a better rough approximation of pi than 22/7 is 355/113
Though see also https://blog.wolfram.com/2011/06/30/all-rational-approximati... - "All Rational Approximations of Pi Are Useless", in the sense that it's no harder to memorize the decimal expansion with the same level of precision.
22/7 can be "better", or at least easier, for hand calculations, if only 2 digits of precision is needed and one of the other terms in the calculation can cancel out the 7 or the 11 (or 22) in the above ratio.
a better rough approximation of pi than 22/7 is 355/113