Determine The Relationship Between The Expressions:${ 4.7 \times 10^{-3} }$and ${ 2^2 }$Choose The Correct Inequality:A. =B. <C. >

In mathematics, comparing and contrasting different expressions is a crucial aspect of problem-solving. In this article, we will delve into the relationship between two expressions: $4.7 \times 10^{-3}$ and $2^2$. We will explore the correct inequality that represents the relationship between these two expressions.

What are the Expressions?

The first expression, $4.7 \times 10^{-3}$, is a scientific notation of a decimal number. It represents a value that is 4.7 multiplied by $10^{-3}$. The second expression, $2^2$, is an exponential expression that represents the value of 2 squared.

Evaluating the Expressions

To determine the relationship between these two expressions, we need to evaluate them separately.

• The first expression, $4.7 \times 10^{-3}$, can be evaluated by multiplying 4.7 by $10^{-3}$. This gives us a value of 0.0047.
• The second expression, $2^2$, can be evaluated by squaring 2. This gives us a value of 4.

Comparing the Expressions

Now that we have evaluated both expressions, we can compare them to determine the correct inequality.

• The value of the first expression, 0.0047, is less than the value of the second expression, 4.
• Therefore, the correct inequality that represents the relationship between these two expressions is $4.7 \times 10^{-3} < 2^2$.

Conclusion

In conclusion, the relationship between the expressions $4.7 \times 10^{-3}$ and $2^2$ is represented by the inequality $4.7 \times 10^{-3} < 2^2$. This means that the value of the first expression is less than the value of the second expression.

Why is this Important?

Understanding the relationship between different expressions is crucial in mathematics and problem-solving. It helps us to compare and contrast different values, and to make informed decisions based on the relationships between them.

Real-World Applications

The concept of comparing and contrasting different expressions has numerous real-world applications. For example, in finance, comparing the interest rates of different loans can help individuals make informed decisions about which loan to take. In science, comparing the values of different variables can help researchers understand the relationships between them and make predictions about future outcomes.

Common Mistakes to Avoid

When comparing and contrasting different expressions, there are several common mistakes to avoid.

• Not evaluating the expressions separately: It is essential to evaluate each expression separately before comparing them.
• Not considering the context: The context in which the expressions are being compared is crucial. For example, in finance, the interest rates of different loans may be compared in different contexts, such as short-term versus long-term loans.
• Not considering the relationships between the expressions: The relationships between the expressions are crucial in determining the correct inequality.

Conclusion

In conclusion, the relationship between the expressions $4.7 \times 10^{-3}$ and $2^2$ is represented by the inequality $4.7 \times 10^{-3} < 2^2$. This means that the value of the first expression is less than the value of the second expression. Understanding the relationship between different expressions is crucial in mathematics and problem-solving, and has numerous real-world applications.

Final Thoughts

In this article, we will address some of the most frequently asked questions related to the relationship between the expressions $4.7 \times 10^{-3}$ and $2^2$.

Q: What is the relationship between the expressions $4.7 \times 10^{-3}$ and $2^2$?

A: The relationship between the expressions $4.7 \times 10^{-3}$ and $2^2$ is represented by the inequality $4.7 \times 10^{-3} < 2^2$. This means that the value of the first expression is less than the value of the second expression.

Q: How do I evaluate the expression $4.7 \times 10^{-3}$?

A: To evaluate the expression $4.7 \times 10^{-3}$, you need to multiply 4.7 by $10^{-3}$. This gives you a value of 0.0047.

Q: How do I evaluate the expression $2^2$?

A: To evaluate the expression $2^2$, you need to square 2. This gives you a value of 4.

Q: Why is it important to evaluate the expressions separately?

A: It is essential to evaluate each expression separately before comparing them. This ensures that you are comparing the correct values and not making any assumptions.

Q: What are some common mistakes to avoid when comparing and contrasting different expressions?

A: Some common mistakes to avoid when comparing and contrasting different expressions include:

• Not evaluating the expressions separately
• Not considering the context
• Not considering the relationships between the expressions

Q: How can I apply the concept of comparing and contrasting different expressions in real-world scenarios?

A: The concept of comparing and contrasting different expressions has numerous real-world applications. For example, in finance, comparing the interest rates of different loans can help individuals make informed decisions about which loan to take. In science, comparing the values of different variables can help researchers understand the relationships between them and make predictions about future outcomes.

Q: What are some tips for solving problems involving the comparison of different expressions?

A: Some tips for solving problems involving the comparison of different expressions include:

• Read the problem carefully and understand what is being asked
• Evaluate each expression separately before comparing them
• Consider the context and relationships between the expressions
• Use mathematical operations to compare the expressions

Q: How can I practice comparing and contrasting different expressions?

A: You can practice comparing and contrasting different expressions by working on problems that involve the comparison of different expressions. You can also try creating your own problems and solving them to practice your skills.

Conclusion

In conclusion, the relationship between the expressions $4.7 \times 10^{-3}$ and $2^2$ is represented by the inequality $4.7 \times 10^{-3} < 2^2$. This means that the value of the first expression is less than the value of the second expression. By understanding the relationship between different expressions, we can make informed decisions and solve complex problems.

Final Thoughts

The concept of comparing and contrasting different expressions is a fundamental aspect of mathematics and problem-solving. By practicing and applying this concept, we can develop our critical thinking skills and become more effective problem-solvers.