What Is The Correct Way To Write $1,550,000,000$ In Scientific Notation?A. $1.55 \times 10^9$ B. \$1.55 \times 10^{10}$[/tex\] C. $15.5 \times 10^8$ D. $15.5 \times 10^9$
Scientific notation is a way of expressing very large or very small numbers in a compact and easy-to-read format. It is commonly used in mathematics, physics, and engineering to simplify calculations and make it easier to understand complex concepts. In this article, we will explore the correct way to write a large number, $1,550,000,000$, in scientific notation.
What is Scientific Notation?
Scientific notation is a method of expressing a number as a product of a number between 1 and 10 and a power of 10. The general form of scientific notation is:
where $a$ is the coefficient and $b$ is the exponent. The coefficient $a$ must be a number between 1 and 10, and the exponent $b$ is an integer.
Writing Large Numbers in Scientific Notation
To write a large number in scientific notation, we need to move the decimal point to the left until we have a number between 1 and 10. The number of places we move the decimal point is equal to the exponent of the power of 10.
For example, let's consider the number $1,550,000,000$. To write this number in scientific notation, we need to move the decimal point 9 places to the left to get $1.55$. Since we moved the decimal point 9 places to the left, the exponent of the power of 10 is 9.
Therefore, the correct way to write $1,550,000,000$ in scientific notation is:
Common Mistakes in Scientific Notation
When writing large numbers in scientific notation, it's easy to make mistakes. Here are some common mistakes to avoid:
- Incorrect exponent: Make sure the exponent is correct. In the example above, we moved the decimal point 9 places to the left, so the exponent is 9.
- Incorrect coefficient: Make sure the coefficient is between 1 and 10. In the example above, the coefficient is 1.55, which is between 1 and 10.
- Incorrect power of 10: Make sure the power of 10 is correct. In the example above, the power of 10 is $10^9$, which is correct.
Examples of Scientific Notation
Here are some examples of scientific notation:
Conclusion
Scientific notation is a powerful tool for expressing large or small numbers in a compact and easy-to-read format. By understanding the rules of scientific notation, you can write numbers in a way that is easy to read and understand. Remember to move the decimal point to the left until you have a number between 1 and 10, and the exponent is equal to the number of places you moved the decimal point.
Answer Key
The correct answer is:
A. $1.55 \times 10^9$
In this article, we will answer some 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 compact and easy-to-read format. It is commonly used in mathematics, physics, and engineering to simplify calculations and make it easier to understand complex concepts.
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 until you have a number between 1 and 10. The number of places you move the decimal point is equal to the exponent of the power of 10.
Q: What is the coefficient in scientific notation?
A: The coefficient in scientific notation is the number between 1 and 10 that is multiplied by the power of 10. For example, in the number $1.55 \times 10^9$, the coefficient is 1.55.
Q: What is the exponent in scientific notation?
A: The exponent in scientific notation is the power of 10 that is multiplied by the coefficient. For example, in the number $1.55 \times 10^9$, the exponent is 9.
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 coefficient by the power of 10. For example, to convert the number $1.55 \times 10^9$ to standard notation, you would multiply 1.55 by 10^9.
Q: What are some common mistakes to avoid when writing numbers in scientific notation?
A: Some common mistakes to avoid when writing numbers in scientific notation include:
- Incorrect exponent: Make sure the exponent is correct. In the example above, we moved the decimal point 9 places to the left, so the exponent is 9.
- Incorrect coefficient: Make sure the coefficient is between 1 and 10. In the example above, the coefficient is 1.55, which is between 1 and 10.
- Incorrect power of 10: Make sure the power of 10 is correct. In the example above, the power of 10 is $10^9$, which is correct.
Q: How do I compare numbers in scientific notation?
A: To compare numbers in scientific notation, you need to compare the coefficients and the exponents. For example, to compare the numbers $1.55 \times 10^9$ and $1.6 \times 10^9$, you would compare the coefficients (1.55 and 1.6) and the exponents (9 and 9). Since the coefficients are equal, you would compare the exponents. Since the exponents are equal, the numbers are equal.
Q: How do I add or subtract numbers in scientific notation?
A: To add or subtract numbers in scientific notation, you need to have the same exponent. For example, to add the numbers $1.55 \times 10^9$ and $1.6 \times 10^9$, you would add the coefficients (1.55 and 1.6) and keep the same exponent (9).
Q: How do I multiply or divide numbers in scientific notation?
A: To multiply or divide numbers in scientific notation, you need to multiply or divide the coefficients and add or subtract the exponents. For example, to multiply the numbers $1.55 \times 10^9$ and $1.6 \times 10^9$, you would multiply the coefficients (1.55 and 1.6) and add the exponents (9 and 9).
Conclusion
Scientific notation is a powerful tool for expressing large or small numbers in a compact and easy-to-read format. By understanding the rules of scientific notation, you can write numbers in a way that is easy to read and understand. Remember to move the decimal point to the left until you have a number between 1 and 10, and the exponent is equal to the number of places you moved the decimal point.
Answer Key
Here are the answers to the questions above:
- 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 compact and easy-to-read format.
- 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 until you have a number between 1 and 10. The number of places you move the decimal point is equal to the exponent of the power of 10.
- Q: What is the coefficient in scientific notation? A: The coefficient in scientific notation is the number between 1 and 10 that is multiplied by the power of 10.
- Q: What is the exponent in scientific notation? A: The exponent in scientific notation is the power of 10 that is multiplied by the coefficient.
- 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 coefficient by the power of 10.
- Q: What are some common mistakes to avoid when writing numbers in scientific notation? A: Some common mistakes to avoid when writing numbers in scientific notation include incorrect exponent, incorrect coefficient, and incorrect power of 10.
- Q: How do I compare numbers in scientific notation? A: To compare numbers in scientific notation, you need to compare the coefficients and the exponents.
- Q: How do I add or subtract numbers in scientific notation? A: To add or subtract numbers in scientific notation, you need to have the same exponent.
- Q: How do I multiply or divide numbers in scientific notation? A: To multiply or divide numbers in scientific notation, you need to multiply or divide the coefficients and add or subtract the exponents.