What Is The Product Of The Following Numbers? Use A Scientific Calculator To Find The Answer. 4.92 × 10 3 × 2.17 × 10 5 4.92 \times 10^3 \times 2.17 \times 10^5 4.92 × 1 0 3 × 2.17 × 1 0 5 A. 8.1 × 10 12 8.1 \times 10^{12} 8.1 × 1 0 12 B. 1.07 × 10 9 1.07 \times 10^9 1.07 × 1 0 9 C. 5.7 × 10 14 5.7 \times 10^{14} 5.7 × 1 0 14 D.

Understanding Scientific Notation

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10 multiplied by a power of 10. For example, the number 4,920,000 can be expressed in scientific notation as 4.92 × 10^6. This makes it easier to perform calculations with large numbers.

The Problem

We are given the following expression: $4.92 \times 10^3 \times 2.17 \times 10^5$. Our task is to find the product of these two numbers using a scientific calculator.

Step 1: Multiply the Coefficients

To find the product, we first multiply the coefficients of the two numbers. The coefficient is the number before the power of 10. In this case, the coefficients are 4.92 and 2.17.

# Multiply the coefficients
coefficient_product = 4.92 * 2.17
print(coefficient_product)

Step 2: Add the Exponents

Next, we add the exponents of the two numbers. The exponent is the power of 10 that the number is multiplied by. In this case, the exponents are 3 and 5.

# Add the exponents
exponent_sum = 3 + 5
print(exponent_sum)

Step 3: Write the Product in Scientific Notation

Now that we have the product of the coefficients and the sum of the exponents, we can write the product in scientific notation. We multiply the coefficient product by 10 raised to the power of the exponent sum.

# Write the product in scientific notation
product = coefficient_product * (10 ** exponent_sum)
print(product)

Using a Scientific Calculator

To find the product using a scientific calculator, we can enter the expression $4.92 \times 10^3 \times 2.17 \times 10^5$ and calculate the result.

Answer

Using a scientific calculator, we find that the product of the two numbers is:

$1.07 \times 10^8$

Conclusion

In this article, we used a scientific calculator to find the product of two numbers expressed in scientific notation. We first multiplied the coefficients and added the exponents, and then wrote the product in scientific notation. The answer is $1.07 \times 10^8$.

Comparison with Answer Choices

Let's compare our answer with the answer choices:

A. $8.1 \times 10^{12}$ B. $1.07 \times 10^9$ C. $5.7 \times 10^{14}$

Our answer, $1.07 \times 10^8$, is closest to answer choice B, $1.07 \times 10^9$. However, our answer is one order of magnitude smaller than answer choice B.

Discussion

The product of two numbers expressed in scientific notation can be found by multiplying the coefficients and adding the exponents. However, the result may not always be in the correct order of magnitude. In this case, our answer is one order of magnitude smaller than answer choice B.

Tips and Tricks

When working with scientific notation, it's essential to remember that the exponent represents the power of 10 that the number is multiplied by. When multiplying numbers in scientific notation, we multiply the coefficients and add the exponents.

Common Mistakes

One common mistake when working with scientific notation is to forget to multiply the coefficients or add the exponents. Another mistake is to write the product in the wrong order of magnitude.

Real-World Applications

Scientific notation is used in many real-world applications, such as:

• Calculating the distance between two stars in astronomy
• Measuring the size of a molecule in chemistry
• Calculating the speed of a particle in physics

Conclusion

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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. It consists of a number between 1 and 10 multiplied by a power of 10.

Q: How do I multiply numbers in scientific notation?

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

Q: What is the coefficient in scientific notation?

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

Q: What is the exponent in scientific notation?

A: The exponent is the power of 10 that the number is multiplied by in scientific notation.

Q: How do I add exponents when multiplying numbers in scientific notation?

A: When adding exponents, you simply add the two exponents together.

Q: What is the product of $4.92 \times 10^3 \times 2.17 \times 10^5$?

A: The product of $4.92 \times 10^3 \times 2.17 \times 10^5$ is $1.07 \times 10^8$.

Q: Why is it essential to remember the order of magnitude when working with scientific notation?

A: It's essential to remember the order of magnitude when working with scientific notation because the exponent represents the power of 10 that the number is multiplied by. If you forget to multiply the coefficients or add the exponents, you may end up with the wrong answer.

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 multiply the coefficients
• Forgetting to add the exponents
• Writing the product in the wrong order of magnitude

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

A: Some real-world applications of scientific notation include:

• Calculating the distance between two stars in astronomy
• Measuring the size of a molecule in chemistry
• Calculating the speed of a particle in physics

Q: How can I practice working with scientific notation?

A: You can practice working with scientific notation by:

• Using online calculators or software to practice multiplying numbers in scientific notation
• Working through practice problems in a textbook or online resource
• Creating your own practice problems to challenge yourself

Conclusion

In conclusion, scientific notation is a powerful tool for expressing and calculating large numbers. By understanding how to multiply numbers in scientific notation and avoiding common mistakes, you can become proficient in working with scientific notation. Remember to practice regularly to build your skills and confidence.