Question

Round each number to the nearest hundred. $$3,845,240$$

Short answer

The number 3,845,240 rounded to the nearest hundred is 3,845,200.

Step-by-step solution

Identify the Hundreds Place

First, locate the digit in the hundreds place. For the number 3,845,240, the hundreds place is occupied by the digit 2.

Look at the Next Smaller Place Value

The digit to the right of the hundreds place will determine how we round the number. In 3,845,240, the next smaller place is the tens place, which is occupied by the digit 4.

Apply Rounding Rules

If the digit in the next smaller place is 5 or more, we round up. If it's 4 or less, we round down. Since the digit is 4, we round down and keep the hundreds digit the same.

Adjust All Lesser Place Values to Zero

After rounding down, change all the digits to the right of the hundreds place to zero. The number 3,845,240 rounded to the nearest hundred is 3,845,200.

Key concepts

Place Value

Understanding place value is fundamental to grasping rounding numbers. The value of a digit depends on its position within a number. Take the number 3,845,240 for example. The place values of this number, from right to left, are ones, tens, hundreds, thousands, ten thousands, hundred thousands, and millions. The digit 2 is in the hundreds place, which means it represents 200 in this context, not just 2.

Place value can be visualized by breaking down the number into its constituents: 3 million, plus 800 thousand, plus 40 thousand, plus 5 thousand, plus 200, plus 40, plus 0 ones. Recognizing each digit's contribution to the full number is critical when performing mathematical operations, such as rounding, addition, or subtraction.

Rounding Rules

Rounding rules simplify numbers by decreasing the precision while maintaining a value close to the original number. The key steps in rounding involve examining digits in specific place values. Here's an easy-to-follow guide:

Firstly, identify the digit in the place value you're rounding to. In the case of 3,845,240, when rounding to the nearest hundred, we look at '2'. Next, examine the digit immediately to the right; this determines whether to round up or down. If this digit (a '4' in our example) is 4 or less, keep the identified digit the same. If it is 5 or more, increase the identified digit by one. Once decided, any digits to the right of the chosen place value are changed to zero, resulting in a rounded number of 3,845,200 for our example.

Mathematical Operations

Mathematical operations often involve working with large numbers, and rounding makes these operations more manageable. By rounding, we can approximate numbers, making it easier to quickly estimate sums, differences, products, or quotients.

In our problem, once the number is rounded to 3,845,200, it is far simpler to use in further calculations than 3,845,240. This can considerably expedite solving complex problems, especially when dealing with multiple large numbers. It's a skill that isn't just academic - rounding is used daily, from calculating expenses to interpreting statistical data. Practicing with various numbers enhances understanding and efficiency in mathematics.