Which Sign Makes The Statement True?$\[3.20 \times 10^1\\] \[$\square\$\] $\[2.30 \times 10^1\\]A. >B. <Select The Correct Sign.
Introduction
When dealing with numbers in scientific notation, it's essential to understand how to compare them. In this article, we will explore the concept of comparing numbers in scientific notation and determine which sign makes the statement true.
Understanding Scientific Notation
Scientific notation is a way of expressing numbers in the form of a product of a number between 1 and 10 and a power of 10. It's a convenient way to represent very large or very small numbers. For example, the number 400 can be expressed in scientific notation as 4 × 10^2.
Comparing Numbers in Scientific Notation
To compare numbers in scientific notation, we need to compare the coefficients (the numbers in front of the powers of 10) and the exponents (the powers of 10). If the coefficients are equal, the number with the larger exponent is larger. If the exponents are equal, the number with the larger coefficient is larger.
The Problem
The problem states that we need to determine which sign makes the statement true: [3.20 × 10^1] [square] [2.30 × 10^1]. To solve this problem, we need to compare the two numbers in scientific notation.
Step 1: Compare the Coefficients
The coefficients of the two numbers are 3.20 and 2.30. Since 3.20 is greater than 2.30, the coefficient of the first number is larger.
Step 2: Compare the Exponents
The exponents of the two numbers are both 10^1, which is equal to 10. Since the exponents are equal, we need to look at the coefficients to determine which number is larger.
Step 3: Determine the Sign
Since the coefficient of the first number is larger, the statement [3.20 × 10^1] [square] [2.30 × 10^1] is true. Therefore, the correct sign is >.
Conclusion
In conclusion, when comparing numbers in scientific notation, we need to compare the coefficients and the exponents. If the coefficients are equal, the number with the larger exponent is larger. If the exponents are equal, the number with the larger coefficient is larger. In this problem, the coefficient of the first number is larger, so the correct sign is >.
Frequently Asked Questions
- 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: What if the coefficients are equal? A: If the coefficients are equal, the number with the larger exponent is larger.
- Q: What if the exponents are equal? A: If the exponents are equal, the number with the larger coefficient is larger.
Example Problems
- Compare the numbers 4 × 10^2 and 3 × 10^2.
- Compare the numbers 2 × 10^3 and 1 × 10^3.
- Compare the numbers 5 × 10^4 and 4 × 10^4.
Practice Problems
- Compare the numbers 6 × 10^1 and 5 × 10^1.
- Compare the numbers 8 × 10^2 and 7 × 10^2.
- Compare the numbers 9 × 10^3 and 8 × 10^3.
Conclusion
In conclusion, comparing numbers in scientific notation requires understanding the concept of coefficients and exponents. By following the steps outlined in this article, you can determine which sign makes the statement true. Remember to compare the coefficients and the exponents, and use the correct sign to indicate the relationship between the numbers.
Introduction
Comparing numbers in scientific notation can be a challenging task, especially for those who are new to the concept. In this article, we will address some of the most frequently asked questions about comparing numbers in scientific notation.
Q: What is scientific notation?
A: Scientific notation is a way of expressing numbers in the form of a product of a number between 1 and 10 and a power of 10. It's a convenient way to represent very large or very small numbers.
Q: How do I compare numbers in scientific notation?
A: To compare numbers in scientific notation, you need to compare the coefficients (the numbers in front of the powers of 10) and the exponents (the powers of 10). If the coefficients are equal, the number with the larger exponent is larger. If the exponents are equal, the number with the larger coefficient is larger.
Q: What if the coefficients are equal?
A: If the coefficients are equal, the number with the larger exponent is larger. For example, 4 × 10^2 and 4 × 10^3 are equal in coefficient, but 4 × 10^3 is larger because it has a larger exponent.
Q: What if the exponents are equal?
A: If the exponents are equal, the number with the larger coefficient is larger. For example, 2 × 10^3 and 1 × 10^3 are equal in exponent, but 2 × 10^3 is larger because it has a larger coefficient.
Q: How do I compare numbers with different exponents?
A: To compare numbers with different exponents, you need to compare the exponents first. If the exponents are equal, you can compare the coefficients. If the exponents are not equal, the number with the larger exponent is larger.
Q: Can I compare numbers with different coefficients and exponents?
A: Yes, you can compare numbers with different coefficients and exponents. You need to compare the coefficients first, and if they are equal, you can compare the exponents.
Q: What is the order of operations when comparing numbers in scientific notation?
A: The order of operations is to compare the coefficients first, and if they are equal, to compare the exponents.
Q: Can I use a calculator to compare numbers in scientific notation?
A: Yes, you can use a calculator to compare numbers in scientific notation. However, it's always a good idea to understand the concept and be able to do it manually.
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, 4 × 10^2 is equal to 400.
Q: How do I convert a number from standard notation to scientific notation?
A: To convert a number from standard notation to scientific notation, you need to express the number as a product of a number between 1 and 10 and a power of 10. For example, 400 can be expressed as 4 × 10^2.
Q: What are some common mistakes to avoid when comparing numbers in scientific notation?
A: Some common mistakes to avoid when comparing numbers in scientific notation include:
- Not comparing the coefficients and exponents correctly
- Not understanding the order of operations
- Not being able to convert numbers between scientific notation and standard notation
Conclusion
In conclusion, comparing numbers in scientific notation requires understanding the concept of coefficients and exponents. By following the steps outlined in this article, you can determine which sign makes the statement true and avoid common mistakes. Remember to compare the coefficients and exponents, and use the correct sign to indicate the relationship between the numbers.