1. **State the problem:** We need to find the sum of $0.291$ and $8.17$. 2. **Formula used:** Addition of decimal numbers is done by aligning the decimal points and adding digit by digit. 3. **Align the numbers:** $$\begin{array}{r} 0.291 \\ +8.170 \\ \hline \end{array}$$ 4. **Add the numbers:** $$\begin{array}{r} 0.291 \\ +8.170 \\ \hline 8.461 \\ \end{array}$$ 5. **Explanation:** We added $1 + 0 = 1$ in the thousandths place, $9 + 7 = 16$ so we write $6$ and carry $1$, $2 + 1 + 1 = 4$ in the hundredths place, and $0 + 8 = 8$ in the units place. 6. **Final answer:** $$0.291 + 8.17 = 8.461$$