Step 1 :Penelope walked \(\frac{1}{4}\) mile from her home to the zoo, \(\frac{9}{10}\) mile around the zoo, and \(\frac{1}{4}\) mile back home.
Step 2 :To find the total distance Penelope walked, we need to add these distances together.
Step 3 :So, the total distance is \(\frac{1}{4} + \frac{9}{10} + \frac{1}{4}\).
Step 4 :Simplifying this, we get \(\frac{7}{5}\) miles.
Step 5 :Final Answer: Penelope walked \(\boxed{\frac{7}{5}}\) miles that morning.