To find out how many days late the book was, we can divide the total fine by the daily penalty. The total fine is $1.08, and the penalty per day is $0.09.
We can calculate the number of days late as follows:
\[ \text{Number of days late} = \frac{\text{Total fine}}{\text{Penalty per day}} = \frac{1.08}{0.09} \]
Now, performing the division:
\[ 1.08 \div 0.09 = 12 \]
So, the book was 12 days late.