Write 32,005,000 In Scientific Notation.A. \[$3.2005 \times 10^7\$\]B. \[$3.2005 \times 10^1\$\]C. \[$0.32005 \times 10^8\$\]D. \[$0.32005 \times 10^0\$\]Please Select The Best Answer From The Choices Provided:- A- B- C- D
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 this article, we will explore how to write the number 32,005,000 in scientific notation.
Understanding Scientific Notation
Scientific notation is a shorthand way of expressing numbers that are too large or too small to be conveniently written in standard decimal notation. It consists of two parts: a coefficient and a power of 10. The coefficient is a number between 1 and 10, and the power of 10 is an exponent that indicates the number of places to move the decimal point.
For example, the number 432,000 can be written in scientific notation as 4.32 × 10^5. This means that the decimal point has been moved 5 places to the left, resulting in a number between 1 and 10.
Writing 32,005,000 in Scientific Notation
To write 32,005,000 in scientific notation, we need to move the decimal point to the left until we have a number between 1 and 10. In this case, we need to move the decimal point 7 places to the left.
32,005,000 → 3.2005 × 10^7
Therefore, the correct answer is A. ${3.2005 \times 10^7\$}.
Why Not the Other Options?
Let's take a look at the other options to see why they are not correct.
- B. ${3.2005 \times 10^1\$}: This option is incorrect because the power of 10 is too small. We need to move the decimal point 7 places to the left, not 1 place.
- C. ${0.32005 \times 10^8\$}: This option is incorrect because the coefficient is too small. We need a coefficient between 1 and 10, not a coefficient less than 1.
- D. ${0.32005 \times 10^0\$}: This option is incorrect because the power of 10 is too small. We need to move the decimal point 7 places to the left, not 0 places.
Conclusion
Writing large numbers in scientific notation can be a useful tool for expressing very large or very small numbers in a more manageable form. By moving the decimal point to the left or right, we can express numbers in a way that is easier to work with. In this article, we have seen how to write the number 32,005,000 in scientific notation, and we have explored why the other options are not correct.
Key Takeaways
- 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.
- 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 power of 10 indicates the number of places to move the decimal point.
Practice Problems
- Write the number 432,000 in scientific notation.
- Write the number 0.000432 in scientific notation.
- Write the number 9,876,543 in scientific notation.
Answers
- 4.32 × 10^5
- 4.32 × 10^-4
- 9.877 × 10^6
Scientific Notation Q&A ==========================
Scientific notation is a powerful tool for expressing very large or very small numbers in a more manageable form. In this article, we will answer some common questions about scientific notation and provide examples to help illustrate the concepts.
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 power of 10 indicates the number of places to move the decimal point.
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 power of 10 in scientific notation?
A: The power of 10 is the exponent that indicates the number of places to move the decimal point. It is the part of the number that is multiplied by the coefficient.
Q: How do I convert a number from standard decimal notation to scientific notation?
A: To convert a number from standard decimal 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. Then, you need to multiply the number by a power of 10 that indicates the number of places you moved the decimal point.
Q: How do I convert a number from scientific notation to standard decimal notation?
A: To convert a number from scientific notation to standard decimal notation, you need to multiply the coefficient by the power of 10. Then, you need to move the decimal point to the right or left by the number of places indicated by the power of 10.
Q: What are some examples of numbers in scientific notation?
A: Here are some examples of numbers in scientific notation:
- 4.32 × 10^5
- 3.21 × 10^-3
- 9.87 × 10^6
- 2.54 × 10^-2
Q: Why is scientific notation useful?
A: Scientific notation is useful because it allows us to express very large or very small numbers in a more manageable form. It makes it easier to perform calculations and comparisons with numbers that are difficult to work with in standard decimal notation.
Q: What are some common applications of scientific notation?
A: Scientific notation is commonly used in a variety of fields, including:
- Physics: to express large or small distances, velocities, or energies
- Chemistry: to express large or small concentrations or quantities of substances
- Engineering: to express large or small dimensions or quantities of materials
- Astronomy: to express large or small distances or quantities of celestial objects
Q: How do I practice using scientific notation?
A: You can practice using scientific notation by converting numbers from standard decimal notation to scientific notation and vice versa. You can also use online resources or worksheets to practice converting numbers in scientific notation.
Conclusion
Scientific notation is a powerful tool for expressing very large or very small numbers in a more manageable form. By understanding the concepts of scientific notation and practicing using it, you can become more confident and proficient in working with numbers in scientific notation.