Significant Figures Chemistry Worksheet Answers

Mastering Significant Figures: A Comprehensive Guide with Worked Examples

Understanding significant figures is crucial in chemistry, ensuring your calculations reflect the accuracy of your measurements. This comprehensive guide provides a detailed explanation of significant figures, along with numerous worked examples to solidify your understanding. We'll cover the rules for determining significant figures, performing calculations involving significant figures, and addressing common misconceptions. By the end, you'll be confident in applying significant figures correctly in your chemistry work. This worksheet-style approach will make learning this essential skill easier and more effective.

Introduction to Significant Figures

Significant figures (sig figs) represent the precision of a measurement. They indicate the digits in a number that are known with certainty, plus one uncertain digit. The more significant figures a number has, the more precise the measurement. Why is this important in chemistry? Because our experimental results are only as good as our measurements. Reporting more significant figures than are justified suggests a higher level of precision than actually exists, while reporting too few can obscure important details.

Rules for Determining Significant Figures

Here are the rules for determining the number of significant figures in a number:

1. Non-zero digits are always significant. For example, in the number 234, all three digits are significant.

2. Zeros between non-zero digits are always significant. In the number 1005, all four digits are significant.

3. Leading zeros (zeros to the left of the first non-zero digit) are never significant. They only serve to place the decimal point. For example, in the number 0.0025, only the 2 and 5 are significant.

4. Trailing zeros (zeros to the right of the last non-zero digit) are significant only if the number contains a decimal point. In the number 250, only two significant figures are present. However, in 250.0, there are four significant figures. The decimal point indicates the precision of the measurement.

5. Exact numbers have infinitely many significant figures. These are often defined constants or numbers obtained through counting. For example, there are exactly 12 inches in a foot.

Worked Examples: Determining Significant Figures

Let's practice identifying significant figures in various numbers:

• 1234: Four significant figures.
• 0.0012: Two significant figures.
• 10.020: Five significant figures.
• 1200: Two significant figures (no decimal point).
• 1200.0: Five significant figures (decimal point present).
• 2.5 x 10³: Two significant figures (scientific notation).
• 6.022 x 10²³ (Avogadro's number): Four significant figures.

Significant Figures in Calculations: Addition and Subtraction

When adding or subtracting numbers, the result should have the same number of decimal places as the measurement with the fewest decimal places.

Example:

Add the following measurements: 12.34 g + 5.2 g + 0.085 g

1. Perform the addition: 12.34 g + 5.2 g + 0.085 g = 17.625 g

2. Identify the measurement with the fewest decimal places: 5.2 g (one decimal place).

3. Round the result to one decimal place: 17.6 g

Therefore, the correct answer is 17.6 g.

Significant Figures in Calculations: Multiplication and Division

When multiplying or dividing numbers, the result should have the same number of significant figures as the measurement with the fewest significant figures.

Example:

Calculate the area of a rectangle with length 12.5 cm and width 3.2 cm.

1. Perform the multiplication: 12.5 cm * 3.2 cm = 40 cm²

2. Identify the measurement with the fewest significant figures: 3.2 cm (two significant figures).

3. Round the result to two significant figures: 40 cm²

Therefore, the correct answer is 40 cm².

Rounding Numbers

Correct rounding is crucial when working with significant figures. Here's a guide:

• If the digit to be dropped is less than 5, round down. For example, 12.34 rounded to two significant figures is 12.

• If the digit to be dropped is greater than or equal to 5, round up. For example, 12.64 rounded to two significant figures is 13.

• If the dropped digit is exactly 5, and followed only by zeros, round to the nearest even number. This helps to minimize bias over many calculations. For example, 12.50 rounds to 12, while 13.50 rounds to 14.

Worked Examples: Calculations with Significant Figures

Let's solve some more complex examples:

Example 1:

(25.67 g + 10.1 g) / 3.25 mL = ?

1. Add the masses: 25.67 g + 10.1 g = 35.77 g (limited to one decimal place)

2. Divide: 35.8 g / 3.25 mL = 11.015 g/mL

3. Round to the correct number of significant figures: 11 g/mL (3.25 mL has three significant figures).

Example 2:

(1.23 x 10⁻²) * (4.56 x 10³) * (7.89 x 10⁻¹) = ?

1. Multiply the numbers: 1.23 * 4.56 * 7.89 = 44.33864

2. Multiply the powers of 10: 10⁻² * 10³ * 10⁻¹ = 10⁰ = 1

3. Combine: 44.33864 * 1 = 44.33864

4. Round to the correct number of significant figures (three, limited by 1.23): 44.3

Example 3:

(6.78 x 10⁻⁴ - 2.34 x 10⁻⁵) / (8.91 x 10²) = ?

1. Subtract the numbers: 6.78 x 10⁻⁴ - 0.234 x 10⁻⁴ = 6.546 x 10⁻⁴ (limited by least precise decimal)

2. Divide: 6.55 x 10⁻⁴ / 8.91 x 10² = 7.349 x 10⁻⁷

3. Round the answer: 7.3 x 10⁻⁷ (limited by 8.91 to three sig figs)

Scientific Notation and Significant Figures

Scientific notation is a convenient way to represent very large or very small numbers. It's also helpful for managing significant figures. Remember, only the digits in the coefficient are considered when determining significant figures.

Common Mistakes to Avoid

• Forgetting the rules: Carefully review the rules before tackling any problem.
• Incorrect rounding: Practice rounding to avoid common errors.
• Ignoring the decimal point: Remember that the position of the decimal significantly impacts the number of significant figures.
• Over-reporting precision: Never report more significant figures than are justified by the least precise measurement.

Frequently Asked Questions (FAQ)

• Q: What happens if I get an answer with more significant figures than allowed?

  • A: You need to round your answer to the correct number of significant figures using the rounding rules described above.

• Q: How do I handle significant figures in complex calculations with multiple steps?

  • A: Keep track of significant figures at each step. It's often best to keep extra digits until the final step and then round to the correct number of significant figures. Avoid premature rounding.

• Q: What if a calculation involves an exact number?

  • A: Exact numbers do not affect the number of significant figures in the result. They are considered to have infinitely many significant figures.

• Q: Are there exceptions to the rules of significant figures?

  • A: While the rules are generally straightforward, some complex situations may require careful consideration. Always prioritize clarity and accuracy in representing your data.

Conclusion

Mastering significant figures is essential for accurate scientific work. By understanding and correctly applying the rules for determining and calculating significant figures, you’ll ensure your results accurately reflect the precision of your measurements. Remember to practice regularly and refer back to these rules and examples as needed. With diligent practice, you'll build confidence and competency in handling significant figures in all your chemical calculations. Don't hesitate to review this guide multiple times – understanding significant figures is a fundamental skill that will serve you well throughout your scientific studies.