Insert the Appropriate Sign in 15,800□15,911

To solve this problem, we'll follow these steps:

• Step 1: Identify the numbers given: $15,800$ and $15,911$.
• Step 2: Compare these two numbers by examining digits from left to right.
• Step 3: Determine the appropriate comparison sign.

Now, let's work through each step:
Step 1: We observe the numbers $15,800$ and $15,911$.
Step 2: Starting from the left, both numbers have the digits 1 and 5 in the ten-thousands and thousands places, respectively, which are equal. At the hundreds place, both numbers show 8. At the tens place, 15,800 has 0, and 15,911 has 1. Since 0 is less than 1, we determine that 15,800 is less than 15,911.
Step 3: Therefore, the correct sign to place between the numbers is $<$.

Therefore, the solution is to place the sign $<$ between the numbers: $15,800 < 15,911$.