- Round \(1,210\) to the nearest hundred by observing the tens digit (\(1 < 5\)), resulting in \(1,200\).
- Round \(1,148\) to the nearest hundred by observing the tens digit (\(4 < 5\)), resulting in \(1,100\).
- Compare the two rounded values: \(1,200\) vs. \(1,100\).
- Conclude that the correct comparison is \(\boxed{1,200 > 1,100}\).
Explanation
- Analysis of Rounding Rules
The goal is to round the numbers \(1,210\) and \(1,148\) to the nearest hundred and compare the results. To round a number to the nearest hundred, we examine the tens digit. If the tens digit is \(0, 1, 2, 3,\) or \(4\), we round down by replacing the tens and units digits with \(0\). If the tens digit is \(5, 6, 7, 8,\) or \(9\), we round up by increasing the hundreds digit by \(1\) and replacing the tens and units digits with \(0\).
- Rounding 1,210 to the Nearest Hundred
For the number \(1,210\), we look at the tens digit, which is \(1\). Since \(1\) is less than \(5\), we round down. Therefore, \(1,210\) rounded to the nearest hundred is \(1,200\).
- Rounding 1,148 to the Nearest Hundred
For the number \(1,148\), we look at the tens digit, which is \(4\). Since \(4\) is less than \(5\), we round down. Therefore, \(1,148\) rounded to the nearest hundred is \(1,100\).
- Comparison and Conclusion
After rounding, we have the values \(1,200\) and \(1,100\). Comparing these two values, we can clearly see that \(1,200\) is greater than \(1,100\). This corresponds to the comparison \(1,200 > 1,100\). Therefore, the correct choice is the first one.
Examples
Rounding to the nearest hundred is a common practice in everyday budgeting. For instance, if you are planning a trip and need to estimate the costs of two different hotels—one costing \(\$1,210\) and the other costing \(\$1,148\)—rounding to the nearest hundred (\(\$1,200\) and \(\$1,100\) respectively) helps you quickly compare which option is more expensive without dealing with the smaller digits. This simplifies decision-making when dealing with large sets of expenses.