits. A rather less known but better approximation for pi is 355/113 (accurate to 7 digits). The fraction has the odd sequence starting from bottom 113 then 355 (two 1s, two 3s, two 5s).
Today, pi has been calculated to over one trillion digits.
11 decimal places is sufficient to calculate the length of the Earth's Equator to the nearest mm and 29 decimal places would give the circumference of the observable Universe to the nearest mm.
Regards, Rob
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