Step 1: Identify the numbers to be added. The numbers are $78$, $20.9$, $017$, $0.9$, and $003$. Step 2: Convert all numbers to their standard decimal form. $78$ remains $78.0$ $20.9$ remains $20.9$ $017$ is equivalent to $17.0$ $0.9$ remains $0.9$ $003$ is equivalent to $3.0$ Step 3: Add the numbers. $$78.0$$ $$20.9$$ $$17.0$$ $$0.9$$ $$+\ 3.0$$ $$\rule{1.5cm}{0.4pt}$$ $$119.8$$ The sum is: $$\boxed{119.8}$$