To locate the treasures on a number line, we can convert the given depths into improper fractions for easier comparison.
Here are the depths represented as improper fractions:
- Gold coin: \(-\frac{1}{2}\) foot
- Bronze cup: \(-\frac{1}{4}\) foot
- Silver necklace: \(-\frac{5}{8}\) foot
- Copper coin: \(-\frac{7}{8}\) foot
Now let's express these fractions with a common denominator to make comparison easier. The least common multiple of the denominators 2, 4, and 8 is 8.
Converting each fraction:
- Gold coin: \(-\frac{1}{2} = -\frac{4}{8}\)
- Bronze cup: \(-\frac{1}{4} = -\frac{2}{8}\)
- Silver necklace: \(-\frac{5}{8}\) (stays the same)
- Copper coin: \(-\frac{7}{8}\) (stays the same)
Now we can list the treasures in order from least to most negative (which indicates depth):
- Bronze cup: \(-\frac{2}{8}\) foot (or -0.25 foot)
- Gold coin: \(-\frac{4}{8}\) foot (or -0.5 foot)
- Silver necklace: \(-\frac{5}{8}\) foot (or -0.625 foot)
- Copper coin: \(-\frac{7}{8}\) foot (or -0.875 foot)
The deepest treasure is the one with the most negative value, which is the copper coin at \(-\frac{7}{8}\) foot.
Conclusion: The deepest treasure is the copper coin located at \(-\frac{7}{8}\) foot.