God didn't get Pi wrong. Rather, He rounded to the nearest cubit.
"Also he made the cast metal sea, ten cubits from brim to brim, circular in form, and its height was five cubits and its circumference thirty cubits."
-2 Chronicles 4:2
If we were to write down the whole value of Pi, or in this case, Pi times 10, we would never finish writing. Therefore, whenever anyone, Creator of the universe or not, writes down the value of Pi for us to read, it is always rounded.
When I was in school, we generally used 3.14 as our estimation, rounding to the nearest hundredth. Some folks go to greater degrees of accuracy if they feel the need. The Biblical author either decided to round Pi to the nearest whole number, making their estimation of Pi equal to 3, or else the author decided to round the circumference to the nearest 5 or 10 cubits, or else the author decided to round the diameter to the nearest cubit. It's also possible that the author did all of the above. Rounding is perfectly legitimate, and here we have an excellent example of proper rounding in action.
It is often forgotten that the Bible is intended to be literature, rather than a mathematically exacting analysis of philosophical or scientific concepts. It is written for average people and presents information in a way that is coherent for them, rather than being written in such a way that only Ph.D.s can comprehend.
The Bible is wholly accurate, but this accuracy must be understood within the context of literature, narrative and poetry, and in the context of the minds of ancient men, rather than placed in the context of a mathematical equation or that of modern culture.
No one would want to read a historical narrative, like the book of Chronicles, if it suddenly stops in the middle to list Pi out to the 500,000th place. It simply would not be appropriate. Further, there would be no need for it. Why would any author do that?
Ancient men writing a historical narrative rounded to the nearest cubit, just as we would expect them to. Modern mathematicians, engineers, scientists, architects and designers writing out Pi for equations will round to, I dunno, maybe 5 or 10 places to the right of the decimal. But they still round.
It is never "wrong" to round, as long as the context provides for it.
Interestingly enough, the fact that Pi exists, the fact that the circumference of a circle can be measured, and the fact that we can comprehend these things all require the existence of the Christian God.
This God who necessarily exists informs us very clearly that our sins condemn us (Rom 3:23), but that He has offered us forgiveness through His Son, Jesus (Rom 6:23). In order to receive this forgiveness, we must accept Jesus as our Savior (Rom 10:9-10).