Question

Round each number to the nearest hundred. $$274,837$$

Short answer

274,837 rounded to the nearest hundred is 274,800.

Step-by-step solution

Identify the Hundreds Digit

Find the digit in the hundreds place. For the number 274,837, the hundreds digit is 8.

Look at the Digit to the Right

Look at the digit to the right of the hundreds digit to determine whether to round up or stay the same. The digit to the right is 3.

Apply Rounding Rules

Since the digit to the right is less than 5, do not increase the hundreds digit. The number becomes 274,800.

Key concepts

Understanding Place Value

Place value is the cornerstone of our number system, which is based on the idea that the value of a digit depends on its position, or place, within a number. For instance, in the number 274,837, each digit has a different value. The digit 7 is in the ten thousands place and represents 70,000, while the digit 8 is in the hundreds place and represents 800.

When rounding numbers, recognizing the place value is crucial because it determines which digit we are looking at and how we treat the digits around it. In the exercise, identifying the hundreds place is the starting point for rounding the number to the nearest hundred. It's important to make students comfortable with counting places from right to left, starting with the units, then tens, hundreds, and so on. Practice identifying the place value in different numbers to build a strong foundation.

Applying Rounding Rules

Rounding rules help us simplify numbers while maintaining their approximate value. These rules hinge upon the digit to the immediate right of the place you're rounding to. If this digit is 4 or lower, the number stays the same, and if it is 5 or higher, the number rounds up.

For example, consider the number 274,837, where you want to round to the nearest hundred. After identifying the hundreds digit (which is 8), check the digit to the right – the tens place. Since it is a 3 (which is less than 5), according to rounding rules, the hundreds digit remains unchanged. Thus, all digits following the hundreds place turn into zeroes, making the rounded number 274,800. It's pivotal to consistently apply these rules to achieve accuracy in rounding different numbers.

Key Tips for Rounding:

• Identify the digit to round to.
• Examine the digit to the right.
• Use the '5 or above, give it a shove; 4 or below, let it go' mnemonic.
• Change all digits following the rounding place to zero.

Working through multiple examples can help reinforce these rules.

Rounding to the Nearest Hundred

Once you've understood place value and rounding rules, applying these concepts to round to the nearest hundred becomes straightforward. The process involves looking at the hundreds place and considering the immediate next digit, the tens place, to make a decision.

Take the number 274,837 – you're focusing on the '8' in the hundreds place. The number in the tens place is '3'. Since '3' is less than '5', we keep the hundreds digit the same and change every digit that follows to zero. Therefore, 274,837 rounds down to 274,800 when rounded to the nearest hundred.

Why Round to the Nearest Hundred?

Rounding to the nearest hundred can make numbers easier to work with, especially when estimating sums and differences or when precise values are not necessary. Teachers can make rounding exercises more intuitive by offering real-world applications, such as estimating costs or distances.

Remember, practicing rounding with various examples can develop a student's confidence and skill in performing these calculations quickly and accurately.