All Rational Approximations of Pi Are Useless -- http://blog.wolfram.com/2011/06/30/all-rational-approximation...

355/113 is a bit better than others. They speak about relative efficiency, while absolute size is also important sometimes. · 9000

I have solved the Pi memorization problem with the help of my cell phone provider. My phone number starts with 6 digits that come after 3.1415 so I know Pi with much more precision that any reasonable rational approximation can yield. · ati