Answer :
First, we convert 3 pounds to ounces. Since there are $16$ ounces in $1$ pound:
$$
3 \text{ pounds} \times 16 \frac{\text{ounces}}{\text{pound}} = 48 \text{ ounces}.
$$
This $48$ ounces represents the total weight of the purchased potatoes.
Next, we know that the weight of the diced potatoes obtained is $31.5$ ounces. To calculate the yield fraction, we take the ratio of the diced potatoes to the purchased weight:
$$
\text{Yield fraction} = \frac{31.5 \text{ ounces}}{48 \text{ ounces}} = 0.65625.
$$
Finally, to convert the yield fraction to a percentage, we multiply by $100$:
$$
\text{Yield percentage} = 0.65625 \times 100\% = 65.625\%.
$$
Thus, the yield percentage is $65.625\%$.
$$
3 \text{ pounds} \times 16 \frac{\text{ounces}}{\text{pound}} = 48 \text{ ounces}.
$$
This $48$ ounces represents the total weight of the purchased potatoes.
Next, we know that the weight of the diced potatoes obtained is $31.5$ ounces. To calculate the yield fraction, we take the ratio of the diced potatoes to the purchased weight:
$$
\text{Yield fraction} = \frac{31.5 \text{ ounces}}{48 \text{ ounces}} = 0.65625.
$$
Finally, to convert the yield fraction to a percentage, we multiply by $100$:
$$
\text{Yield percentage} = 0.65625 \times 100\% = 65.625\%.
$$
Thus, the yield percentage is $65.625\%$.