Problem 27 - Prealgebra

Question

In the following exercises, name each number in words. There are projected to be 23,867,000 college and university students in the US in five years.

Step-by-Step Solution

Answer

Twenty-three million, eight hundred sixty-seven thousand.

Step 1 - Identify Each Group

Break down the number 23,867,000 into groups. There are three groups: 23, 867, and 000.

Step 2 - Name Each Group in Words

The number 23 is twenty-three, the number 867 is eight hundred sixty-seven, and the number 000 represents thousand (since it's in the thousands place).

Step 3 - Combine the Groups

Combine the words from each group to form the final number name: twenty-three million, eight hundred sixty-seven thousand.

Key Concepts

Understanding Place Value

Place value is the foundation of our number system and represents the value of each digit in a number based on its position. Each position in a number has a different value, and this value increases tenfold as you move from right to left.

For instance, in the number 23,867,000, each digit has a different place value:

• The first digit 2 is in the ten million's place and represents 20,000,000.
• The second digit 3 is in the million's place and represents 3,000,000.
• The third digit 8 is in the hundred thousand's place and represents 800,000.
• The fourth digit 6 is in the ten thousand's place and represents 60,000.
• The fifth digit 7 is in the thousand's place and represents 7,000.
• The last three digits 000 are in the hundred's, ten's, and unit's places, representing zeros, often denoted as thousands.

Understanding place value allows us to read and write large numbers correctly by breaking them down into manageable parts.

Working with Large Numbers

Large numbers can initially seem intimidating, but they become easier to handle once we know how to break them down. To simplify reading large numbers, we often group digits in sets of three, starting from the right.

Each group represents a different place value category: units, thousands, millions, etc. This method helps us to quickly identify and verbalize large numbers. For example, in 23,867,000, we break it down as follows:

• 23 is in the millions group.
• 867 is in the thousands group.
• 000 is in the units group.

We then read each group individually and combine them to name the whole number. This approach makes it easier to understand and ensures that we pronounce it correctly.

Number Grouping and Its Importance

Grouping numbers into smaller sections is crucial for managing and understanding large numbers. Number grouping simplifies complex numbers by dividing them into three-digit sections.

For example, consider the number 23,867,000:

• The first group is 23, representing millions.
• The middle group is 867, representing thousands.
• The last group is 000, often referred to simply as thousand for simplicity.

This structured breakdown helps in reading, writing, and comprehending large numbers. It prevents errors and facilitates clear communication. When naming large numbers, always ensure you recognize the grouping to maintain accuracy in both speaking and writing.