Step 1 :Let the distances the dog ran be represented as distance1, distance2, and distance3 respectively. So, distance1 = 300 meters, distance2 = 200 meters, and distance3 = 500 meters.
Step 2 :The total distance traveled by the dog can be calculated by adding up all the distances the dog ran, regardless of the direction. So, total_distance = distance1 + distance2 + distance3 = 300 meters + 200 meters + 500 meters = 1000 meters.
Step 3 :\(\boxed{1000}\) meters is the total distance traveled by the dog.