Understanding the Concept of Scientific Notation

Oct 13, 2025 by thesweetdesigns.com 36 views

**What is the Value of $12.5 \times 10^7$?**

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 $12.5 \times 10^7$ . To find the value of this expression, we need to understand the concept of scientific notation and how to multiply numbers in this form.

Q: What is the value of $12.5 \times 10^7$ ?

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

Q: How do I multiply numbers in scientific notation?

A: To multiply numbers in scientific notation, we follow these steps:

Multiply the numbers: Multiply the numbers in front of the powers of 10.
Add the exponents: Add the exponents of the powers of 10.
Write the result in scientific notation: Write the result in the form $a \times 10^b$ , where $a$ is the product of the numbers and $b$ is the sum of the exponents.

Q: Can you show me an example of how to multiply numbers in scientific notation?

A: Let's consider the example $4.2 \times 10^3 \times 2.5 \times 10^4$ . To multiply these numbers, we follow the steps above:

Multiply the numbers: $4.2 \times 2.5 = 10.5$
Add the exponents: $3 + 4 = 7$
Write the result in scientific notation: $10.5 \times 10^7$

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

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

Multiply the number by the power of 10: Multiply the number in front of the power of 10 by the power of 10.
Write the result in standard form: Write the result in the form $a.b$ , where $a$ is the product of the number and the power of 10, and $b$ is the decimal part.

Q: Can you show me an example of how to convert a number from scientific notation to standard form?

A: Let's consider the example $3.4 \times 10^5$ . To convert this number to standard form, we follow the steps above:

Multiply the number by the power of 10: $3.4 \times 10^5 = 340,000$
Write the result in standard form: $340,000$

Q: What is the value of $12.5 \times 10^7$ ?

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

$12.5 \times 10^7 = 12.5 \times 10^7 = 125,000,000$

Conclusion

In this article, we have discussed the concept of scientific notation and how to multiply numbers in this form. We have also provided examples of how to multiply numbers in scientific notation and how to convert a number from scientific notation to standard form. Finally, we have found the value of $12.5 \times 10^7$ .

Key Takeaways

Scientific notation is a way of expressing very large or very small numbers in a more manageable form.
To multiply numbers in scientific notation, we multiply the numbers and add the exponents of the powers of 10.
To convert a number from scientific notation to standard form, we multiply the number by the power of 10 and write the result in the form $a.b$ .

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 multiply numbers in scientific notation? A: To multiply numbers in scientific notation, we multiply the numbers and add the exponents of the powers of 10.
Q: Can you show me an example of how to multiply numbers in scientific notation? A: Let's consider the example $4.2 \times 10^3 \times 2.5 \times 10^4$ . To multiply these numbers, we follow the steps above.
Q: How do I convert a number from scientific notation to standard form? A: To convert a number from scientific notation to standard form, we multiply the number by the power of 10 and write the result in the form $a.b$ .

Recommended Resources

Khan Academy: Scientific Notation
Mathway: Scientific Notation
Wolfram Alpha: Scientific Notation

Final Thoughts

In conclusion, scientific notation is a powerful tool for expressing very large or very small numbers in a more manageable form. By understanding how to multiply numbers in scientific notation and how to convert a number from scientific notation to standard form, we can solve a wide range of mathematical problems. We hope this article has been helpful in understanding the concept of scientific notation and how to apply it in real-world problems.