Significant Figures Worksheet Chemistry Answers

Mastering Significant Figures: A Comprehensive Guide with Worked Examples

Understanding significant figures is crucial in chemistry and other scientific fields. It directly impacts the accuracy and precision of your calculations and reporting. This comprehensive worksheet will guide you through the rules of significant figures, provide numerous worked examples, and help you confidently tackle any problem involving significant figures in chemistry. This guide covers everything from identifying significant figures in a given number to performing calculations involving addition, subtraction, multiplication, and division, ensuring a thorough understanding of this fundamental concept.

Introduction to Significant Figures

Significant figures (sig figs) represent the digits in a number that carry meaning contributing to its precision. They reflect the uncertainty inherent in any measurement. Understanding sig figs is vital because reporting an answer with excessive or insufficient digits implies a level of accuracy that isn't justified by the measurements used.

Why are significant figures important?

• Accuracy: They indicate the level of accuracy of a measurement.
• Precision: They show the precision of the measuring instrument used.
• Scientific Communication: They ensure consistent and clear communication of experimental results.
• Error Propagation: They help minimize the propagation of errors in calculations.

Rules for Determining Significant Figures

Before we delve into calculations, let's master identifying significant figures in a number. Follow these rules:

1. All non-zero digits are significant. For example, in the number 245, all three digits are significant.

2. Zeros between non-zero digits are significant. In 205, the zero is significant.

3. Leading zeros (zeros to the left of the first non-zero digit) are not significant. In 0.0025, only 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 2500, only 2 and 5 are significant. However, in 2500., all four digits are significant. In 25.00, all four digits are significant.

5. Trailing zeros in a number without a decimal point are ambiguous. To avoid ambiguity, it's best to use scientific notation. For instance, writing 2500 as 2.5 x 10³ clearly indicates two significant figures.

Examples:

• 1234 has 4 significant figures.
• 0.0123 has 3 significant figures.
• 10.012 has 5 significant figures.
• 1000 has 1 significant figure.
• 1000. has 4 significant figures.
• 1.000 x 10³ has 4 significant figures.

Significant Figures in Calculations

Now let's move on to how significant figures affect calculations. The rules differ slightly for addition/subtraction versus multiplication/division.

A. Addition and Subtraction:

The result of addition or subtraction should have the same number of decimal places as the measurement with the fewest decimal places.

Example:

25.45 g + 12.3 g + 0.053 g = 37.803 g

The least number of decimal places is one (in 12.3 g). Therefore, the final answer should be rounded to one decimal place: 37.8 g

B. Multiplication and Division:

The result of multiplication or division should have the same number of significant figures as the measurement with the fewest significant figures.

Example:

12.5 cm x 2.5 cm = 31.25 cm²

12.5 cm has three significant figures, while 2.5 cm has two. The final answer should have two significant figures: 31 cm².

Worked Examples: Significant Figures in Chemistry Problems

Let's work through some detailed examples to solidify your understanding:

Example 1: Density Calculation

A student measures the mass of a metal sample to be 25.67 g and its volume to be 10.2 cm³. Calculate the density, expressing the answer with the correct number of significant figures.

• Solution:

Density = mass/volume = 25.67 g / 10.2 cm³ = 2.516666... g/cm³

The mass has four significant figures, and the volume has three. Therefore, the answer should be rounded to three significant figures: 2.52 g/cm³

Example 2: Molar Mass Calculation

Calculate the molar mass of water (H₂O) given the atomic masses: H = 1.008 g/mol and O = 16.00 g/mol.

• Solution:

Molar mass of H₂O = (2 x 1.008 g/mol) + (1 x 16.00 g/mol) = 18.016 g/mol

The atomic mass of hydrogen has four significant figures, and the atomic mass of oxygen has four significant figures. Thus, the answer should have four significant figures: 18.02 g/mol.

Example 3: Multiple Calculations

A rectangular block has dimensions of 15.2 cm x 5.8 cm x 2.1 cm. Calculate the volume and then the surface area.

• Solution:

Volume = 15.2 cm x 5.8 cm x 2.1 cm = 184.536 cm³ (Should be rounded to two significant figures because 5.8 cm has the fewest: 180 cm³)

Surface area = 2(15.2 cm x 5.8 cm) + 2(15.2 cm x 2.1 cm) + 2(5.8 cm x 2.1 cm) = 176.68 + 64.08 + 24.36 = 265.12 cm² (Should be rounded to two significant figures: 270 cm²)

Frequently Asked Questions (FAQ)

Q1: What happens if I have to round up a 5?

A1: The common practice is to round up if the digit after the 5 is greater than or equal to 5 and round down if it is less than 5.

Q2: Can I use significant figures with exact numbers?

A2: Exact numbers (like the number of atoms in a molecule or the number of students in a class) have infinite significant figures and do not affect the number of significant figures in a calculation.

Q3: How do significant figures apply to scientific notation?

A3: In scientific notation, all digits in the coefficient are significant. For example, 1.23 x 10⁴ has three significant figures.

Q4: What if I'm using a calculator that displays many decimal places?

A4: Calculators usually display more digits than are significant. Always round your final answer to the correct number of significant figures based on the rules discussed earlier.

Conclusion

Mastering significant figures is essential for any student or professional working with quantitative data in chemistry and related fields. By accurately applying the rules for determining and calculating with significant figures, you ensure that your results reflect the true precision of your measurements and calculations, promoting clarity and accuracy in scientific communication. Remember to practice regularly, working through various examples to build your confidence and understanding. This worksheet provides a solid foundation, enabling you to approach significant figure problems with precision and confidence. Through consistent practice and a clear grasp of the principles, you can confidently navigate the world of chemical calculations.