Write The Number In Expanded Form 47

Writing the Number 47 in Expanded Form: A Deep Dive into Place Value and Number Representation

Understanding the expanded form of a number is a fundamental concept in mathematics, crucial for grasping place value, number systems, and more advanced mathematical operations. This article will explore the expanded form of the number 47 in detail, delving into the underlying principles and demonstrating its application in various contexts. We will also touch upon related concepts such as place value, base-ten systems, and how expanded form aids in understanding larger numbers.

What is Expanded Form?

In mathematics, the expanded form of a number represents the number as a sum of its individual place values. Each digit in the number is multiplied by its corresponding place value (ones, tens, hundreds, thousands, and so on) and then added together to get the original number. This process helps visualize the value of each digit within the number.

Expanding the Number 47

The number 47 consists of two digits: 4 and 7. To write it in expanded form, we analyze the place value of each digit:

• 4 is in the tens place, representing 4 tens, or 4 x 10 = 40.
• 7 is in the ones place, representing 7 ones, or 7 x 1 = 7.

Therefore, the expanded form of 47 is 40 + 7.

Understanding Place Value

The concept of place value is integral to understanding expanded form. In the base-ten system (the number system we commonly use), each place value represents a power of 10:

• Ones: 10⁰ = 1
• Tens: 10¹ = 10
• Hundreds: 10² = 100
• Thousands: 10³ = 1000
• And so on...

Each digit in a number occupies a specific place value, contributing to its overall value. In the number 47, the 4 occupies the tens place and contributes 40 to the total value, while the 7 occupies the ones place and contributes 7.

Expanded Form and Larger Numbers

The principle of expanded form applies equally to larger numbers. Let's consider the number 3,456:

• 3 is in the thousands place (3 x 1000 = 3000)
• 4 is in the hundreds place (4 x 100 = 400)
• 5 is in the tens place (5 x 10 = 50)
• 6 is in the ones place (6 x 1 = 6)

Therefore, the expanded form of 3,456 is 3000 + 400 + 50 + 6.

Applications of Expanded Form

The expanded form of a number is not merely a mathematical curiosity; it serves several crucial functions:

• Addition and Subtraction: Expanded form simplifies addition and subtraction, particularly with larger numbers. By adding or subtracting the corresponding place values, calculations become easier to manage.

• Multiplication and Division: Expanded form facilitates understanding the distributive property of multiplication. It allows for easier multiplication of numbers by breaking them down into their place values.

• Understanding Number Systems: Understanding expanded form provides a solid foundation for learning about different number systems, including those with bases other than ten (e.g., binary, hexadecimal).

• Word Problems: Expanded form often clarifies word problems involving numbers, aiding in comprehension and problem-solving.

• Estimation: Expanded form allows for easy estimation by rounding off the numbers to the nearest place value.

Expanded Form and Decimal Numbers

The concept of expanded form also extends to decimal numbers. Consider the number 12.34:

• 1 is in the tens place (1 x 10 = 10)
• 2 is in the ones place (2 x 1 = 2)
• 3 is in the tenths place (3 x 0.1 = 0.3)
• 4 is in the hundredths place (4 x 0.01 = 0.04)

Thus, the expanded form of 12.34 is 10 + 2 + 0.3 + 0.04.

Why is Expanded Form Important?

The importance of understanding expanded form can't be overstated. It is a cornerstone of elementary mathematics, providing a strong foundation for more advanced concepts:

• Improved Number Sense: It develops a stronger understanding of number values and relationships between digits.
• Easier Calculations: It simplifies complex arithmetic operations.
• Problem-Solving Skills: It enhances problem-solving abilities in various mathematical contexts.
• Foundation for Algebra: It lays the groundwork for understanding algebraic expressions and equations.

Beyond the Basics: Exploring Different Number Systems

While the base-ten system is prevalent, other number systems exist. Expanded form can be adapted to represent numbers in these systems. For example, in the binary system (base-2), numbers are represented using only 0 and 1. The expanded form would involve powers of 2 instead of powers of 10.

Conclusion: The Power of Expanded Form

In conclusion, the expanded form of a number is a powerful tool for understanding and manipulating numbers. Its application extends far beyond basic arithmetic, serving as a cornerstone for more advanced mathematical concepts and problem-solving. By understanding the place value of each digit and applying the principles of expanded form, learners can significantly improve their number sense, computational skills, and overall mathematical abilities. From the simple case of 47 (40 + 7) to more complex numbers, the underlying principles remain consistent, providing a valuable framework for mathematical understanding. Mastering expanded form unlocks a deeper comprehension of numbers and their representation, paving the way for success in higher-level mathematics.