Evaluate The Following Expression And Express Your Answer In Scientific Notation:$\[ 6.89 \times 10^{-4} - 4.23 \times 10^{-4} \\]Answer: \[$\square \times 10^{\square}\$\]

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Introduction

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It is commonly used in mathematics, physics, and engineering to simplify calculations and make it easier to understand complex concepts. In this article, we will evaluate the given expression and express the answer in scientific notation.

The Expression

The given expression is:

6.89×10−4−4.23×10−4{ 6.89 \times 10^{-4} - 4.23 \times 10^{-4} }

Evaluating the Expression

To evaluate the expression, we need to subtract the two numbers. Since they are in scientific notation, we can subtract the coefficients (the numbers in front of the powers of 10) and keep the same power of 10.

6.89×10−4−4.23×10−4=(6.89−4.23)×10−4{ 6.89 \times 10^{-4} - 4.23 \times 10^{-4} = (6.89 - 4.23) \times 10^{-4} }

Calculating the Coefficient

Now, we need to calculate the coefficient by subtracting 4.23 from 6.89.

6.89−4.23=2.66{ 6.89 - 4.23 = 2.66 }

Expressing the Answer in Scientific Notation

Now that we have the coefficient, we can express the answer in scientific notation.

(6.89−4.23)×10−4=2.66×10−4{ (6.89 - 4.23) \times 10^{-4} = 2.66 \times 10^{-4} }

Conclusion

In this article, we evaluated the given expression and expressed the answer in scientific notation. We used the rules of scientific notation to simplify the calculation and make it easier to understand.

Frequently Asked Questions

Q: What is scientific notation?

A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form.

Q: How do I evaluate an expression in scientific notation?

A: To evaluate an expression in scientific notation, you need to subtract or add the coefficients (the numbers in front of the powers of 10) and keep the same power of 10.

Q: What is the coefficient in scientific notation?

A: The coefficient is the number in front of the power of 10 in scientific notation.

Example Use Cases

Scientific notation is commonly used in mathematics, physics, and engineering to simplify calculations and make it easier to understand complex concepts. Here are a few example use cases:

  • Calculating the distance between two stars in astronomy
  • Measuring the speed of a particle in physics
  • Expressing the amount of a substance in chemistry

Tips and Tricks

  • When evaluating an expression in scientific notation, make sure to keep the same power of 10.
  • Use the rules of scientific notation to simplify calculations and make it easier to understand complex concepts.
  • Practice evaluating expressions in scientific notation to become more comfortable with the concept.

Conclusion

In this article, we evaluated the given expression and expressed the answer in scientific notation. We used the rules of scientific notation to simplify the calculation and make it easier to understand. Scientific notation is a powerful tool that can be used to simplify calculations and make it easier to understand complex concepts.

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Introduction

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It is commonly used in mathematics, physics, and engineering to simplify calculations and make it easier to understand complex concepts. In this article, we will answer some frequently asked questions about scientific notation.

Q&A

Q: What is scientific notation?

A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It is commonly used in mathematics, physics, and engineering to simplify calculations and make it easier to understand complex concepts.

Q: How do I write a number in scientific notation?

A: To write a number in scientific notation, you need to express it as a product of a number between 1 and 10 and a power of 10. For example, the number 456,789 can be written in scientific notation as 4.56789 × 10^5.

Q: What is the coefficient in scientific notation?

A: The coefficient is the number in front of the power of 10 in scientific notation. For example, in the number 4.56789 × 10^5, the coefficient is 4.56789.

Q: How do I evaluate an expression in scientific notation?

A: To evaluate an expression in scientific notation, you need to subtract or add the coefficients (the numbers in front of the powers of 10) and keep the same power of 10. For example, the expression 3.45 × 10^2 - 2.12 × 10^2 can be evaluated as (3.45 - 2.12) × 10^2 = 1.33 × 10^2.

Q: What is the power of 10 in scientific notation?

A: The power of 10 is the exponent that is multiplied by the coefficient in scientific notation. For example, in the number 4.56789 × 10^5, the power of 10 is 5.

Q: How do I convert a number from scientific notation to standard notation?

A: To convert a number from scientific notation to standard notation, you need to multiply the coefficient by the power of 10. For example, the number 4.56789 × 10^5 can be converted to standard notation as 456,789.

Q: What are some common applications of scientific notation?

A: Scientific notation is commonly used in mathematics, physics, and engineering to simplify calculations and make it easier to understand complex concepts. Some common applications of scientific notation include:

  • Calculating the distance between two stars in astronomy
  • Measuring the speed of a particle in physics
  • Expressing the amount of a substance in chemistry

Q: What are some common mistakes to avoid when working with scientific notation?

A: Some common mistakes to avoid when working with scientific notation include:

  • Forgetting to keep the same power of 10 when evaluating an expression
  • Not using the correct coefficient when converting a number from scientific notation to standard notation
  • Not understanding the concept of significant figures when working with scientific notation

Conclusion

In this article, we answered some frequently asked questions about scientific notation. We covered topics such as how to write a number in scientific notation, how to evaluate an expression in scientific notation, and how to convert a number from scientific notation to standard notation. We also discussed some common applications and mistakes to avoid when working with scientific notation.

Frequently Asked Questions

Q: What is the difference between scientific notation and standard notation?

A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form, while standard notation is the usual way of writing numbers.

Q: How do I know when to use scientific notation?

A: You should use scientific notation when working with very large or very small numbers, or when you need to simplify calculations and make it easier to understand complex concepts.

Q: Can I use scientific notation with negative numbers?

A: Yes, you can use scientific notation with negative numbers. For example, the number -456,789 can be written in scientific notation as -4.56789 × 10^5.

Q: Can I use scientific notation with fractions?

A: Yes, you can use scientific notation with fractions. For example, the fraction 3/4 can be written in scientific notation as 0.75 × 10^0.

Example Use Cases

Scientific notation is commonly used in mathematics, physics, and engineering to simplify calculations and make it easier to understand complex concepts. Here are a few example use cases:

  • Calculating the distance between two stars in astronomy
  • Measuring the speed of a particle in physics
  • Expressing the amount of a substance in chemistry

Tips and Tricks

  • When working with scientific notation, make sure to keep the same power of 10.
  • Use the rules of scientific notation to simplify calculations and make it easier to understand complex concepts.
  • Practice evaluating expressions in scientific notation to become more comfortable with the concept.