In mathematics there are approximations to pi such as:
$\pi\approx\dfrac{355}{113}$
that have extraordinary accuracy and are useful ways of remembering or being able to calculate a value close to pi that may be used in calculations.
I noticed the the ratio of the diameter of the moon to the earth seems unreasonably close to $\frac{3}{11}$.
Is my observation correct?
And are there other useful ways of remembering approximate metrics of various heavenly bodies with surprising economy?