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Eff
Lv 5
Eff asked in Science & MathematicsMathematics · 4 years ago

Is there a base numbering system in which pi has an exact value? How about e?

3 Answers

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  • 4 years ago

    This really depends on what you mean. Pi and e have an exact value in any base system, but no finite representation. Pi and e are irrational, so no finite sequence of rational numbers (which have finite representations in integer bases, sometimes repeating) would equal pi or e (pi and e are also both transcendental, so there is no polynomial with integer to coefficients that has pi or e as a root). Therefore, only in certain transcendental bases does pi have a finite representation, most notably base pi (where pi is 1), but also bases a*pi where a is a rational number.

  • 4 years ago

    No

  • ?
    Lv 7
    4 years ago

    sure, pi in base pi has the exact value 10

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