What does this fractional portion mean? Roughly speaking, logarithms measure not only how long a number is, but also how much that number is really using its digits\. 12 and 99 are both two\-digit numbers, but intuitively, 12 is "barely" two digits long, whereas 97 is "nearly" three digits\. Logarithms formalize this intuition, and tell us that 12 is really only using about 1\.08 digits, while 97 is using about 1\.99\.
You use an example of "99" then switch to "97".