troubleshooting Question

900,000th digit of pi

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DanRollinsFlag for United States of America asked on
Math / Science
18 Comments1 Solution916 ViewsLast Modified:
I'm not innumerate, but when the numbers get really large, my eyes glaze over.

Can someone use their common sense and a good calulator's scientifc notation ability to calculate this for me?

     If you had a circle the size of the Known Universe -- say 15,000,000 Light Years
     in diameter -- you could calculate its circumference by using pi.   How accurate
     would you need the value of pi to be to get a correct circumference, within say
     an inch or two?  How about to within a nanometer?  How about to within a
     Compton radius (a distance comparable to the size of an electron).

Coming at it another way:
   If you have a value of pi calculated to 1 million digits, and there was a typo at
   digit number 900,000 so that it was off by 1 in that position, how much
   would that affect your calculation of the circumferance of astronomical-scale
   objects, such as the Visible Universe?

This is just to satisfy my curiousity.  I've stated a sort of interesting proposition here:

And I'm basing my supposition only on gut instinct and a vague memory of something I read *long ago* -- that you need surprizingly few digits of pi to get an accurate measure of circles the size of, say the orbit of Neptune (bonus if you can verify that with some data :-)

-- Dan
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