Writing the Answer in Scientific Notation

Oct 13, 2025 by thesweetdesigns.com 32 views

Introduction

When it comes to measuring the length of a football field, we often use standard units such as inches or yards. However, in scientific notation, we can express large numbers in a more compact and manageable form. In this article, we will explore how to express the length of a football field, which is 4,320 inches, in scientific notation.

What is Scientific Notation?

Scientific notation is a way of expressing very large or very small numbers in a more compact form. It consists of a number between 1 and 10, multiplied by a power of 10. The power of 10 is usually expressed as an exponent, which indicates the number of places to move the decimal point.

Expressing 4,320 in Scientific Notation

To express 4,320 in scientific notation, we need to move the decimal point to the left until we have a number between 1 and 10. In this case, we can move the decimal point 4 places to the left, resulting in 0.432. Since we moved the decimal point 4 places to the left, we need to multiply 0.432 by 10^4 to get back to the original number.

Calculating the Exponent

The exponent in scientific notation is the number of places we moved the decimal point. In this case, we moved the decimal point 4 places to the left, so the exponent is 4.

Writing the Answer in Scientific Notation

Now that we have the number and the exponent, we can write the answer in scientific notation. The correct answer is:

4.32 × 10^4

Comparing the Answer to the Options

Let's compare our answer to the options provided:

A. 4.32 × 10^4
B. 4.32 × 10^7
C. 4.32 × 10^3
D. 4.32 × 10^5

Our answer matches option A, which is 4.32 × 10^4.

Conclusion

In conclusion, expressing the length of a football field, which is 4,320 inches, in scientific notation requires moving the decimal point to the left until we have a number between 1 and 10, and then multiplying that number by a power of 10. The correct answer is 4.32 × 10^4.

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 compact form.

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

A: To express a number in scientific notation, move the decimal point to the left until you have a number between 1 and 10, and then multiply that number by a power of 10.

Q: What is the exponent in scientific notation?

A: The exponent in scientific notation is the number of places you moved the decimal point.

Q: How do I write the answer in scientific notation?

A: To write the answer in scientific notation, combine the number and the exponent, with the number between 1 and 10 and the exponent as a power of 10.

Additional Resources

For more information on scientific notation, check out the following resources:

Wikipedia: Scientific notation
Math is Fun: Scientific notation
Khan Academy: Scientific notation
Scientific Notation Q&A ==========================

Q: What is the purpose of scientific notation?

A: The purpose of scientific notation is to express very large or very small numbers in a more compact and manageable form. It makes it easier to perform calculations and comparisons with numbers that have many digits.

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

A: To convert a number to scientific notation, 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. This will be the exponent.
Write the number with the decimal point moved to the left, followed by the exponent in the form 10^n.

Q: What is the exponent in scientific notation?

A: The exponent in scientific notation is the number of places you moved the decimal point. It indicates the power of 10 to multiply the number by.

Q: How do I multiply numbers in scientific notation?

A: To multiply numbers in scientific notation, multiply the numbers and add the exponents.

Example: (3.4 × 10^2) × (2.1 × 10^3)

Multiply the numbers: 3.4 × 2.1 = 7.14 Add the exponents: 2 + 3 = 5 Write the result in scientific notation: 7.14 × 10^5

Q: How do I divide numbers in scientific notation?

A: To divide numbers in scientific notation, divide the numbers and subtract the exponents.

Example: (3.4 × 10^2) ÷ (2.1 × 10^3)

Divide the numbers: 3.4 ÷ 2.1 = 1.62 Subtract the exponents: 2 - 3 = -1 Write the result in scientific notation: 1.62 × 10^(-1)

Q: Can I have a negative exponent in scientific notation?

A: Yes, you can have a negative exponent in scientific notation. A negative exponent indicates that the decimal point should be moved to the right instead of the left.

Example: 4.2 × 10^(-3)

Move the decimal point 3 places to the right: 0.0042 Write the result in scientific notation: 4.2 × 10^(-3)

Q: Can I have a zero exponent in scientific notation?

A: Yes, you can have a zero exponent in scientific notation. A zero exponent indicates that the number should be written as 1.

Example: 4.2 × 10^0

Write the result in scientific notation: 4.2

Q: What are some common applications of scientific notation?

A: Scientific notation is commonly used in:

Physics and engineering to express large or small numbers
Chemistry to express the concentration of solutions
Biology to express the size of cells or other biological structures
Computer science to express large or small numbers in programming

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

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

Multiply the number by 10 raised to the power of the exponent.
Move the decimal point to the right by the number of places indicated by the exponent.

Example: 4.2 × 10^3

Multiply the number by 10^3: 4.2 × 1000 = 4200 Move the decimal point 3 places to the right: 4200

Write the result in standard notation: 4200