Python3, 7
Runs in the interactive shell
355/113 Output: 3.1415929203539825, correct to 6 decimal places
And finally I have a solution that beats APL!
Oh, and in case you are wondering, this ratio is called the 密率 (literally "precise ratio"), and is proposed by the Chinese mathematician Zu Chongzhi (429-500 AD). A related wikipedia article can be found here. Zu also gave the ratio 22/7 as the "rough ratio", and he is known to be the first mathematician to propose that 3.1415926 <= pi <=3.1415927