SOLUTION: what is average of 3^30,3^60 and 3^80

Question 883966: what is average of 3^30,3^60 and 3^80

Answer by SmithWillSuffice(4) (Show Source): You can put this solution on YOUR website!
This is a funky question because those numbers are so vastly different in magnitude. When averaging, if there is one number that is far, far larger than the rest, so that the sum of all the smaller numbers is still way smaller than the one really super big number, then the really super big number will dominate the average.
In fact the larger number does not have to be "super big", it just needs to be super large compared to the others.
For "what is average of 3^30,3^60 and 3^80" the 3^80 will dominate. So we'd guess the average would be about .
But let's calculate the average anyway to see for sure:
Average =
=
=
=
This is dominated by = .
In floating point this estimate is = . On my calculator the full average is to the same floating point precision = .
So indeed, the large term dominance was the decisive influence, it gives an answer accurate to 9 significant figures (one in a billion).
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