Evaluate The Expression And Express Your Answer In Scientific Notation:$7.03 \times 10^4 - 5.78 \times 10^3$

Mar 12, 2025 by ADMIN 111 views

Evaluate the Expression and Express Your Answer in Scientific Notation

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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 a method of expressing numbers as a product of a number between 1 and 10 and a power of 10. In this article, we will evaluate the given expression and express the answer in scientific notation.

Understanding the Expression

The given expression is:

7.03 \times 10^4 - 5.78 \times 10^3

This expression involves two terms, each of which is a product of a number and a power of 10. The first term is $7.03 \times 10^4$ , and the second term is $5.78 \times 10^3$ .

Evaluating the Expression

To evaluate the expression, we need to subtract the second term from the first term. However, since the powers of 10 are different, we need to adjust the second term to have the same power of 10 as the first term.

We can do this by multiplying the second term by $10^1$ , which is equal to 10. This gives us:

5.78 \times 10^3 \times 10^1 = 5.78 \times 10^4

Now we can subtract the two terms:

7.03 \times 10^4 - 5.78 \times 10^4 = 1.25 \times 10^4

Expressing the Answer in Scientific Notation

The answer we obtained is $1.25 \times 10^4$ . This is already in scientific notation, so we don't need to do anything further.

Conclusion

In this article, we evaluated the given expression and expressed the answer in scientific notation. We used the rules of scientific notation to adjust the second term to have the same power of 10 as the first term, and then subtracted the two terms. The final answer was $1.25 \times 10^4$ .

Tips for Evaluating Expressions in Scientific Notation

When evaluating expressions in scientific notation, it's essential to follow these tips:

Make sure to adjust the terms to have the same power of 10 before subtracting or adding them.
Use the rules of scientific notation to simplify the expression.
Be careful when multiplying or dividing terms in scientific notation.

Common Mistakes to Avoid

When evaluating expressions in scientific notation, it's easy to make mistakes. Here are some common mistakes to avoid:

Failing to adjust the terms to have the same power of 10 before subtracting or adding them.
Not using the rules of scientific notation to simplify the expression.
Making errors when multiplying or dividing terms in scientific notation.

Real-World Applications

Scientific notation has many real-world applications. Here are a few examples:

In physics, scientific notation is used to express large or small numbers, such as the speed of light or the Planck constant.
In chemistry, scientific notation is used to express the concentrations of solutions or the amounts of substances.
In engineering, scientific notation is used to express large or small numbers, such as the dimensions of buildings or the capacities of tanks.

Conclusion

In conclusion, evaluating expressions in scientific notation requires careful attention to the rules of scientific notation. By following these rules and avoiding common mistakes, you can simplify complex expressions and obtain accurate results. Scientific notation has many real-world applications, and it's an essential tool for scientists, engineers, and mathematicians.

Frequently Asked Questions

Here are some frequently asked questions about evaluating expressions in scientific notation:

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 expressions in scientific notation? A: To evaluate expressions in scientific notation, you need to follow the rules of scientific notation and adjust the terms to have the same power of 10 before subtracting or adding them.
Q: What are some common mistakes to avoid when evaluating expressions in scientific notation? A: Some common mistakes to avoid when evaluating expressions in scientific notation include failing to adjust the terms to have the same power of 10, not using the rules of scientific notation to simplify the expression, and making errors when multiplying or dividing terms in scientific notation.

References

Here are some references for further reading on evaluating expressions in scientific notation:

"Scientific Notation" by Math Is Fun: This article provides a comprehensive introduction to scientific notation and its applications.
"Evaluating Expressions in Scientific Notation" by Khan Academy: This video tutorial provides a step-by-step guide to evaluating expressions in scientific notation.
"Scientific Notation: A Guide for Scientists and Engineers" by the National Institute of Standards and Technology: This guide provides a detailed overview of scientific notation and its applications in science and engineering.

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Introduction

Evaluating expressions in scientific notation can be a challenging task, especially for those who are new to the concept. In this article, we will provide a comprehensive Q&A guide to help you understand and evaluate expressions in scientific notation.

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 a method of expressing numbers as a product of a number between 1 and 10 and a power of 10.

Q: How do I evaluate expressions in scientific notation?

A: To evaluate expressions in scientific notation, you need to follow the rules of scientific notation and adjust the terms to have the same power of 10 before subtracting or adding them. Here are the steps to follow:

Identify the terms in the expression that need to be evaluated.
Adjust the terms to have the same power of 10.
Subtract or add the terms as needed.
Simplify the expression by combining like terms.

Q: What are some common mistakes to avoid when evaluating expressions in scientific notation?

A: Some common mistakes to avoid when evaluating expressions in scientific notation include:

Failing to adjust the terms to have the same power of 10 before subtracting or adding them.
Not using the rules of scientific notation to simplify the expression.
Making errors when multiplying or dividing terms in scientific notation.

Q: How do I multiply or divide terms in scientific notation?

A: To multiply or divide terms in scientific notation, you need to follow the rules of exponents. Here are the steps to follow:

When multiplying terms, add the exponents.
When dividing terms, subtract the exponents.

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

A: Scientific notation and standard notation are two different ways of expressing numbers. Standard notation is the way we normally write numbers, while scientific notation is a way of expressing very large or very small numbers in a more manageable form.

Q: When should I use scientific notation?

A: You should use scientific notation when:

You need to express very large or very small numbers.
You need to simplify complex expressions.
You need to make calculations easier.

Q: What are some real-world applications of scientific notation?

A: Scientific notation has many real-world applications, including:

In physics, scientific notation is used to express large or small numbers, such as the speed of light or the Planck constant.
In chemistry, scientific notation is used to express the concentrations of solutions or the amounts of substances.
In engineering, scientific notation is used to express large or small numbers, such as the dimensions of buildings or the capacities of tanks.

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

A: To convert a number from standard notation to scientific notation, you need to follow these steps:

Move the decimal point to the left until you have a number between 1 and 10.
Count the number of places you moved the decimal point.
Write the number in scientific notation, with the number between 1 and 10 and the power of 10.

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 follow these steps:

Multiply the number between 1 and 10 by the power of 10.
Move the decimal point to the right by the number of places indicated by the power of 10.

Conclusion

Frequently Asked Questions

Here are some frequently asked questions about evaluating expressions in scientific notation:

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 expressions in scientific notation? A: To evaluate expressions in scientific notation, you need to follow the rules of scientific notation and adjust the terms to have the same power of 10 before subtracting or adding them.
Q: What are some common mistakes to avoid when evaluating expressions in scientific notation? A: Some common mistakes to avoid when evaluating expressions in scientific notation include failing to adjust the terms to have the same power of 10, not using the rules of scientific notation to simplify the expression, and making errors when multiplying or dividing terms in scientific notation.

References

Here are some references for further reading on evaluating expressions in scientific notation:

"Scientific Notation" by Math Is Fun: This article provides a comprehensive introduction to scientific notation and its applications.
"Evaluating Expressions in Scientific Notation" by Khan Academy: This video tutorial provides a step-by-step guide to evaluating expressions in scientific notation.
"Scientific Notation: A Guide for Scientists and Engineers" by the National Institute of Standards and Technology: This guide provides a detailed overview of scientific notation and its applications in science and engineering.