How to get around an overflow error in Ti-84 plus calculator?

so i'm having a problem where i'm trying to find the answer to this equation

Ŷ = (10^-509.0738)(2020^158.0975)

The problem is that when i plug it into my calculator, it says an overflow error. Is there anyway to get around this or is there an alternative way of solving it?


3 Answers

  • ?
    Lv 7
    9 years ago
    Favorite Answer

    Yeah, the TI-84 Plus can only handle a maximum exponent of 99. Anything over that will get you Err:Overflow.


    y = (10^-509.0738)(2020^158.0975)

    Take the appropriate logs:

    log y = log(10^-509.0738)(2020^158.0975))

    log y = log(10^-509.0738) + log(2020^158.0975)

    log y = -509.0738 + 158.0975log(2020)

    log y = -509.0738 + 522.5677881

    log y = -509.0738 + 522.5677881

    log y = 13.49

    y = 10^13.49

    y ≈ 3.1188 × 10^13

  • 9 years ago

    Yes. Use base 10 logarithms, plus some pencil and paper (or memory registers).

    log Ŷ = -509.0738 + (log 2020)*158.0975

    = 13.493988

    The integer part of your answer is the power of 10 of the answer in scientific notation, and the decimal fraction is the base-10 log of the significant digits.

    Ŷ = 3.118804 x 10^13

    That works because 13.493988 = 13 + 0.493988

    If you got a negative answer, like -13.493988, then this is not -13 + 0.493988. Instead you have

    -13 - 0.493988 = -14 + 1 - 0.493988 = -14 + 0.506012

    1/Ŷ is then 3.206358 x 10^-14

    In this problem, the integer part was small enough that you could just use your 10^x or x^y function on the calculator. In other problems, the integer part might be too large to represent, so you'd manually separate the integer and fraction parts of the logarithm to get a pencil-and-paper answer in scientific notation.

  • 3 years ago

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