Calculate The Following Expression:$\[ \frac{1}{3} \left(3.14 \cdot 0.5^2\right) \times 2.2 \\]

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Introduction

In this article, we will delve into the world of mathematics and calculate a given expression step by step. The expression is a combination of multiplication, division, and exponentiation, making it a great example of how to tackle complex mathematical problems. We will break down the expression into smaller parts, calculate each part, and then combine the results to get the final answer.

The Expression

The given expression is:

{ \frac{1}{3} \left(3.14 \cdot 0.5^2\right) \times 2.2 \}

This expression involves several operations, including multiplication, division, and exponentiation. Let's break it down into smaller parts to make it easier to understand and calculate.

Step 1: Calculate the Exponentiation

The first step is to calculate the exponentiation part of the expression, which is 0.520.5^2. This means we need to raise 0.5 to the power of 2.

{ 0.5^2 = 0.5 \times 0.5 = 0.25 \}

Step 2: Calculate the Multiplication

Next, we need to calculate the multiplication part of the expression, which is 3.14â‹…0.253.14 \cdot 0.25. This means we need to multiply 3.14 by 0.25.

{ 3.14 \cdot 0.25 = 0.785 \}

Step 3: Calculate the Division

Now, we need to calculate the division part of the expression, which is 13â‹…0.785\frac{1}{3} \cdot 0.785. This means we need to divide 0.785 by 3.

{ \frac{1}{3} \cdot 0.785 = 0.26167 \}

Step 4: Calculate the Final Multiplication

Finally, we need to calculate the final multiplication part of the expression, which is 0.26167×2.20.26167 \times 2.2. This means we need to multiply 0.26167 by 2.2.

{ 0.26167 \times 2.2 = 0.575 \}

Conclusion

In conclusion, we have successfully calculated the given expression step by step. We broke down the expression into smaller parts, calculated each part, and then combined the results to get the final answer. The final answer is 0.575.

Tips and Tricks

When working with complex mathematical expressions, it's essential to break them down into smaller parts and calculate each part step by step. This will help you avoid mistakes and ensure that you get the correct answer. Additionally, make sure to use the correct order of operations (PEMDAS) to ensure that you perform the calculations in the correct order.

Frequently Asked Questions

Q: What is the correct order of operations?

A: The correct order of operations is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I avoid mistakes when working with complex mathematical expressions?

A: To avoid mistakes, make sure to break down the expression into smaller parts, calculate each part step by step, and use the correct order of operations.

Q: What is the final answer to the given expression?

A: The final answer to the given expression is 0.575.

Related Topics

  • Calculating Exponents
  • Multiplication and Division
  • Order of Operations
  • Complex Mathematical Expressions

References

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Introduction

In our previous article, we calculated the expression ${ \frac{1}{3} \left(3.14 \cdot 0.5^2\right) \times 2.2 }$. We broke down the expression into smaller parts, calculated each part step by step, and then combined the results to get the final answer. In this article, we will answer some frequently asked questions related to calculating the expression.

Q&A

Q: What is the correct order of operations?

A: The correct order of operations is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I avoid mistakes when working with complex mathematical expressions?

A: To avoid mistakes, make sure to break down the expression into smaller parts, calculate each part step by step, and use the correct order of operations.

Q: What is the final answer to the given expression?

A: The final answer to the given expression is 0.575.

Q: Can I use a calculator to calculate the expression?

A: Yes, you can use a calculator to calculate the expression. However, it's essential to understand the steps involved in calculating the expression to ensure that you get the correct answer.

Q: How do I calculate the exponentiation part of the expression?

A: To calculate the exponentiation part of the expression, you need to raise the base number to the power of the exponent. For example, in the expression 0.520.5^2, you need to raise 0.5 to the power of 2.

Q: How do I calculate the multiplication part of the expression?

A: To calculate the multiplication part of the expression, you need to multiply the two numbers together. For example, in the expression 3.14â‹…0.253.14 \cdot 0.25, you need to multiply 3.14 by 0.25.

Q: How do I calculate the division part of the expression?

A: To calculate the division part of the expression, you need to divide the dividend by the divisor. For example, in the expression 13â‹…0.785\frac{1}{3} \cdot 0.785, you need to divide 0.785 by 3.

Q: Can I use a different order of operations to calculate the expression?

A: No, you cannot use a different order of operations to calculate the expression. The correct order of operations is PEMDAS, and you must follow this order to ensure that you get the correct answer.

Tips and Tricks

When working with complex mathematical expressions, it's essential to break them down into smaller parts and calculate each part step by step. This will help you avoid mistakes and ensure that you get the correct answer. Additionally, make sure to use the correct order of operations (PEMDAS) to ensure that you perform the calculations in the correct order.

Related Topics

  • Calculating Exponents
  • Multiplication and Division
  • Order of Operations
  • Complex Mathematical Expressions

References

Conclusion

In conclusion, we have answered some frequently asked questions related to calculating the expression ${ \frac{1}{3} \left(3.14 \cdot 0.5^2\right) \times 2.2 }$. We hope that this article has been helpful in clarifying any doubts you may have had about calculating the expression. If you have any further questions, please don't hesitate to ask.