Which Answer Shows 0.00897 Written In Scientific Notation?A. 0.897 × 10 − 2 0.897 \times 10^{-2} 0.897 × 1 0 − 2 B. 8.97 × 10 − 3 8.97 \times 10^{-3} 8.97 × 1 0 − 3 C. 8.97 × 10 − 2 8.97 \times 10^{-2} 8.97 × 1 0 − 2 D. 8.97 × 10 3 8.97 \times 10^3 8.97 × 1 0 3
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. This notation is commonly used in mathematics, physics, and engineering to simplify calculations and make it easier to understand and compare large or small numbers.
What is Scientific Notation?
Scientific notation is a method of expressing numbers in the form of a product of a number between 1 and 10, and a power of 10. The number between 1 and 10 is called the coefficient, and the power of 10 is called the exponent. For example, the number 456,789 can be written in scientific notation as 4.56789 × 10^5.
How to Write Numbers in Scientific Notation
To write a number in scientific notation, we need to move the decimal point to the left or right until we have a number between 1 and 10. The number of places we move the decimal point is the exponent of the power of 10. If we move the decimal point to the left, the exponent is positive, and if we move it to the right, the exponent is negative.
Example: Writing 0.00897 in Scientific Notation
To write 0.00897 in scientific notation, we need to move the decimal point to the right until we have a number between 1 and 10. We move the decimal point 3 places to the right, so the exponent is -3. The number 0.00897 becomes 8.97 × 10^-3.
Which Answer Shows 0.00897 Written in Scientific Notation?
Now that we have understood how to write numbers in scientific notation, let's look at the options given in the question.
A. B. C. D.
From our previous discussion, we know that 0.00897 can be written in scientific notation as 8.97 × 10^-3. Therefore, the correct answer is:
B.
Conclusion
Scientific notation is a powerful tool for expressing very large or very small numbers in a more manageable form. By understanding how to write numbers in scientific notation, we can simplify calculations and make it easier to understand and compare large or very small numbers. In this article, we have discussed how to write numbers in scientific notation and have used this knowledge to determine which answer shows 0.00897 written in scientific notation.
Common Mistakes to Avoid
When writing numbers in scientific notation, it's essential to remember the following:
- The coefficient should be between 1 and 10.
- The exponent should be a power of 10.
- The decimal point should be moved to the left or right until we have a number between 1 and 10.
By following these guidelines, we can ensure that our numbers are written in scientific notation correctly.
Real-World Applications of Scientific Notation
Scientific notation has numerous real applications, including:
- Calculating large or small distances, such as the distance between stars or the size of atoms.
- Expressing large or small quantities, such as the number of particles in a sample or the amount of energy released in a reaction.
- Simplifying complex calculations, such as those involved in physics or engineering.
By understanding scientific notation, we can better understand and work with these complex calculations and quantities.
Practice Problems
To practice writing numbers in scientific notation, try the following problems:
- Write 456,789 in scientific notation.
- Write 0.000456 in scientific notation.
- Write 9.876 × 10^4 in standard notation.
By practicing these problems, you can improve your understanding of scientific notation and become more confident in your ability to write numbers in this form.
Conclusion
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 write a number in scientific notation?
A: To write 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. The number of places you move the decimal point is the exponent of the power of 10.
Q: What is the coefficient in scientific notation?
A: The coefficient is the number between 1 and 10 in scientific notation. It is the part of the number that is multiplied by the power of 10.
Q: What is the exponent in scientific notation?
A: The exponent is the power of 10 in scientific notation. It is the part of the number that is multiplied by the coefficient.
Q: How do I determine the exponent in scientific notation?
A: To determine the exponent in scientific notation, you need to count the number of places you moved the decimal point. If you moved the decimal point to the left, the exponent is positive. If you moved the decimal point to the right, the exponent is negative.
Q: What is the difference between standard notation and scientific notation?
A: Standard notation is the way we normally write numbers, with a decimal point and digits. Scientific notation is a way of expressing numbers in a more compact form, with a coefficient and an exponent.
Q: When should I use scientific notation?
A: You should use scientific notation when you need to express very large or very small numbers in a more manageable form. This is often the case in science, engineering, and mathematics.
Q: How do I convert between standard notation and scientific notation?
A: To convert between standard notation and scientific notation, you need to move the decimal point to the left or right until you have a number between 1 and 10. The number of places you move the decimal point is the exponent of the power of 10.
Q: What are some common mistakes to avoid when using scientific notation?
A: Some common mistakes to avoid when using scientific notation include:
- Not moving the decimal point far enough to the left or right.
- Not counting the number of places you moved the decimal point correctly.
- Not using the correct exponent.
Q: How do I simplify calculations using scientific notation?
A: You can simplify calculations using scientific notation by multiplying or dividing the coefficients and adding or subtracting the exponents.
Q: What are some real-world applications of scientific notation?
A: Some real-world applications of scientific notation include:
- Calculating large or small distances, such as the distance between stars or the size of atoms.
- Expressing large or small quantities, such as the number of particles in a sample or the amount of energy released in a reaction.
- Simplifying complex calculations, such as those involved in physics or.
Q: How do I practice using scientific notation?
A: You can practice using scientific notation by trying the following problems:
- Write 456,789 in scientific notation.
- Write 0.000456 in scientific notation.
- Write 9.876 × 10^4 in standard notation.
By practicing these problems, you can improve your understanding of scientific notation and become more confident in your ability to write numbers in this form.
Conclusion
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 write numbers in scientific notation, you can simplify calculations and make it easier to understand and compare large or very small numbers. We hope this Q&A article has helped you to better understand scientific notation and how to use it in your everyday life.