Looking at a table of numbers and there is a pattern starting with the number 501, then shaded numbers every 8th number starting with 509. How do I use place value to describe how the numbers change?

To use place value to describe how the numbers change, we need to analyze the digits in each number.

Let's start with the number 501.

The digit in the hundreds place is 5.
The digit in the tens place is 0.
The digit in the ones place is 1.

Next, let's look at the shaded numbers that follow every 8th number starting with 509.

The digit in the hundreds place remains the same (5).
The digit in the tens place increases by 1 each time (0, 1, 2, 3, and so on).
The digit in the ones place increases by 8 each time (9, 7, 5, 3, and so on).

Therefore, using place value, we can describe the pattern as follows:

The hundreds place remains constant at 5.
The tens place increases by 1 for each shaded number.
The ones place decreases by 2 for each shaded number.

So, in summary, when looking at the numbers in the table, you can observe that there is a pattern based on place value. The hundreds place remains constant, the tens place increases by 1, and the ones place decreases by 2 for each shaded number.