Fun fact, 22/7 is only accurate to one part in 2,500, or 0.04%, netting you one extra digit (i.e 3.14 is less accurate with 3 digits but 3.142 is more).
Most remember 3.14159 which is way better than 22/7, but pi has an even better unusual rational approximation, 355/113 gets you two extra digits, it is accurate to one part in 12 million, or 0.000008% . So you have to go to 3.1415927 to beat it.
That's not saying much as it appears to just be double precision, but yeah, rational approximations only save you one or two digits and after a certain point it’s more nerdy to just memorize pi.
Most remember 3.14159 which is way better than 22/7, but pi has an even better unusual rational approximation, 355/113 gets you two extra digits, it is accurate to one part in 12 million, or 0.000008% . So you have to go to 3.1415927 to beat it.