Problem 1 - Fundamentals of Mathematics

Question

Use the method of rounding whole numbers to solve each problem. Round 3387 to the nearest hundred.

Step-by-Step Solution

Answer

3387 rounded to the nearest hundred is 3400.

Step 1: Identify the Place Value

To round the number 3387 to the nearest hundred, first identify the digit in the hundreds place. In 3387, the digit in the hundreds place is 3, which is the second digit from the left.

Step 2: Look at the Next Digit

Now, look at the digit immediately to the right of the hundreds place, which is in the tens place. In this case, that digit is 8.

Step 3: Apply Rounding Rule

According to rounding rules, if the digit in the tens place is 5 or more, you increase the hundred's digit by 1. Since the digit is 8, which is greater than 5, increase the hundred's digit from 3 to 4.

Step 4: Adjust Remaining Digits

Change the digits to the right of the hundreds place to zero. Thus, 3387 rounded to the nearest hundred becomes 3400.

Key Concepts

Understanding Place Value

Place value is a fundamental concept in mathematics that helps us understand the numerical worth of any digit in a number. In the number 3387, each digit has a specific place value:

• The digit '3' in the thousands place represents 3000.
• The next '3' is in the hundreds place, meaning 300.
• The '8' is in the tens place, representing 80.
• Finally, '7' is in the ones place, which is simply 7.

Place value helps us break down and organize numbers in a way that makes it easier to perform operations like rounding. By identifying the place value of each digit, we can effectively pinpoint which digit is important for our rounding operation and which digit should be adjusted or left unchanged.

Simplifying Using Rounding Rules

Rounding rules are simple guidelines that inform us how to adjust numbers to make them simpler while maintaining their general value. To round a number, we:

• Determine which digit is in the place we are rounding to.
• Examine the next digit to decide whether to round up or keep the same number.

In our example of rounding 3387 to the nearest hundred, we looked at the digit directly to the right of the hundreds place (which is 8). The general rounding rule states:

• If this digit is 5 or greater, add 1 to the digit in the place we are rounding to.
• If the digit is less than 5, leave it unchanged.

Therefore, 3387 rounds to 3400 because 8 is greater than 5, indicating we should increase the hundreds digit from 3 to 4.

Rounding to the Nearest Hundred

Rounding to the nearest hundred means changing a number so that it is closest to a specific hundred value.
This can make numbers easier to work with, especially for estimation or mental math. To round to the nearest hundred, follow these steps:

• Identify the digit in the hundreds place.
• Check the digit immediately to the right, located in the tens place.

Using 3387, since the tens digit is 8, and according to our rounding rules, we increase the hundreds digit by 1 and change all digits following it into zeros. We adjust the number from 3387 to 3400.
Rounding helps simplify complex numbers, effectively making calculations more manageable without losing significant accuracy.