Rewrite $4.86 \times 10^4$ In Decimal Notation.A. 4.86 B. 48,600 C. 4,860,000 D. 0.000486

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Understanding Exponential Notation

Exponential notation is a way of expressing very large or very small numbers in a more compact form. It consists of a coefficient (or base) and an exponent. The coefficient is multiplied by 10 raised to the power of the exponent. In the given expression $4.86 \times 10^4$, the coefficient is 4.86 and the exponent is 4.

Rewriting Exponential Notation in Decimal Form

To rewrite the given expression in decimal notation, we need to multiply the coefficient by 10 raised to the power of the exponent. In this case, we have:

4.86×104=4.86×10×10×10×104.86 \times 10^4 = 4.86 \times 10 \times 10 \times 10 \times 10

Multiplying the Coefficient by 10 Raised to the Power of the Exponent

Now, let's multiply the coefficient 4.86 by 10 raised to the power of 4:

4.86×10×10×10×10=4.86×100004.86 \times 10 \times 10 \times 10 \times 10 = 4.86 \times 10000

Performing the Multiplication

Now, let's perform the multiplication:

4.86×10000=486004.86 \times 10000 = 48600

Conclusion

Therefore, the decimal notation of $4.86 \times 10^4$ is 48,600.

Answer

The correct answer is B. 48,600.

Why is this Important?

Understanding how to rewrite exponential notation in decimal form is an essential skill in mathematics, particularly in algebra and calculus. It allows us to work with very large or very small numbers in a more manageable way, making it easier to perform calculations and solve problems.

Real-World Applications

Rewriting exponential notation in decimal form has many real-world applications, such as:

  • Calculating large or small quantities in science and engineering
  • Working with financial data, such as large or small investments
  • Performing calculations in computer programming

Tips and Tricks

Here are some tips and tricks to help you rewrite exponential notation in decimal form:

  • Make sure to multiply the coefficient by 10 raised to the power of the exponent
  • Use the correct order of operations (PEMDAS) when performing the multiplication
  • Be careful when working with large or small numbers to avoid errors

Common Mistakes

Here are some common mistakes to avoid when rewriting exponential notation in decimal form:

  • Forgetting to multiply the coefficient by 10 raised to the power of the exponent
  • Making errors when performing the multiplication
  • Not using the correct order of operations (PEMDAS)

Conclusion

Frequently Asked Questions

Q: What is exponential notation?

A: Exponential notation is a way of expressing very large or very small numbers in a more compact form. It consists of a coefficient (or base) and an exponent. The coefficient is multiplied by 10 raised to the power of the exponent.

Q: How do I rewrite exponential notation in decimal form?

A: To rewrite exponential notation in decimal form, you need to multiply the coefficient by 10 raised to the power of the exponent. For example, to rewrite $4.86 \times 10^4$ in decimal form, you would multiply 4.86 by 10,000.

Q: What is the correct order of operations when rewriting exponential notation in decimal form?

A: The correct order of operations is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). When rewriting exponential notation in decimal form, you should follow this order to ensure accuracy.

Q: What are some common mistakes to avoid when rewriting exponential notation in decimal form?

A: Some common mistakes to avoid include:

  • Forgetting to multiply the coefficient by 10 raised to the power of the exponent
  • Making errors when performing the multiplication
  • Not using the correct order of operations (PEMDAS)

Q: Why is rewriting exponential notation in decimal form important?

A: Rewriting exponential notation in decimal form is an essential skill in mathematics, particularly in algebra and calculus. It allows us to work with very large or very small numbers in a more manageable way, making it easier to perform calculations and solve problems.

Q: What are some real-world applications of rewriting exponential notation in decimal form?

A: Some real-world applications of rewriting exponential notation in decimal form include:

  • Calculating large or small quantities in science and engineering
  • Working with financial data, such as large or small investments
  • Performing calculations in computer programming

Q: How can I practice rewriting exponential notation in decimal form?

A: You can practice rewriting exponential notation in decimal form by working through examples and exercises. You can also use online resources, such as calculators and worksheets, to help you practice.

Q: What are some tips and tricks for rewriting exponential notation in decimal form?

A: Some tips and tricks for rewriting exponential notation in decimal form include:

  • Make sure to multiply the coefficient by 10 raised to the power of the exponent
  • Use the correct order of operations (PEMDAS) when performing the multiplication
  • Be careful when working with large or small numbers to avoid errors

Q: Can I use a calculator to rewrite exponential notation in decimal form?

A: Yes, you can use a calculator to rewrite exponential notation in decimal form. However, it's also important to understand the underlying math and be able to perform the calculations manually.

Q: How do I know if I'm rewriting exponential notation in decimal form correctly?

A: To ensure that you're rewriting exponential notation in decimal form correctly, make sure to:

  • Multiply the coefficient by 10 raised to the power of the exponent
  • Use the correct order of operations (PEMDAS) when performing the multiplication
  • Double-check your work to avoid errors

Conclusion

In conclusion, rewriting exponential notation in decimal form is an essential skill in mathematics. By understanding how to rewrite $4.86 \times 10^4$ in decimal notation, we can work with very large or very small numbers in a more manageable way, making it easier to perform calculations and solve problems.