Problem 473 - Prealgebra

Question

Round to the nearest hundred. $$38,975$$

Step-by-Step Solution

Answer

The rounded number is 39,000.

Step 1: Identify the Hundred's Place

Locate the hundred's place in the number 38,975. The digit in the hundred's place is 9.

Step 2: Look at the Digit to the Right

Check the digit to the right of the hundred's place. In this case, the digit to the right of 9 is 7.

Step 3: Apply Rounding Rules

If the digit to the right of the hundred's place is 5 or greater, increase the hundred's digit by 1. Here, 7 is greater than 5, so increase 9 by 1 to get 10.

Step 4: Adjust the Number

Since 9 increased by 1 becomes 10, this carries over to the thousand's place. Therefore, the thousand's digit 8 also increases by 1, and the hundred's place becomes 0. The tens and units digits are replaced by zeros.

Step 5: Write the Rounded Number

The number 38,975 rounded to the nearest hundred is 39,000.

Key Concepts

place value

Understanding place value is essential for rounding numbers accurately. In a number like 38,975, each digit has a specific value depending on its position. From right to left, the digits are: ones, tens, hundreds, thousands, and ten-thousands. For instance, in the number 38,975, the digit 5 is in the ones place, 7 in the tens place, 9 in the hundreds place, 8 in the thousands place, and 3 in the ten-thousands place. Recognizing these positions helps you manipulate and understand the number better.

rounding rules

Rounding helps simplify numbers, making them easier to work with. Here are the basic rules:

• If the digit to the right of the place you are rounding to is less than 5, keep the target digit the same.
• If the digit to the right is 5 or more, increase the target digit by 1.

For example, in 38,975, focusing on the hundreds place (9), you look at the digit to its right (7). Since 7 is greater than 5, you increase 9 by 1, making it 10. Because 10 overflows, it impacts the next higher place value, which we will discuss next.

carrying over

The concept of carrying over comes into play when the rounded digit increases beyond its limit. In the number 38,975, rounding the 9 in the hundreds place to 10 affects the next place value: the thousands place. In this case, 9 turns into 0 (hundreds place), and 1 is added to 8 (thousands place). This changes 38,975 to 39,000. Carrying over is crucial for proper rounding, ensuring all digits correctly reflect the rounded value.