To round numbers, we first need to understand place values. In the number 8321, each digit represents a different place value. The 8 is in the thousands place, 3 in the hundreds place, 2 in the tens place, and 1 in the ones place. Understanding these positions is crucial for rounding.
The fundamental rule of rounding is to look at the digit immediately to the right of the place you're rounding to. If that digit is 5 or greater, we round up. If it's less than 5, we round down. For example, when rounding to the nearest ten, if the ones digit is 5 or greater, we round up to the next ten. If it's less than 5, we round down to the previous ten.
In our number 8321, to round to the nearest hundred, we need to identify the key digits. The hundreds digit is 3, and the tens digit is 2. The ones digit (1) doesn't affect rounding to hundreds. We look at the tens digit (2) to decide whether to round the hundreds digit up or down. Since 2 is less than 5, we round down.
Now we apply the rounding rule to 8321. First, we identify that we're rounding to the nearest hundred, so we look at the hundreds digit (3) and the tens digit (2). Since the tens digit is 2, which is less than 5, we round down. This means the hundreds digit stays the same, and all digits to the right become zeros. Therefore, 8321 rounded to the nearest hundred is 8300.
To verify our answer, let's visualize it on a number line. We can see that 8321 is much closer to 8300 than to 8400. The distance from 8321 to 8300 is only 21 units, while the distance to 8400 is 79 units. Since 8321 is closer to 8300, our rounding decision is correct. Therefore, 8321 rounded to the nearest hundred is indeed 8300.
Let's look at a few more examples to solidify our understanding. In the first example, 8371, we look at the hundreds digit (3) and the tens digit (7). Since 7 is greater than 5, we round up, making it 8400. In the second example, 8249, we look at the hundreds digit (2) and the tens digit (4). Since 4 is less than 5, we round down, making it 8200. These examples show how the tens digit determines whether we round up or down.