If Jennifer used 2 parts out of 4 parts of the barrel over a 4-day period, that means she used \(\frac{2}{4}\) of the barrel, which simplifies to \(\frac{1}{2}\).
To find out how much she used per day, we divide this amount by the number of days (4 days):
\[ \text{Water used per day} = \frac{1/2}{4} = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \]
Thus, the fraction of a full barrel of water that Jennifer used per day is \(\frac{1}{8}\).
The correct answer is:
D. \( \frac{1}{8} \)