Problem 48 - Prealgebra

Question

In the following exercises, round to the indicated place value. $$\begin{array}{l}{\text { Round to the nearest }} \\ {\text { thousand: }} \\\ {\text { (a) } 2,391 \text { (b) } 2,795}\end{array}$$

Step-by-Step Solution

Answer

2,391 rounded to the nearest thousand is 2,000. 2,795 rounded to the nearest thousand is 3,000.

Step 1: Identify the place value

Observe that you need to round each number to the nearest thousand. The place value in question is the thousand's place.

Step 2: Focus on each number individually

First, take the number 2,391. Identify the thousand's place, which is '2'.

Step 3: Look at the digit to the right

Check the digit immediately to the right of the thousand's place for 2,391. The digit is '3'.

Step 4: Apply rounding rules

According to rounding rules, if the digit to the right is less than 5, round down. Therefore, 2,391 rounded to the nearest thousand is 2,000.

Step 5: Repeat for the second number

Now take the number 2,795. Identify the thousand's place, which is '2'.

Step 6: Look at the digit to the right

For the number 2,795, the digit immediately to the right of the thousand's place is '7'.

Step 7: Apply rounding rules

Since the digit to the right is 5 or greater, round up. Thus, 2,795 rounded to the nearest thousand is 3,000.

Key Concepts

place value

Place value is a fundamental concept in mathematics that helps us understand the value of each digit in a number. Each digit in a number has a different place value depending on its position. For example, in the number 2,795, each digit represents a different value:

• 2 is in the 'thousands place' and represents 2,000
• 7 is in the 'hundreds place' and represents 700
• 9 is in the 'tens place' and represents 90
• 5 is in the 'ones place' and represents 5

Understanding place value is crucial when rounding numbers because it tells us which digit's value we need to focus on.

rounding rules

Rounding numbers makes them easier to work with, especially when you need an approximate value rather than a precise figure. Here are the basic rounding rules:

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

Using these rules, let's apply them to the given examples:
For 2,391, the digit to the right of the thousand's place is 3. Since 3 is less than 5, we round down to 2,000.
For 2,795, the digit to the right of the thousand's place is 7. Since 7 is 5 or greater, we round up to 3,000.

thousands place

The thousands place is often used in rounding larger numbers. It helps simplify numbers to make them easier to work with or understand. Let's revisit our examples:

• For the number 2,391, the thousands place is '2'
• For the number 2,795, the thousands place is '2'

To round these numbers to the nearest thousand, we need to look at the digit immediately to the right of the thousands place:

• In 2,391, the digit to the right is 3, so we round down to 2,000
• In 2,795, the digit to the right is 7, so we round up to 3,000

This helps us get a simplified and approximate value quickly.