Why is e.g. $e^{0,1*10^{-15}}$ equal to 1?

Question

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

Answer 1

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

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.