What Is The Correct Way To Write $1,550,000,000$ In Scientific Notation?A. $1.55 \times 10^9$ B. $ 1.55 × 10 10 1.55 \times 10^{10} 1.55 × 1 0 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 form. 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, specifically $1,550,000,000$, 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 a number between 1 and 10, and $b$ is an integer that represents the power of 10.
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. We then multiply the number by 10 raised to the power of the number of places we moved the decimal point.
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 $1.55$. We then multiply $1.55$ by $10^9$ to get:
Analyzing the Options
Now that we have understood the concept of scientific notation, let's analyze the options provided:
A. $1.55 \times 10^9$
B. $1.55 \times 10^{10}$
C. $15.5 \times 10^8$
D. $15.5 \times 10^9$
Option A: $1.55 \times 10^9$
Option A is the correct answer. We have already seen that $1,550,000,000$ can be written as $1.55 \times 10^9$ in scientific notation.
Option B: $1.55 \times 10^{10}$
Option B is incorrect. We moved the decimal point 9 places to the left to get $1.55$, so we should multiply it by $10^9$, not $10^{10}$.
Option C: $15.5 \times 10^8$
Option C is incorrect. We moved the decimal point 9 places to the left to get $1.55$, not $15.5$. We should multiply $1.55$ by $10^9$, not $10^8$.
Option D: $15.5 \times 10^9$
Option D is incorrect. We moved the decimal point 9 places to the left to get $1.55$, not $15.5$. We should multiply $1.55$ by $10^9$, not $10^9$ multiplied by $10$.
Conclusion
In conclusion, the correct way to write $1,550,000,000$ in scientific notation is $1.55 \times 10^9$. This is because we moved the decimal point 9 places to the left to get $1.55$, and then multiplied it by $10^9$ to get the correct scientific notation.
Common Mistakes to Avoid
When writing large numbers in scientific notation, it's easy to make mistakes. Here are some common mistakes to avoid:
- Moving the decimal point the wrong number of places
- Multiplying the number by the wrong power of 10
- Not checking the answer to make sure it's in the correct range (between 1 and 10)
Practice Problems
To practice writing large numbers in scientific notation, try the following problems:
- Write $2,300,000$ in scientific notation.
- Write $4,500,000$ in scientific notation.
- Write $6,000,000$ in scientific notation.
Answer Key
Here are the answers to the practice problems:
Conclusion
Q: What is scientific notation?
A: Scientific notation is a way of expressing very large or very small numbers in a compact form. 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 large number in scientific notation?
A: To write a large number in scientific notation, you need to move the decimal point to the left 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 general form of scientific notation?
A: The general form of scientific notation is:
where $a$ is a number between 1 and 10, and $b$ is an integer that represents the power of 10.
Q: How do I determine the power of 10 in scientific notation?
A: To determine the power of 10 in scientific notation, you need to count the number of places you moved the decimal point to the left. For example, if you moved the decimal point 3 places to the left, the power of 10 would be 3.
Q: What is the correct way to write $1,550,000,000$ in scientific notation?
A: The correct way to write $1,550,000,000$ in scientific notation is $1.55 \times 10^9$.
Q: What are some common mistakes to avoid when writing large numbers in scientific notation?
A: Some common mistakes to avoid when writing large numbers in scientific notation include:
- Moving the decimal point the wrong number of places
- Multiplying the number by the wrong power of 10
- Not checking the answer to make sure it's in the correct range (between 1 and 10)
Q: How do I practice writing large numbers in scientific notation?
A: You can practice writing large numbers in scientific notation by trying the following problems:
- Write $2,300,000$ in scientific notation.
- Write $4,500,000$ in scientific notation.
- Write $6,000,000$ in scientific notation.
Q: What are some real-world applications of scientific notation?
A: Scientific notation has many real-world applications, including:
- Calculating large distances and speeds in physics and astronomy
- Expressing small and large numbers in chemistry and biology
- Simplifying complex calculations in engineering and mathematics
Q: Can I use scientific notation with negative numbers?
A: Yes, you can use scientific notation with negative numbers. To do this, you need to move the decimal point to the left until you have a number between 1 and 10, and then multiply the number by 10 raised to the power of the number of places you moved the decimal point. For example, to write $-4,500,000$ in scientific notation, you would move the decimal point 6 places to the left to get $-4.5$, and then multiply it by $10^6$ to get $-4.5 \times 10^6$.
Q: Can I use scientific notation with decimal points?
A: Yes, you can use scientific notation with decimal points. To do this, you need to move the decimal point to the left until you have a number between 1 and 10, and then multiply the number by 10 raised to the power of the number of places you moved the decimal point. For example, to write $3.4 \times 10^6$ in scientific notation, you would move the decimal point 6 places to the left to get $3.4$, and then multiply it by $10^6$ to get $3.4 \times 10^6$.
Conclusion
In conclusion, scientific notation is a powerful tool for expressing large and small numbers in a compact form. By understanding the general form of scientific notation and how to determine the power of 10, you can write large numbers in scientific notation with ease. Remember to avoid common mistakes and practice writing large numbers in scientific notation to become proficient.