It's easy to determine how many digits you'll have in the resulting number.
In your example : 100*100 is actually 10
2*10
2 hence 10
4 which turns out to be 5 digits. The rule, hence is :
Take any number, divide repeatedly by ten until you reach a number greater than or equal to 1 and strictly lower than 10. The number of times you divided that number is actually the number of digits minus 1 that number has.Example :
84212 divided by 10 is 8421.2 (1)
8421.2 divided by 10 is 842.12 (2)
842.12 divided by 10 is 84.212 (3)
84.212 divided by 10 is 8.4212 (4)
Hence the number has 4+1=5 digits !!!