To compare the numbers 1,092 and 1,100 using inequality symbols, let's break down each of the numbers by their place values:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Value} & \text{Thousands Place} & \text{Hundreds Place} & \text{Tens Place} & \text{Ones Place} \\
\hline
1092 & 1 & 0 & 9 & 2 \\
1100 & 1 & 1 & 0 & 0 \\
\hline
\end{array}
\][/tex]
We proceed with the comparison step-by-step:
1. Thousands Place:
- 1,092 has a digit of 1 in the thousands place.
- 1,100 has a digit of 1 in the thousands place.
- Since both digits are equal, we move to the next place value.
2. Hundreds Place:
- 1,092 has a digit of 0 in the hundreds place.
- 1,100 has a digit of 1 in the hundreds place.
- Here, 0 is less than 1, indicating that 1,092 is less than 1,100.
Since the digits in the hundreds place are different and 0 is less than 1, we can conclude that:
[tex]\[
1,092 < 1,100
\][/tex]
Therefore, the correct comparison using inequality symbols is:
[tex]\[
1,092 < 1,100
\][/tex]
