# 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?

Thanks.

Relevance

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

Given:

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

• 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.

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