Perform The Following Calculation And Choose The Answer With The Correct Number Of Significant Figures: ( 5.60 × 3.2 ) + 4.321 (5.60 \times 3.2) + 4.321 ( 5.60 × 3.2 ) + 4.321 A. 22.2 B. 22 C. 22.241 D. 22.24

Introduction

Significant figures are a crucial aspect of scientific calculations, as they determine the precision and accuracy of the results. In this article, we will explore the concept of significant figures, how to perform calculations with them, and how to choose the correct answer with the correct number of significant figures.

What are Significant Figures?

Significant figures are the digits in a measurement that are known to be reliable and certain. They are used to express the precision and accuracy of a measurement or calculation. The number of significant figures in a measurement or calculation depends on the instrument or method used to obtain the measurement.

Rules for Significant Figures

There are several rules for significant figures that must be followed when performing calculations:

• Non-zero digits are always significant: Any non-zero digit in a measurement or calculation is considered significant.
• Zeros between non-zero digits are significant: Zeros that appear between non-zero digits in a measurement or calculation are considered significant.
• Leading zeros are not significant: Zeros that appear at the beginning of a measurement or calculation are not considered significant.
• Trailing zeros are significant only if the number contains a decimal point: Zeros that appear at the end of a measurement or calculation are only considered significant if the number contains a decimal point.

Performing Calculations with Significant Figures

When performing calculations with significant figures, the following rules must be followed:

• Add and subtract numbers with the same number of significant figures: When adding or subtracting numbers with the same number of significant figures, the result should have the same number of significant figures as the numbers being added or subtracted.
• Multiply and divide numbers with the same number of significant figures: When multiplying or dividing numbers with the same number of significant figures, the result should have the same number of significant figures as the numbers being multiplied or divided.
• Round the result to the correct number of significant figures: The result of a calculation should be rounded to the correct number of significant figures.

Example Calculation

Let's perform the following calculation and choose the answer with the correct number of significant figures:

$(5.60 \times 3.2) + 4.321$

To perform this calculation, we must follow the rules for significant figures:

• Multiply 5.60 and 3.2: $5.60 \times 3.2 = 17.92$
• Add 4.321 to the result: $17.92 + 4.321 = 22.241$

The result of the calculation is 22.241. However, we must round this result to the correct number of significant figures.

Choosing the Correct Answer

The correct answer with the correct number of significant figures is:

• C. 22.241: This answer has the correct number of significant figures, which is 4.

Conclusion

Significant figures are a crucial aspect of scientific calculations, as they determine the precision and accuracy of the results. By following the rules for significant figures and performing calculations with them, we can ensure that our results are accurate and reliable. In this article, we have explored the concept of significant figures, how to perform calculations with them, and how to choose the correct answer with the correct number of significant figures.

Common Mistakes to Avoid

When performing calculations with significant figures, there are several common mistakes to avoid:

• Not following the rules for significant figures: Failing to follow the rules for significant figures can lead to inaccurate results.
• Not rounding the result to the correct number of significant figures: Failing to round the result to the correct number of significant figures can lead to inaccurate results.
• Not using the correct number of significant figures: Using the wrong number of significant figures can lead to inaccurate results.

Best Practices for Significant Figures

To ensure accurate results when performing calculations with significant figures, follow these best practices:

• Use the correct number of significant figures: Use the correct number of significant figures for each measurement or calculation.
• Follow the rules for significant figures: Follow the rules for significant figures when performing calculations.
• Round the result to the correct number of significant figures: Round the result to the correct number of significant figures.
• Double-check your work: Double-check your work to ensure that you have followed the rules for significant figures and have rounded the result to the correct number of significant figures.

By following these best practices and avoiding common mistakes, you can ensure that your results are accurate and reliable.

Conclusion

Frequently Asked Questions about Significant Figures

Q: What are significant figures?

A: Significant figures are the digits in a measurement that are known to be reliable and certain. They are used to express the precision and accuracy of a measurement or calculation.

Q: How do I determine the number of significant figures in a measurement?

A: To determine the number of significant figures in a measurement, look for the following:

• Non-zero digits: Any non-zero digit in a measurement is considered significant.
• Zeros between non-zero digits: Zeros that appear between non-zero digits in a measurement are considered significant.
• Leading zeros: Zeros that appear at the beginning of a measurement are not considered significant.
• Trailing zeros: Zeros that appear at the end of a measurement are only considered significant if the number contains a decimal point.

Q: What are the rules for significant figures in calculations?

A: The rules for significant figures in calculations are as follows:

• Add and subtract numbers with the same number of significant figures: When adding or subtracting numbers with the same number of significant figures, the result should have the same number of significant figures as the numbers being added or subtracted.
• Multiply and divide numbers with the same number of significant figures: When multiplying or dividing numbers with the same number of significant figures, the result should have the same number of significant figures as the numbers being multiplied or divided.
• Round the result to the correct number of significant figures: The result of a calculation should be rounded to the correct number of significant figures.

Q: How do I round a result to the correct number of significant figures?

A: To round a result to the correct number of significant figures, follow these steps:

1. Determine the correct number of significant figures: Determine the correct number of significant figures based on the rules for significant figures.
2. Round the result: Round the result to the correct number of significant figures.

Q: What is the difference between significant figures and decimal places?

A: Significant figures and decimal places are related but distinct concepts.

• Significant figures: Significant figures are the digits in a measurement that are known to be reliable and certain.
• Decimal places: Decimal places are the digits in a measurement that appear after the decimal point.

Q: How do I handle calculations with different numbers of significant figures?

A: When performing calculations with different numbers of significant figures, follow these steps:

1. Determine the correct number of significant figures: Determine the correct number of significant figures for each measurement or calculation.
2. Round the result: Round the result to the correct number of significant figures.

Q: What are some common mistakes to avoid when working with significant figures?

A: Some common mistakes to avoid when working with significant figures include:

• Not following the rules for significant figures: Failing to follow the rules for significant figures can lead to inaccurate results.
• Not rounding the result to the correct number of significant figures: Failing to round the result to the correct number of significant figures can lead to inaccurate results.
• Not using the correct number of significant figures: Using the wrong number of significant figures can lead to inaccurate results.

Q: How can I ensure accurate results when working with significant figures?

A: To ensure accurate results when working with significant figures, follow these best practices:

• Use the correct number of significant figures: Use the correct number of significant figures for each measurement or calculation.
• Follow the rules for significant figures: Follow the rules for significant figures when performing calculations.
• Round the result to the correct number of significant figures: Round the result to the correct number of significant figures.
• Double-check your work: Double-check your work to ensure that you have followed the rules for significant figures and have rounded the result to the correct number of significant figures.

By following these best practices and avoiding common mistakes, you can ensure that your results are accurate and reliable.