I did this a couple of years ago. As an engineer, I deal with tolerance. Not the racial, ethnic,or gender kind but parts tolerance. Meaning how far off can the value of a part be from what I designed and still have the thing work? This is something an engineer has to do for every design.
A news story that got my attention was that some legislative body had decreed that the mathematical constant Pi would, hence forth, have the value of 3.000.
How nice of them.
But as an engineer, I wondered how far off your results would be if you used 3.000 for Pi. And since it was easy to do in a spread sheet, why not see how each significant digit changed that error?
From a commercially available spread sheet program, whose manufacturer will not be named, I used the Pi() function (cell contents are “=Pi()”) which gave me an approximation of Pi to 15 significant digits as a reference value. The column “How Close?” is simply the estimated value divided by the reference value. The “Error” is the difference between How Close and unity.
The Table:
Table of Approximations to Pi and the resulting error.
The results are interesting. Using just 3.000 means that you are within 5 five percent from the actual value. Often this is well within what is considered “engineering accuracy”. Better yet, adding only two significant digits to the approximation of Pi gets your error to down to the range of hundreths of percent. But as you go further the adding of each significant digit improves your estimate only slightly.
Were the legislatures right? That might depend on if you are buying something or selling something.
As for me, I will do my own calculations thank you very kindly.
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