Why does my TI-83 give zero for 0.001^100?

[CarbonBased]

This is probably an ignorant question...but why when I attempt to calculate .001 to the 100th power on my TI-83 does it give me an answer of zero? Is the calculator assuming that the answer is so close to zero that it is negligible? If so, that's probably not the accuracy I'm looking for.

 

[kkrizka]

Yup, the calculator sees it just like a 0. Calculators can't store numbers with inifinite digits, plus you get roundinig erros with very small numbers.

 

[Diffy]

.001 = 10^(-3)

.001^(100) = (10^(-3))^100 = 10^(-300) = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001

 

[Tedjn]

My TI-84+ can't handle anything with exponents greater than 99 or less than -99, probably some sort of memory limitation. I don't think the 83 is any better. You can probably find better arbitrary precision calculators online, or the TI-89 seems to handle this calculation fine. (Although, for something like this, you would just figure it out normally like Diffy did.)

 

[HallsofIvy]

That's interesting. Even in "scientific" or "engineering" mode, the TI83 gives an answer of "0E0".

The TI85 and TI89, however, give "1.00E-300".

 

[CarbonBased]

Ok...that makes sense. And yea I suppose it's pretty simple to work out mentally; I just wanted to diagnose my TI's issues. Thanks for the insight:)