Specific Comparison Task with Numbers: Determine the Appropriate Sign in 400,040 □ 400,400

To determine the appropriate sign for the expression $400,040\Box400,400$, we should compare the two numbers digit by digit from left to right:

• Hundred-thousands place: Both numbers have a 4. So, they are equal in this place value.
• Ten-thousands place: Both numbers have a 0. So, they are equal in this place value as well.
• Thousands place: Both numbers have a 0. They remain equal here.
• Hundreds place: The first number, $400,040$, has a 0, and the second number, $400,400$, has a 4. Hence, this is where the numbers differ.

In the hundreds place, the second number, 400,400, has a greater digit than the first number. Therefore,
$400,040 < 400,400$.

Accordingly, the correct sign to place in the expression is $<$, indicating that 400,040 is less than 400,400.

The solution to the problem is $<$.