Expanded Form Of 720 080 With Exponents

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The concept of expanded form with exponents is a fundamental aspect of mathematics, particularly in the realm of algebra and arithmetic operations. To understand the expanded form of a number with exponents, let's first delve into the basics of exponents and how they are used to represent numbers in a more compact form.

Understanding Exponents

Exponents are shorthand for repeated multiplication of the same number. For instance, instead of writing 2 × 2 × 2 × 2, we can express it as 2^4, where the exponent 4 indicates that the base number 2 is multiplied by itself four times. This notation significantly simplifies complex arithmetic operations and makes it easier to work with large numbers.

Expanded Form: A Detailed Explanation

Expanded form refers to the process of expressing a number in terms of its place value, where each digit is multiplied by its corresponding power of 10. For example, the number 456 can be written in expanded form as 400 + 50 + 6, where each digit is multiplied by its place value (100, 10, and 1, respectively).

When dealing with exponents, the expanded form takes on a slightly different form. Instead of multiplying each digit by its place value, we multiply the base number by its corresponding exponent.

Expanded Form of 720 080 with Exponents

To express 720 080 in expanded form with exponents, we need to break down the number into its constituent parts and express each part as a power of 10.

720 080 = 7 × 10^5 + 2 × 10^4 + 0 × 10^3 + 0 × 10^2 + 8 × 10^1 + 0 × 10^0

In this expression, each digit is multiplied by its corresponding power of 10, and the exponents are used to represent the place value of each digit.

Working Mechanism: Step-by-Step Explanation

To better understand the expanded form of 720 080 with exponents, let's break down the process into a step-by-step explanation:

1. Start with the original number: 720 080
2. Identify the place value of each digit:
   • 7: hundreds of thousands (10^5)
   • 2: tens of thousands (10^4)
   • 0: thousands (10^3)
   • 0: hundreds (10^2)
   • 8: tens (10^1)
   • 0: ones (10^0)
3. Express each digit as a power of 10:
   • 7 × 10^5
   • 2 × 10^4
   • 0 × 10^3
   • 0 × 10^2
   • 8 × 10^1
   • 0 × 10^0
4. Combine the expressions to form the expanded form:
   • 7 × 10^5 + 2 × 10^4 + 0 × 10^3 + 0 × 10^2 + 8 × 10^1 + 0 × 10^0

Benefits and Applications

The expanded form of 720 080 with exponents offers several benefits and applications:

• Simplifies arithmetic operations: By expressing numbers in expanded form, we can simplify complex arithmetic operations and make calculations more manageable.
• Enhances understanding of place value: The expanded form helps to reinforce the concept of place value and how each digit contributes to the overall value of the number.
• Facilitates comparisons: By expressing numbers in expanded form, we can easily compare and contrast different values.

Real-World Applications

The expanded form of 720 080 with exponents has numerous real-world applications:

• Financial calculations: The expanded form can be used to simplify financial calculations, such as computing interest rates or investment returns.
• Scientific notation: The expanded form is used in scientific notation to express extremely large or small numbers in a more compact form.
• Computer programming: The expanded form is used in computer programming to represent numbers in a more efficient and compact manner.

Conclusion

In conclusion, the expanded form of 720 080 with exponents is a powerful tool for simplifying arithmetic operations, enhancing understanding of place value, and facilitating comparisons. By breaking down the number into its constituent parts and expressing each part as a power of 10, we can gain a deeper understanding of the number and its underlying structure.