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Wow, @RZ923, that's awesome! You are absolutely right. This is the closest next rational fraction that people can get.
We can also get a similar approximation using the following: \(\frac{04348}{33215}=3.141592654,\) \(\frac{208341} {66317}=3.141592653,\) or \(\frac{312689}{99532}=3.141592654.\)
Nevertheless, the number \(\frac{355}{113}\) is still very interesting. To read more about it, click here