Which Choice Correctly Expresses The Number Below In Scientific Notation?0.0000000744A. $744 \cdot 10^{-8}$ B. $7.44 \cdot 10^{-8}$ C. $74.4 \cdot 10^{-9}$ D. $744 \cdot 10^{-10}$ E. $7.44 \cdot 10^{-7}$
Understanding Scientific Notation: A Guide to Expressing Numbers in Scientific Form
Scientific notation is a way of expressing very large or very small numbers in a more manageable and concise form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10. In this article, we will explore the concept of scientific notation and how to correctly express numbers in this form.
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 456,000 can be expressed in scientific notation as 4.56 × 10^5.
How to Express Numbers in Scientific Notation
To express 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 1: Expressing a Large Number in Scientific Notation
Let's consider the number 456,000. To express this number in scientific notation, we need to move the decimal point to the left until we have a number between 1 and 10. We move the decimal point 5 places to the left, resulting in 4.56. The exponent is 5, since we moved the decimal point 5 places to the left. Therefore, the number 456,000 can be expressed in scientific notation as 4.56 × 10^5.
Example 2: Expressing a Small Number in Scientific Notation
Let's consider the number 0.0000000744. To express this number 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 8 places to the right, resulting in 7.44. The exponent is -8, since we moved the decimal point 8 places to the right. Therefore, the number 0.0000000744 can be expressed in scientific notation as 7.44 × 10^-8.
Which Choice Correctly Expresses the Number in Scientific Notation?
Now that we have a good understanding of scientific notation, let's consider the options provided in the question:
A. B. C. D. E.
To determine which choice correctly expresses the number in scientific notation, we need to consider the exponent. The correct exponent is -8, since we moved the decimal point 8 places to the right. Therefore, the correct choice is the one that has an exponent of -8.
Conclusion
In conclusion, scientific notation is a way of expressing very large or very small numbers in a more manageable and concise form. To express 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. By following these steps, we can correctly express numbers in scientific notation.
Answer
The correct answer is B. . This choice correctly expresses the number 0.0000000744 in scientific notation, with an exponent of -8.
Scientific Notation Q&A: Frequently Asked Questions and Answers
Scientific notation is a powerful tool for expressing very large or very small numbers in a more manageable and concise form. However, it can be challenging to understand and apply, especially for those who are new to the concept. In this article, we will answer some of the most frequently asked questions about scientific notation.
Q: What is the purpose of scientific notation?
A: The purpose of scientific notation is to express very large or very small numbers in a more manageable and concise form. It allows us to simplify complex numbers and make them easier to work with.
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. 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 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: Can I have a negative coefficient in scientific notation?
A: Yes, you can have a negative coefficient in scientific notation. However, the exponent will be positive, indicating that the decimal point was moved to the left.
Q: Can I have a negative exponent in scientific notation?
A: Yes, you can have a negative exponent in scientific notation. This indicates that the decimal point was moved to the right.
Q: How do I convert a number from scientific notation to standard form?
A: To convert a number from scientific notation to standard form, you need to multiply the coefficient by the power of 10. For example, 3.45 × 10^4 can be converted to standard form by multiplying 3.45 by 10,000.
Q: How do I convert a number from standard form to scientific notation?
A: To convert a number from standard form to 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 applications of scientific notation?
A: Scientific notation is commonly used in physics, chemistry, and engineering to express large or small numbers. It is also used in finance and economics to express large or small amounts of money.
Q: Can I use scientific notation with fractions?
A: Yes, you can use scientific notation with fractions. However, the fraction must be expressed as a decimal before it can be converted to scientific notation.
Q: Can I use scientific notation with decimals?
A: Yes, you can use scientific notation with decimals. However, the decimal must be expressed as a fraction before it can be converted to scientific notation.
Conclusion
In conclusion, scientific notation is a powerful tool for expressing very large or very small numbers in a more manageable and concise form. By understanding the concept of scientific notation and how to apply it, you can simplify complex numbers and make them easier to work with. We hope this Q&A article has been helpful in answering some of the most frequently asked questions about scientific notation.