e (Euler's Number)
The first few digits are:
2.7182818284590452353602874713527 (and more ...)
It is often called Euler's number after Leonhard Euler (pronounced "Oiler").
e is the base of the Natural Logarithms (invented by John Napier). e is found in many interesting areas, so it is worth learning about.
Calculating
There are many ways of calculating the value of e, but none of them ever give a totally exact answer, because e is irrational (not the ratio of two integers).But it is known to over 1 trillion digits of accuracy!
For example, the value of (1 + 1/n)n approaches e as n gets bigger and bigger:
n | (1 + 1/n)n |
1 | 2.00000 |
2 | 2.25000 |
5 | 2.48832 |
10 | 2.59374 |
100 | 2.70481 |
1,000 | 2.71692 |
10,000 | 2.71815 |
100,000 | 2.71827 |
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