Select Numbers Within Inequality: 330,099 < Box < 380,105

To solve this problem, let's examine each choice to see if it lies within the bounds established by the interval:

• Step 1: Check if each choice is greater than 330,099.
• Step 2: Check if each choice is less than 380,105.
• Step 3: Identify the choice that satisfies both conditions.

Now, let's execute the steps:

Step 1: Compare each choice to 330,099:
- Choice 1: $380,199 > 330,099$
- Choice 2: $330,001 > 330,099$ (False)
- Choice 3: $360,999 > 330,099$ (True)
- Choice 4: $309,456 > 330,099$ (False)

Step 2: Compare each valid choice from Step 1 to 380,105:
- Choice 1: $380,199 < 380,105$ (False)
- Choice 3: $360,999 < 380,105$ (True)

Step 3: Conclusion:
The choice that satisfies both conditions is choice 3: $360,999$.

Therefore, the appropriate number for the range $330,099 < \Box < 380,105$ is $360,999$.