Problem 17 - Prealgebra

Question

In the following exercises, name each number in words. $$5,846,103$$

Step-by-Step Solution

Answer

Five million, eight hundred forty-six thousand, one hundred three.

Step 1: Identify the Number

Look at the given number: 5,846,103.

Step 2: Break the Number into Groups of Three Digits

Separate the number into groups of three digits from right to left: 5,846,103 becomes 5 | 846 | 103.

Step 3: Name Each Group Separately

Identify and name each group individually: - 5 (million) - 846 (thousand) - 103 (hundred)

Step 4: Assemble the Full Name

Combine the names from each group: Five million, eight hundred forty-six thousand, one hundred three.

Key Concepts

Place Value

In mathematics, the place value of a digit in a number determines its value depending on its position. Each position represents a different power of 10. For instance, in the number 5,846,103:
5 is in the millions place.
8 is in the hundred thousands place.
4 is in the ten thousands place.
6 is in the thousands place.
1 is in the hundreds place.
0 is in the tens place.
3 is in the ones place.
Understanding place value is essential for correctly naming and writing large numbers in words.

Writing Numbers in Words

When writing numbers in words, we follow certain rules to ensure clarity and correctness. Breaking the number into smaller groups simplifies this process. Let's break down the number 5,846,103:
First, separate the number into groups of three digits from right to left: `5|846|103`.
Now, name each group separately: 5 (million), 846 (thousand), 103 (hundred).
Combine these groups into a single phrase: Five million, eight hundred forty-six thousand, one hundred three. Some key tips include:

• Always start from the leftmost group.
• Include the place value name (like million, thousand) for each group except for the last one.
• Use 'and' for hundreds within thousands and millions groups if applicable.

Following these steps helps in creating an accurate and easily readable written form of numbers.

Large Numbers

Dealing with large numbers can be intimidating initially, but understanding their structure can make it easier. Large numbers are comprised of multiple periods, each containing three digits. For instance, the number 5,846,103 is divided into periods as follows:
5 (million)
846 (thousand)
103 (hundred).
Each period represents a group of three digits:

• The Millions period: Contains numbers from 1,000,000 up to, but not including, 1,000,000,000.
• The Thousands period: Contains numbers from 1,000 up to, but not including, 1,000,000.
• The Hundreds period: Contains numbers from 1 up to, but not including, 1,000.

Organizing large numbers into smaller periods helps in reading and writing them correctly. Practice with various numbers in different ranges to become comfortable with handling large numbers.