I have been trying to write a program, that will allow me to calculate the constant e to an extremely precice value.
This is the equation I used:
1 + 1/1! + 1/2! and so on
My goal, was to calculate e to 9001 digits in precision (aka, OVER 9000!)
However, with the equation I used, I had to do some rounding.For example, 1/(1*2*3) would end up getting me 0.16666666666 (the 6 repeats until the 9001st digit, where it is rounded to a 7).
the rounding rules I used were, if the number cannot be divided evenly within 9001 digits, I would look at the 9002nd digit, if it is 5 or above, round up. else, round down.
Now my question is, in my circumstance, is it possible to figure out at most how many digits at the end would be made inaccurate because of the rounding?