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I mean it is logical that $e^0$ would be 1. Does the result for the calculation in the title just get rounded to 1, because the exponent is nearly 0? Every calculator gets me 1 as result for this calculation

Iti Shree
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A. Aoe
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1 Answers1

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$$e^{0.1 \times 10^{-15}} \approx 1.0000000000000001000000000000000050000000000000001667 $$

All calculators have hardware limitations that basically force the calculators to round all answers after a certain digit. There are fifteen zeroes after the "$1.$" and before the next "$1$" in the expansion above. For some high-powered calculators, this won't be an issue. But most, if not all, standard desktop calculators and perhaps even most scientific (non-graphing) calculators can't handle this many digits.

  • So my guess was right, that it just gets rounded? Thank you – A. Aoe May 16 '17 at 19:42
  • @A.Aoe, yes, that's correct. –  May 16 '17 at 19:43
  • Can I ask you another related thing? When I got the function $$(e^x - 1)/x$$ and the x is in the range of 0 until 0,2 * 10^-15. The graph of that function is constantly at 0 for some values until a little bit over 0,1 * 10^-15. Well I guess that's because e^x gets rounded to 1 for those values. But then suddenly it directly jumps from 0 to 2. Why? I just can't understand it. I hope you can understand my question. Sorry if my english isn't enough – A. Aoe May 16 '17 at 20:12
  • @A.Aoe, not sure where the $2$ is coming from. Sounds like it could just be an error introduced by dividing a very small number ($e^x-1$ when $x$ is very tiny) by another very small number ($x$). The only value of $x$ for which $\dfrac{e^x-1}x = 2$ is $x \approx 1.2564$. –  May 16 '17 at 23:44
  • Alright thank you for the help. Have a nice day – A. Aoe May 17 '17 at 05:39