What is the value of $e^{-10000}$?

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We know that the function $e$ does not attain value $0$ anymore.

But in R and Matlab the value of $e^{-10000}$ is given as $0$ which is not correct anymore.

I understand theat this is happening only because of the rounding error in Matlab as well as in R.

could anyone help me in finding the exact value of $e^{-10000}$?

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1 Answer

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$$\log_{10}(e^{-10000}) = -10000 * (0.4342944819) = -4342.944819$$

Thus, $$e^{-1000}=10^{ -4342.944819} = 10^{-4343} 10^{ 0.05518} = 1.13548386531 \times 10^{-4343}$$

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