Expressing 13762 in Expanded Form

Oct 13, 2025 by magicalceylontours.com 87 views

Introduction

In mathematics, expressing numbers in expanded form is a fundamental concept that helps us understand the value and structure of numbers. It involves breaking down a number into its individual digits and representing each digit as a product of a coefficient and a power of 10. In this article, we will explore the concept of expressing numbers in expanded form using powers of 10, and we will use the number 13762 as an example.

What is Expanded Form?

Expanded form is a way of representing a number as a sum of its individual digits, each multiplied by a power of 10. For example, the number 1234 can be expressed in expanded form as:

${ 1234 = (1 \times 10^3) + (2 \times 10^2) + (3 \times 10^1) + (4 \times 10^0) }$

Expressing 13762 in Expanded Form

Now, let's apply the concept of expanded form to the number 13762. We can break down this number into its individual digits and represent each digit as a product of a coefficient and a power of 10.

${ 13762 = (1 \times 10^4) + (3 \times 10^3) + (7 \times 10^2) + (6 \times 10^1) + (2 \times 10^0) }$

Understanding the Powers of 10

In the expanded form of 13762, we see that each digit is multiplied by a power of 10. The powers of 10 are:

${ 10^4 }$ (10,000)
${ 10^3 }$ (1,000)
${ 10^2 }$ (100)
${ 10^1 }$ (10)
${ 10^0 }$ (1)

Why Do We Use Powers of 10?

We use powers of 10 because they provide a convenient way to represent large numbers in a compact form. By multiplying each digit by a power of 10, we can easily read and write large numbers without having to write out all the zeros.

Real-World Applications

Expressing numbers in expanded form has many real-world applications. For example, in finance, accountants use expanded form to represent large numbers in financial statements. In science, researchers use expanded form to represent large numbers in scientific notation.

Conclusion

In conclusion, expressing numbers in expanded form using powers of 10 is a fundamental concept in mathematics that helps us understand the value and structure of numbers. By breaking down a number into its individual digits and representing each digit as a product of a coefficient and a power of 10, we can easily read and write large numbers. The concept of expanded form has many real-world applications, and it is an essential tool for anyone who works with numbers.

Additional Examples

Here are a few more examples of numbers expressed in expanded form using powers of 10:

4567 = (4 × 10^3) + (5 × 10^2) + (6 × 10^1) + (7 × 10^0)
9821 = (9 × 10^3) + (8 × 10^2) + (2 × 10^1) + (1 × 10^0)
13579 = (1 × 10^4) + (3 × 10^3) + (5 × 10^2) + (7 × 10^1) + (9 × 10^0)

Practice Problems

Here are a few practice problems to help you understand the concept of expanded form:

Express the number 2468 in expanded form using powers of 10.
Express the number 13579 in expanded form using powers of 10.
Express the number 9876 in expanded form using powers of 10.

Answer Key

Here are the answers to the practice problems:

2468 = (2 × 10^3) + (4 × 10^2) + (6 × 10^1) + (8 × 10^0)
13579 = (1 × 10^4) + (3 × 10^3) + (5 × 10^2) + (7 × 10^1) + (9 × 10^0)
9876 = (9 × 10^3) + (8 × 10^2) + (7 × 10^1) + (6 × 10^0)
Expanded Form Q&A: Frequently Asked Questions =============================================

Q: What is expanded form?

A: Expanded form is a way of representing a number as a sum of its individual digits, each multiplied by a power of 10.

Q: Why do we use powers of 10 in expanded form?

A: We use powers of 10 because they provide a convenient way to represent large numbers in a compact form. By multiplying each digit by a power of 10, we can easily read and write large numbers without having to write out all the zeros.

Q: How do I express a number in expanded form?

A: To express a number in expanded form, you need to break down the number into its individual digits and represent each digit as a product of a coefficient and a power of 10.

Q: What are some examples of numbers expressed in expanded form?

A: Here are a few examples of numbers expressed in expanded form:

4567 = (4 × 10^3) + (5 × 10^2) + (6 × 10^1) + (7 × 10^0)
9821 = (9 × 10^3) + (8 × 10^2) + (2 × 10^1) + (1 × 10^0)
13579 = (1 × 10^4) + (3 × 10^3) + (5 × 10^2) + (7 × 10^1) + (9 × 10^0)

Q: Can I use expanded form with negative numbers?

A: Yes, you can use expanded form with negative numbers. To do this, you need to multiply each digit by a power of 10 and then add a negative sign to the result.

Q: How do I express a decimal number in expanded form?

A: To express a decimal number in expanded form, you need to break down the number into its integer and fractional parts. Then, you can represent each part as a product of a coefficient and a power of 10.

Q: What are some real-world applications of expanded form?

A: Expanded form has many real-world applications, including:

Finance: Accountants use expanded form to represent large numbers in financial statements.
Science: Researchers use expanded form to represent large numbers in scientific notation.
Engineering: Engineers use expanded form to represent large numbers in technical calculations.

Q: Can I use expanded form with fractions?

A: Yes, you can use expanded form with fractions. To do this, you need to multiply each digit by a power of 10 and then add a fraction to the result.

Q: How do I convert a number from expanded form to standard form?

A: To convert a number from expanded form to standard form, you need to add up the products of each digit and its corresponding power of 10.

Q: What are some common mistakes to avoid when using expanded form?

A: Here are a few common mistakes to avoid when using expanded form:

Not using powers of 10 correctly
Not breaking down the number into its individual digits
Not representing each digit as a product of a coefficient and a power of 10

Q: Can I use expanded form with exponents?

A: Yes, you can use expanded form with exponents. To do this, you need to multiply each digit by a power of 10 and then add an exponent to the result.

Q: How do I express a number in expanded form using scientific notation?

A: To express a number in expanded form using scientific notation, you need to break down the number into its coefficient and exponent parts. Then, you can represent each part as a product of a coefficient and a power of 10.

Q: What are some benefits of using expanded form?

A: Here are a few benefits of using expanded form:

It provides a convenient way to represent large numbers in a compact form.
It helps to avoid errors when working with large numbers.
It is a useful tool for problem-solving and calculations.