Lecture Notes: Uncertainty in Measurements

Overview

• Discussion on the importance of understanding and dealing with uncertainty in laboratory measurements.
• Focus on various measurement tools and their precision and accuracy.

Measurement Tools

Balances

• Used to measure mass.
• Digital readout: Displays mass with a specified number of significant digits (e.g., two before and four after the decimal).
• Record all displayed digits despite potential uncertainty.

Volumetric Glassware

• Pipettes and Flasks: Deliver precise volumes (e.g., 25 ml for pipettes, 250 ml for flasks).
• Measure from the meniscus, the lowest point in the liquid curve.

Graduated Cylinders

• Have graduation marks for measurement.
• Larger lines indicate larger increments (e.g., 10 ml), smaller lines for finer increments (e.g., 2 ml).

Burettes

• Measure volume delivered by noting the change in meniscus position.
• Precision involves estimating between marked graduations.

Uncertainty in Measurements

• Uncertain digits: Last digit in a measurement is often estimated and represents uncertainty.

Precision vs. Accuracy

• Precision: Agreement among repeated measurements.
• Accuracy: How close a measurement is to the true value.

Types of Errors

• Random Error: Unpredictable variations causing spread in measurements. Results in indeterminate errors.
• Systematic Error: Consistent, repeatable error. Can often be corrected with calibration.

Handling Uncertainty with Significant Figures

Rules for Significant Figures

1. Non-zero integers are always significant.
2. Leading zeros aren't significant.
3. Captive zeros (between non-zero digits) are significant.
4. Trailing zeros are significant if a decimal point is present.

Exact Numbers

• Obtained by counting or defined values (e.g., 1 inch = 2.54 cm).
• Considered to have an infinite number of significant figures.

Mathematical Operations with Significant Figures

Multiplication and Division

• Resultant significant figures equal to the least precise measure.

Addition and Subtraction

• Result should reflect the least number of decimal places.

Rounding Rules

1. If the digit to be dropped is <5, do not change the last retained digit.
2. If >5, increase the last retained digit by 1.
3. If =5, round up if non-zero digits follow.

Sample Calculations

• Importance of order of operations (PEMDAS) and tracking significant figures.
• Example: Calculation setup and determining significant figures step-by-step.

Conclusion

• Participation question: Calculate average mass with significant figures.
• Emphasized strategy: Setup, solve, verify.
• Instructor support available for queries.