1. Understand the conversion factor between decimeters (dm) and meters (m): 1 \, \text{dm} = 0.1 \, \text{m}
2. Multiply the given value in decimeters by the conversion factor: 77.8 \, \text{dm} \times 0.1 \, \text{m/dm} = 7.78 \, \text{m}
3. Hence, the final answer is: 77.8 \, \text{dm} = 7.78 \, \text{m}