A Piece Of The Pi

A Piece Of The Pi

Fractional Pi

I just had a thought pop into my head. I have not explored it enough yet to know if it has even the slightest merit so let's explore it together for a bit shall we?

Pi can be expressed as a fraction. I figure one of the most famous is 22/7.

I just saw another mentioned on Slashdot:

""355/113 -- Not the famous irrational number PI, but an incredible simulation!""

So, the thought is to find a fraction that matches pi to the "most" decimal places such that the ratio of the number of digits in the fraction to the number of digits of Pi matched is smallest.

Number of digits in 22/7 is 3.
Number of digits in 355/113 is 6.

3.14159265358979323846 (Pi to 20)
3.14159292 (355/113)
3.142857143 (22/7)
3.14159265358979323846 (Pi to 20)

22/7 matches to 3.14 or 3 digits, ratio is 3:3 or 3/3 = 1.
355/113 matches to 3.141592 or 7 digits, ratio is 6:7 or 6/7 = 0.857142857

Get it?

Is this a known thing?

If not, off the top of your head, how do you think it will behave?

Obviously, no tricks with Pi up top and 1 below...