Select The Best Answer For The Question.1. What Is The Value Of 12.5 × 10 7 12.5 \times 10^7 12.5 × 1 0 7 ?A. 1,250,000 B. 125,000,000 C. 1.2500000 D. 12.5000000

When dealing with exponential expressions, it's essential to understand the concept of scientific notation and how to evaluate expressions that involve multiplication and powers of 10. In this article, we'll explore the value of $12.5 \times 10^7$ and help you select the best answer from the given options.

What is Scientific Notation?

Scientific notation is a way of expressing very large or very small numbers in a compact form. It consists of a number between 1 and 10, multiplied by a power of 10. For example, the number 100 can be written as $1 \times 10^2$, and the number 0.01 can be written as $1 \times 10^{-2}$.

Evaluating Exponential Expressions

To evaluate an exponential expression, we need to multiply the coefficient (the number in front of the power of 10) by the power of 10. In the case of $12.5 \times 10^7$, we have a coefficient of 12.5 and a power of 10 raised to the 7th power.

Step 1: Multiply the Coefficient by the Power of 10

To evaluate the expression, we need to multiply 12.5 by $10^7$. This can be done by moving the decimal point in 12.5 seven places to the right, resulting in 125,000,000.

Step 2: Write the Result in Standard Form

The result of multiplying 12.5 by $10^7$ is 125,000,000. This is the value of the expression $12.5 \times 10^7$.

Selecting the Best Answer

Based on our evaluation of the expression, we can select the best answer from the given options. The correct answer is:

B. 125,000,000

This is the value of $12.5 \times 10^7$.

Conclusion

In this article, we explored the value of $12.5 \times 10^7$ and helped you understand how to evaluate exponential expressions. We used scientific notation to express the number 12.5 in a compact form and then multiplied it by the power of 10 to get the final result. By following these steps, you can evaluate any exponential expression and select the best answer from the given options.

Frequently Asked Questions

• Q: What is the value of $12.5 \times 10^7$? A: The value of $12.5 \times 10^7$ is 125,000,000.
• Q: How do I evaluate an exponential expression? A: To evaluate an exponential expression, multiply the coefficient by the power of 10.
• Q: What is scientific notation? A: Scientific notation is a way of expressing very large or very small numbers in a compact form.

Additional Resources

• Scientific Notation Tutorial
• Exponential Expressions Tutorial
• Mathematics Formulas and Equations
  Q&A: Exponential Expressions and Scientific Notation =====================================================

In our previous article, we explored the value of $12.5 \times 10^7$ and helped you understand how to evaluate exponential expressions using scientific notation. In this article, we'll answer some frequently asked questions about exponential expressions and scientific notation.

Q: What is the difference between exponential expressions and scientific notation?

A: Exponential expressions and scientific notation are related but distinct concepts. Exponential expressions involve the use of exponents to represent repeated multiplication, while scientific notation is a way of expressing very large or very small numbers in a compact form.

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

A: To convert a number to scientific notation, you need to express it as a number between 1 and 10, multiplied by a power of 10. For example, the number 100 can be written as $1 \times 10^2$, and the number 0.01 can be written as $1 \times 10^{-2}$.

Q: What is the rule for multiplying exponential expressions?

A: When multiplying exponential expressions, you need to add the exponents. For example, $(2 \times 10^3) \times (3 \times 10^4) = 6 \times 10^7$.

Q: How do I divide exponential expressions?

A: When dividing exponential expressions, you need to subtract the exponents. For example, $(2 \times 10^3) \div (3 \times 10^4) = \frac{2}{3} \times 10^{-1}$.

Q: What is the rule for raising a power to a power?

A: When raising a power to a power, you need to multiply the exponents. For example, $(2 \times 10^3)^4 = 2^4 \times 10^{12}$.

Q: How do I evaluate an expression with multiple exponential terms?

A: To evaluate an expression with multiple exponential terms, you need to follow the order of operations (PEMDAS):

1. Evaluate any expressions inside parentheses.
2. Evaluate any exponential expressions.
3. Multiply and divide from left to right.
4. Add and subtract from left to right.

Q: What are some common mistakes to avoid when working with exponential expressions?

A: Some common mistakes to avoid when working with exponential expressions include:

• Forgetting to multiply or divide exponential expressions correctly.
• Not following the order of operations (PEMDAS).
• Not using scientific notation correctly.

Q: How can I practice working with exponential expressions and scientific notation?

A: You can practice working with exponential expressions and scientific notation by:

• Using online resources and calculators to evaluate expressions.
• Working through practice problems and exercises.
• Creating your own problems and solutions.

Conclusion

In this article, we answered some frequently asked questions about exponential expressions and scientific notation. We hope this helps you better understand these concepts and how to apply them in your math studies.

Frequently Asked Questions

• Q: What is the value of $12.5 \times 10^7$? A: The value of $12.5 \times 10^7$ is 125,000,000.
• Q: How do I evaluate an exponential expression? A: To evaluate an exponential expression, multiply the coefficient by the power of 10.
• Q: What is scientific notation? A: Scientific notation is a way of expressing very large or very small numbers in a compact form.

Additional Resources

• Scientific Notation Tutorial
• Exponential Expressions Tutorial
• Mathematics Formulas and Equations