What Is The Value Of $12.5 \times 10^7$?A. $1,250,000$ B. $125,000,000$ C. $1.2500000$ D. $12.5000000$

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Understanding the Concept of 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. In the given problem, we have the number $12.5$ multiplied by $10^7$. To find the value of this expression, we need to understand the concept of scientific notation and how to multiply numbers in this form.

Multiplying Numbers in Scientific Notation

When multiplying numbers in scientific notation, we multiply the numbers and add the exponents of the powers of 10. In this case, we have $12.5 \times 10^7$. To find the value of this expression, we need to multiply $12.5$ by $10^7$.

Calculating the Value

To calculate the value of $12.5 \times 10^7$, we can start by multiplying $12.5$ by $10^7$. Since $10^7$ is equal to $10,000,000$, we can rewrite the expression as $12.5 \times 10,000,000$. Multiplying $12.5$ by $10,000,000$ gives us $125,000,000$.

Understanding the Answer Choices

Now that we have calculated the value of $12.5 \times 10^7$, we can compare it to the answer choices. The answer choices are $1,250,000$, $125,000,000$, $1.2500000$, and $12.5000000$. We can see that the correct answer is $125,000,000$.

Conclusion

In conclusion, the value of $12.5 \times 10^7$ is $125,000,000$. This is because when multiplying numbers in scientific notation, we multiply the numbers and add the exponents of the powers of 10. In this case, we had $12.5 \times 10^7$, which is equal to $125,000,000$.

Frequently Asked Questions

  • What is the value of $12.5 \times 10^7$?
  • How do we multiply numbers in scientific notation?
  • What is the correct answer choice for the value of $12.5 \times 10^7$?

Step-by-Step Solution

  1. Understand the concept of scientific notation and how to multiply numbers in this form.
  2. Multiply $12.5$ by $10^7$.
  3. Rewrite $10^7$ as $10,000,000$.
  4. Multiply $12.5$ by $10,000,000$.
  5. Compare the calculated value to the answer choices.

Common Mistakes to Avoid

  • Not understanding the concept of scientific notation.
  • Not multiplying the numbers correctly.
  • Not adding the exponents of the powers of 10 correctly.

Real-World Applications

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

  • Calculating large distances or speeds.
  • Expressing very small or very large numbers.
  • Performing calculations in physics, engineering, and other fields.

Tips and Tricks

  • Make sure to understand the concept of scientific notation before attempting to multiply numbers in this form.
  • Use the correct exponent when multiplying numbers in scientific notation.
  • Compare the calculated value to the answer choices to ensure accuracy.

Conclusion

In conclusion, the value of $12.5 \times 10^7$ is $125,000,000$. This is because when multiplying numbers in scientific notation, we multiply the numbers and add the exponents of the powers of 10. By following the steps outlined in this article, you can accurately calculate the value of any expression in scientific notation.