Problem 92 - Fundamentals of Mathematics

Question

Round 6,842 to the nearest hundred.

Step-by-Step Solution

Answer

6,842 rounded to the nearest hundred is 6,800.

Step 1: Identify the Place Value

To round to the nearest hundred, identify the digit in the hundreds place. In 6,842, the hundreds digit is 8.

Step 2: Look at the Next Digit

Next, look at the digit to the immediate right of the hundreds place, which is the tens digit in this case. The tens digit in 6,842 is 4.

Step 3: Determine Whether to Round Up or Down

If the digit in the tens position is 5 or greater, increase the hundreds digit by one. If it's less than 5, the hundreds digit remains the same. Here, the tens digit is 4, which is less than 5, so we don't round up.

Step 4: Replace Digits to the Right

Since the hundreds digit remains the same, the digits following it (the tens and the ones) become zeros. Thus, the number becomes 6,800.

Key Concepts

Place Value

Understanding place value is key to rounding numbers effectively. Place value refers to the value of each digit in a number, based on its position. Every position in a number has a different value, like ones, tens, hundreds, and so on. For example, in the number 6,842, the digit 8 is in the hundreds place. This means its value is 800, not just 8.

• Ones place: The last digit which is 2.
• Tens place: The second-last digit which is 4.
• Hundreds place: The third digit from the right which is 8.

Each of these places is 10 times more valuable than the one to its right. Recognizing these patterns helps in rounding because you need to know which digit affects the rounding process.

Nearest Hundred

When rounding to the nearest hundred, you are simplifying to the largest nearest hundred number. Imagine it like deciding which hundred marker on a number line your number is closer to. In our example, 6,842, we want to simplify it to either 6,800 or 6,900.
First, identify the hundreds digit, which is 8 in this instance. Next, observe the tens digit to determine if your number should be rounded up or stay the same.
Choosing between these two options means finding the closest hundred indicator—either staying at 6,800 or moving up to 6,900. This visual thinking can make rounding a number to the nearest hundred much more intuitive.

Mathematical Rounding Rules

Mathematical rounding rules are guidelines to help decide whether to round a number up or keep it the same. The basic rule for rounding is to look at the digit directly right of your target place value.

• If this digit is 5 or greater, you round up.
• If it is less than 5, you keep the rounding digit unchanged.

In the case of 6,842, since the tens digit (4) is less than 5, we do not round up. Therefore, the hundreds digit remains as 8. The tens and ones become zero, simplifying our rounded number to 6,800.
Using these rules consistently ensures accuracy whenever you need to round numbers, whether it's for estimating sums or simplifying data for analysis.