How many digits are there in 2^1000 (2 to the power of 1000)?

Asking how many digits (in base 10) is related to what power of ten the number is (10^x). Something that is 2 digits will have a value of 1 <= x < 2 (i.e, 1.something), 3 digits will have an x of 2.something, 4 digits will have an x of 3.something, and so on. In other words, the base 10 logarithm of the number, rounded down, plus one, will be the number of digits for the number in base 10.

log(2^1000) = 1000*log(2) = 1000*.30103 = 301.03
Rounding down and adding one yields 302, so there are 302 digits (base 10) in 2^1000.

Posted by Ender on 2003-02-20 04:07:32