Complete the Number: Make 512_ Even by Filling the Blank

To solve this problem, we'll identify which digit can be placed in the blank space to make the number divisible by 2.

Step 1: Review the divisibility rule for 2.
A number is divisible by 2 if its last digit is even.

Step 2: Evaluate each possible choice for the blank in $512\_.$

• Choice 1: If we fill the blank with 1, the number becomes 5121, which ends with 1, an odd number. This is not divisible by 2.
• Choice 2: If we fill the blank with 2, the number becomes 5122, which ends with 2, an even number. This number is divisible by 2.
• Choice 3: If we fill the blank with 3, the number becomes 5123, which ends with 3, an odd number. This is not divisible by 2.
• Choice 4: If we fill the blank with 5, the number becomes 5125, which ends with 5, an odd number. This is not divisible by 2.

Conclusion: Among all choices, only when the blank is filled with 2, the resulting number 5122 is divisible by 2.

Therefore, the correct answer is $2$.