Step 1 :Convert the mixed number to an improper fraction: \(11 \frac{1}{8} = \frac{11*8+1}{8} = \frac{89}{8}\)
Step 2 :Divide the fraction by 100: \(\frac{89}{8} \% = \frac{89}{8*100} = \frac{89}{800}\)
Step 3 :Simplify the fraction: The fraction \(\frac{89}{800}\) is already in its simplest form, as 89 and 800 have no common factors other than 1.
Step 4 :\(\boxed{11 \frac{1}{8} \% = \frac{89}{800}}\)