Problem 475 - Prealgebra

Question

Round to the nearest hundred. $$81,486$$

Step-by-Step Solution

Answer

81,500

Step 1: Identify the Hundreds Place

First, locate the hundreds place in the number. In the number 81,486, the hundreds place is the 4.

Step 2: Locate the Next Digit

Now, look at the next digit to the right of the hundreds place. In 81,486, the next digit is 8.

Step 3: Determine Rounding Rule

According to rounding rules, if the next digit (to the right of the hundreds place) is 5 or greater, you round up. If it is less than 5, you round down. In this case, 8 is greater than 5.

Step 4: Apply the Rounding

Since 8 is greater than 5, add 1 to the hundreds place digit (4). So, 4 becomes 5.

Step 5: Adjust the Remaining Digits

Change all digits to the right of the hundreds place to 0. Thus, 81,486 becomes 81,500.

Key Concepts

nearest hundred

Rounding to the nearest hundred is a fundamental math skill. It involves simplifying a number so that it's easier to work with while remaining reasonably close to the original value. This is especially useful in everyday calculations and estimates.

To round a number to the nearest hundred, follow these steps:

• Identify the hundreds place in the number.
• Look at the next digit to the right (the tens place) to decide whether to round up or down.
• Apply the rounding rule based on this digit.
• Change all digits to the right of the hundreds place to 0.

Let's use the number 81,486 as an example. Here, the hundreds place is 4, and the next digit is 8. Since 8 is greater than 5, we round up by adding 1 to the hundreds place. Therefore, 81,486 to the nearest hundred becomes 81,500.

Practicing will help you get more comfortable and faster at rounding numbers to the nearest hundred.

rounding rules

Understanding rounding rules is crucial for accurate rounding. Rounding helps simplify numbers, making them easier to work with. The basic rules are straightforward and universally used:

• If the digit to the right of the place you are rounding to is 5 or more, round up.
• If the digit is less than 5, round down.

Let's break it down with an example:

For the number 81,486, the hundreds place is 4. The digit right next to it is 8. Since 8 is greater than 5, we follow the rule and round up the 4 to 5, turning the original number into 81,500.

This simple approach allows you to quickly determine how to adjust the digit in the place value you are rounding to, making it an invaluable skill in both basic arithmetic and more complex math problems.

place value

Place value is a fundamental concept in mathematics, essential for understanding rounding and other arithmetic operations. Each digit in a number has a different value depending on its position.

Take the number 81,486 as an example:

• 8 is in the ten-thousands place
• 1 is in the thousands place
• 4 is in the hundreds place
• 8 is in the tens place
• 6 is in the ones place

When rounding to the nearest hundred, we focus on the hundreds place. In our example, it's the 4. The technique primarily hinges on understanding which digit impacts the rounding decision.

Knowing place values makes it easier to follow the rounding rules and ensures you get the correct adjusted number. With 81,486, recognizing the hundreds place (4) and the influencing tens place (8) allows you to correctly round it to 81,500.