Incorrect calculation of 100! - but why

Question

HI,
I just tried to calculate 100! (using the FACT function) in Numbers, and it gave me an answer that is:
93326215443944200000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000
While the actual answer should be:
93326215443944152681699238856266700490715968264381621468592963895217599993229915 608941463976156518286253697920827223758251185 210916864000000000000000000000000
Numbers seems to be rounding up the answer after 15 digits. But can someone explain why is this happening?
I suppose I might need to change the default settings somewhere, Can someone please guide!
Thanks

Answer 1

Hello
Spreadsheet is not the right tool for arbitrary precision calculation. As far as Numbers is concerned, it uses double precision binary floating point arithmetic whose mantissa can hold only 52-bit binary digits. In other words, 2 ^ 53 is the maximum exact integer it can represent.
I don't know what your goal is, and also I guess you already know what alternatives are, but here you may use bc(1) in shell, such as -
#!/bin/bash
bc -l <<EOF
define fact (n)
    m = 1
    for (i = 1; i <= n; i++) { m *= i }
    return m
print fact(100)
EOF
or ruby, such as -
#!/usr/bin/ruby -w
def fact (n)
    m = 1
    for i in (1 .. n)
        m *= i
    end
    return m
end
print fact(100)
Regards,
H