Problem 49 - Prealgebra

Question

In the following exercises, round to the indicated place value. $$\begin{array}{l}{\text { Round to the nearest }} \\ {\text { hundred: }} \\\ {\text { (a) } 63,994 \quad \text { (b) } 63,949}\end{array}$$

Step-by-Step Solution

Answer

(a) 64,000. (b) 63,900.

Step 1: Identify the place value

Locate the hundreds place in each number. For both numbers 63,994 and 63,949, the hundreds place is the third digit from the right.

Step 2: Look at the digit to the right

Identify the digit to the right of the hundreds place (the tens place). In 63,994, the digit in the tens place is 9. In 63,949, the digit in the tens place is 4.

Step 3: Apply rounding rules

If the digit in the tens place is 5 or more, round up the hundreds place. If it is less than 5, keep the hundreds place the same. For 63,994, the tens digit is 9, so round up the hundreds place from 9 to 10. For 63,949, the tens digit is 4, so keep the hundreds place 9.

Step 4: Rewrite the numbers

Rewrite each number with the appropriately rounded hundreds place and replace the digits to the right with zeros. Thus, 63,994 rounded to the nearest hundred is 64,000. 63,949 rounded to the nearest hundred is 63,900.

Key Concepts

place value

Understanding place value is critical for rounding numbers accurately. Each digit in a number has a specific value depending on its position. For example, in the number 63,994, the digit '6' is in the ten thousand place, '3' is in the thousand place, '9' is in the hundred place, and so on. The place value tells us the importance of each digit in forming the number. For rounding to the nearest hundred, we primarily focus on the hundreds, tens, and units digits. This is because the digit in the hundreds place determines the group we are rounding to, while the tens and units provide context for making rounding decisions.

rounding rules

Rounding numbers requires us to follow certain rules. These rules help in simplifying numbers while maintaining their approximate value. Here are the basic rounding rules you need to remember:

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

For example, in rounding 63,994 to the nearest hundred, we look at the tens place, which is 9. Since 9 is greater than 5, we round up from 9 (hundreds place) to 10. Similarly, for 63,949, the tens place is 4. Since 4 is less than 5, the hundreds place stays the same and becomes 900 instead of 1000.

educational exercises

Practicing rounding through educational exercises helps in understanding and reinforcing these concepts. It is beneficial to work with various numbers and different place values to become proficient in rounding. Let's consider our examples again for practice:

• First, locate the place value you need to round to. In this case, the hundreds place.
• Next, identify the digit to the right of the hundreds place, which is the tens place.
• Apply the rounding rules: In 63,994, the tens digit is 9, so round up the hundreds from 9 to 10, resulting in 64,000. For 63,949, the tens digit is 4, so the hundreds digit remains 9, resulting in 63,900.

Regular practice with exercises like these will solidify your understanding and make rounding numbers second nature.