Which Choice Correctly Expresses The Number Below In Scientific Notation?0.00000636A. $636 \cdot 10^{-6}$ B. $6.36 \cdot 10^{-6}$ C. $6.36 \cdot 10^{-7}$ D. $6.36 \cdot 10^{-5}$ E. $63.6 \cdot 10^{-7}$
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 complex calculations and to express numbers in a more compact and readable format.
What is Scientific Notation?
Scientific notation is a way of expressing a number as 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.
Expressing 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. We then multiply the number by 10 raised to the power of the number of places we moved the decimal point.
Example 1: Expressing 456,000 in Scientific Notation
To express 456,000 in scientific notation, we move the decimal point 5 places to the left to get 4.56. We then multiply 4.56 by 10^5, since we moved the decimal point 5 places to the left.
Example 2: Expressing 0.00000636 in Scientific Notation
To express 0.00000636 in scientific notation, we move the decimal point 6 places to the right to get 6.36. We then multiply 6.36 by 10^(-6), since we moved the decimal point 6 places to the right.
Which Choice Correctly Expresses the Number in Scientific Notation?
Now that we have a good understanding of scientific notation, let's look at the choices and determine which one correctly expresses the number 0.00000636 in scientific notation.
A.
This choice is incorrect because the coefficient is not between 1 and 10. We need to move the decimal point to the left to get a number between 1 and 10.
B.
This choice is correct because the coefficient is between 1 and 10, and the exponent is -6, which is the correct power of 10 to express the number 0.00000636 in scientific notation.
C.
This choice is incorrect because the exponent is -7, which is not the correct power of 10 to express the number 0.00000636 in scientific notation.
D.
This choice is incorrect because the exponent is -5, which is not the correct power of 10 to express the number 0.00000636 in scientific notation.
E.
This choice is incorrect because the coefficient is not between 1 and 10, and the exponent is -7, which is not the correct power of 10 to express the number 0.00000636 in scientific notation.
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 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. You then multiply the number by 10 raised to the power of the number of places you moved 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 exponent in scientific notation?
A: The exponent is the power of 10 in scientific notation. It is the part of the number that tells you how many places to move the decimal point.
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 will be positive. If you moved the decimal point to the right, the exponent will be negative.
Q: What is the difference between positive and negative exponents in scientific notation?
A: Positive exponents in scientific notation indicate that the decimal point was moved to the left, resulting in a number greater than 1. Negative exponents in scientific notation indicate that the decimal point was moved to the right, resulting in a number less than 1.
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. You then multiply the number by 10 raised to the power of the number of places you moved the decimal point.
Q: What are some common applications of scientific notation?
A: Scientific notation is commonly used in mathematics, physics, and engineering to simplify complex calculations and to express numbers in a more compact and readable format. It is also used in chemistry, biology, and other fields where large or small numbers are encountered.
Q: How do I use scientific notation in real-life situations?
A: Scientific notation can be used in a variety of real-life situations, such as calculating the area of a circle, determining the volume of a cube, or expressing the speed of a car in miles per hour. It can also be used to simplify complex calculations and to express numbers in a more compact and readable format.
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 to the correct place
- Not using the correct exponent
- Not converting the number to standard form when necessary
- Not using scientific notation when it is more convenient than standard 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 use scientific notation, you can simplify complex calculations and make it easier to work with numbers in mathematics, physics, and engineering.