How many digits are there in 2^1000 (2 to the power of 1000)?
Using Excel I made two columns an x and a y. X was numbered from 0-1000. In column Y, was the formula =2^x. At x=1000 the 'answer' given by excel was 1.07150860718627E+301 . So since there are 301 places to move the decimal to the right plus the one for the actual digit at the beginning of the number we arrive at the answer of 302 digits in the number 2^1000.