Use Division Of Numbers In Scientific Notation To Answer The Question.${ \frac{8.64 \times 10^4}{2.4 \times 10^2} }$What Is The Quotient In Scientific Notation?A. ${ 3.6 \times 10^2\$} B. ${ 6.24 \times 10^2\$} C.

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Introduction

Scientific notation is a powerful tool used to express very large or very small numbers in a compact and manageable form. It is widely used in various fields, including physics, chemistry, engineering, and mathematics. In this article, we will focus on the division of numbers in scientific notation and provide a step-by-step guide on how to solve the given problem.

Understanding Scientific Notation

Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10. For example, the number 456,000 can be written in scientific notation as 4.56 × 10^5. The exponent, in this case, 5, indicates the power of 10 to which the number should be raised.

Division of Numbers in Scientific Notation

When dividing numbers in scientific notation, we need to follow a specific set of rules. The rules are as follows:

  1. Divide the coefficients (the numbers in front of the exponents) as you would normally divide numbers.
  2. Subtract the exponents of the two numbers.

Step-by-Step Solution

Now, let's apply these rules to the given problem:

8.64×1042.4×102{ \frac{8.64 \times 10^4}{2.4 \times 10^2} }

Step 1: Divide the Coefficients

To divide the coefficients, we simply divide 8.64 by 2.4.

8.64 ÷ 2.4 = 3.6

Step 2: Subtract the Exponents

Next, we subtract the exponents of the two numbers.

10^4 ÷ 10^2 = 10^(4-2) = 10^2

Step 3: Write the Quotient in Scientific Notation

Now that we have the quotient of the coefficients and the result of the exponent subtraction, we can write the quotient in scientific notation.

3.6 × 10^2

Conclusion

In conclusion, dividing numbers in scientific notation involves dividing the coefficients and subtracting the exponents. By following these simple rules, we can easily solve problems involving division in scientific notation.

Answer

The correct answer is:

3.6×102{ 3.6 \times 10^2 }

This is option A.

Additional Examples

To reinforce your understanding of division in scientific notation, let's consider a few more examples.

Example 1

9.2×1034.8×101{ \frac{9.2 \times 10^3}{4.8 \times 10^1} }

Step 1: Divide the Coefficients

9.2 ÷ 4.8 = 1.92

Step 2: Subtract the Exponents

10^3 ÷ 10^1 = 10^(3-1) = 10^2

Step 3: Write the Quotient in Scientific Notation

1.92 × 10^2

Example 2

6.4×1022.1×103{ \frac{6.4 \times 10^2}{2.1 \times 10^3} }

Step 1: Divide the Coefficients

6.4 ÷ 2.1 = 3.05

Step 2: Subtract the Exponents

10^2 ÷ 10^3 = 10^(2-3) = 10^(-1)

Step 3: Write the Quotient in Scientific Notation

3.05 × 10^(-1)

Example 3

4.8×1041.2×102{ \frac{4.8 \times 10^4}{1.2 \times 10^2} }

Step 1: Divide the Coefficients

4.8 ÷ 1.2 = 4

Step 2: Subtract the Exponents

10^4 ÷ 10^2 = 10^(4-2) = 10^2

Step 3: Write the Quotient in Scientific Notation

4 × 10^2

These examples demonstrate how to divide numbers in scientific notation by following the simple rules of dividing the coefficients and subtracting the exponents.

Final Thoughts

Q: What is scientific notation?

A: Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10. For example, the number 456,000 can be written in scientific notation as 4.56 × 10^5.

Q: How do I divide numbers in scientific notation?

A: To divide numbers in scientific notation, you need to follow these steps:

  1. Divide the coefficients (the numbers in front of the exponents) as you would normally divide numbers.
  2. Subtract the exponents of the two numbers.

Q: What if the exponents are the same?

A: If the exponents are the same, you can simply divide the coefficients and keep the same exponent.

Q: What if the exponents are different?

A: If the exponents are different, you need to subtract the exponents of the two numbers.

Q: Can I use a calculator to divide numbers in scientific notation?

A: Yes, you can use a calculator to divide numbers in scientific notation. However, make sure to enter the numbers in scientific notation correctly, with the coefficient and exponent separated by a multiplication sign.

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

A: To write the quotient in scientific notation, you need to multiply the result of the coefficient division by the result of the exponent subtraction.

Q: What if the quotient is a very large or very small number?

A: If the quotient is a very large or very small number, you can express it in scientific notation by using a coefficient between 1 and 10 and a power of 10.

Q: Can I use division in scientific notation to solve real-world problems?

A: Yes, division in scientific notation can be used to solve a wide range of real-world problems, including problems in physics, chemistry, engineering, and mathematics.

Q: What are some common mistakes to avoid when dividing numbers in scientific notation?

A: Some common mistakes to avoid when dividing numbers in scientific notation include:

  • Forgetting to divide the coefficients
  • Forgetting to subtract the exponents
  • Entering the numbers in scientific notation incorrectly
  • Not using a calculator to check the result

Q: How can I practice dividing numbers in scientific notation?

A: You can practice dividing numbers in scientific notation by working through examples and exercises, such as the ones provided in this article. You can also use online resources and calculators to help you practice.

Q: What are some advanced topics related to division in scientific notation?

A: Some advanced topics related to division in scientific notation include:

  • Multiplication and division of numbers in scientific notation with different exponents
  • Exponents and logarithms
  • Scientific notation and significant figures
  • Applications of scientific notation in real-world problems

By understanding the basics of division in scientific notation and practicing with examples and exercises, you can become proficient in using this powerful tool to solve a wide range of problems in mathematics, physics, chemistry, and engineering.