What Is The Value Of $12.5 \times 10^7$?A. $1,250,000$ B. 125000000 C. \$125,000,000$[/tex\] D. 12500000
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 expression $12.5 \times 10^7$. To evaluate 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 coefficients (the numbers before the powers of 10) and add the exponents of the powers of 10. In this case, we have $12.5 \times 10^7$. To evaluate this expression, we need to multiply 12.5 by $10^7$.
Evaluating the Expression
To evaluate the expression $12.5 \times 10^7$, we can start by multiplying 12.5 by $10^7$. We can rewrite $10^7$ as 10,000,000. Then, we can multiply 12.5 by 10,000,000.
Conclusion
Therefore, the value of $12.5 \times 10^7$ is 125,000,000.
Common Mistakes to Avoid
When evaluating expressions in scientific notation, it's easy to make mistakes. Here are some common mistakes to avoid:
- Not 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's essential to understand this concept before evaluating expressions in scientific notation.
- Not multiplying the coefficients correctly: When multiplying numbers in scientific notation, we multiply the coefficients and add the exponents of the powers of 10. It's essential to multiply the coefficients correctly to get the correct answer.
- Not adding the exponents correctly: When multiplying numbers in scientific notation, we add the exponents of the powers of 10. It's essential to add the exponents correctly to get the correct answer.
Real-World Applications
Scientific notation has many real-world applications. Here are a few examples:
- Physics and engineering: Scientific notation is used to express large or small numbers in physics and engineering. For example, the speed of light is approximately 299,792,458 meters per second, which can be expressed in scientific notation as $3.00 \times 10^8$ meters per second.
- Chemistry: Scientific notation is used to express large or small numbers in chemistry. For example, the Avogadro's number is approximately 6.02214076 × 10^23, which can be expressed in scientific notation as $6.022 \times 10^{23}$.
- Computer science: Scientific notation is used to express large or small numbers in computer science. For example, the number of bytes in a gigabyte is approximately 1,073,741,824, which can be expressed in scientific notation as $1.07 \times 10^9$.
Conclusion
In conclusion, the value of $12.5 \times 10^7$ is 125,000,000. Scientific notation is a powerful tool for expressing large or small numbers in a more manageable form. It's essential to understand the concept of scientific notation and how to multiply numbers in this form to evaluate expressions correctly.
Frequently Asked Questions
Here are some frequently asked questions about scientific notation:
- What is 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.
- How do I multiply numbers in scientific notation?: When multiplying numbers in scientific notation, we multiply the coefficients and add the exponents of the powers of 10.
- What are some real-world applications of scientific notation?: Scientific notation has many real-world applications, including physics and engineering, chemistry, and computer science.
Final Thoughts
In conclusion, the value of $12.5 \times 10^7$ is 125,000,000. Scientific notation is a powerful tool for expressing large or small numbers in a more manageable form. It's essential to understand the concept of scientific notation and how to multiply numbers in this form to evaluate expressions correctly.
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 express a number in scientific notation?
A: To express a number in scientific notation, you need to move the decimal point to the left or right until you have a number between 1 and 10. Then, you need to multiply the number by a power of 10.
Q: What is the exponent in scientific notation?
A: The exponent in scientific notation is the power of 10 that the number is multiplied by. For example, in the number $3.5 \times 10^4$, the exponent is 4.
Q: How do I multiply numbers in scientific notation?
A: When multiplying numbers in scientific notation, you need to multiply the coefficients (the numbers before the powers of 10) and add the exponents of the powers of 10.
Q: How do I divide numbers in scientific notation?
A: When dividing numbers in scientific notation, you need to divide the coefficients and subtract the exponents of the powers of 10.
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:
- Not understanding the concept of scientific notation
- Not multiplying the coefficients correctly
- Not adding the exponents correctly
- Not subtracting the exponents correctly when dividing
Q: What are some real-world applications of scientific notation?
A: Scientific notation has many real-world applications, including:
- Physics and engineering
- Chemistry
- Computer science
- Astronomy
- Mathematics
Q: How do I convert a number from scientific notation to standard notation?
A: To convert a number from scientific notation to standard notation, you need to multiply the number by the power of 10 that it is multiplied by.
Q: How do I convert a number from standard notation to scientific notation?
A: To convert a number from standard notation to scientific notation, you need to move the decimal point to the left or right until you have a number between 1 and 10, and then multiply the number by a power of 10.
Q: What is the difference between scientific notation and exponential notation?
A: Scientific notation and exponential notation are both ways of expressing very large or very small numbers in a more manageable form. However, scientific notation is typically used to express numbers in a more compact form, while exponential notation is typically used to express numbers in a more general form.
Q: How do I use a calculator to evaluate expressions in scientific notation?
A: To use a calculator to evaluate expressions in scientific notation, you need to enter the expression in the calculator and use the scientific notation function to evaluate it.
Q: What are some tips for working with scientific notation?
A: Some tips for working with scientific notation include:
- Understanding the concept of scientific notation
- Practicing multiplying and dividing numbers in scientific notation
- Using a calculator to evaluate expressions in scientific notation
- Converting numbers between scientific notation and standard notation
Q: How do I use scientific notation in real-world applications?
A: Scientific notation is used in many real-world applications, including:
- Physics and engineering
- Chemistry
- Computer science
- Astronomy
- Mathematics
Q: What are some common uses of scientific notation in everyday life?
A: Scientific notation is used in many everyday applications, including:
- Measuring distances and speeds
- Calculating areas and volumes
- Working with large or small numbers
- Using calculators and computers
Q: How do I teach scientific notation to students?
A: To teach scientific notation to students, you can use a variety of methods, including:
- Using real-world examples
- Practicing multiplying and dividing numbers in scientific notation
- Using calculators and computers to evaluate expressions in scientific notation
- Converting numbers between scientific notation and standard notation
Q: What are some resources for learning more about scientific notation?
A: Some resources for learning more about scientific notation include:
- Textbooks and online resources
- Calculators and computers
- Online tutorials and videos
- Practice problems and worksheets