Every measurement in chemistry has some uncertainty because instruments, samples, and people are never perfectly exact. A balance reading, a buret volume, or a temperature value should be treated as a measured quantity with a limited number of reliable digits. Understanding error and uncertainty helps you decide whether lab results are trustworthy and whether two results truly agree.
It also helps you communicate results honestly instead of reporting more precision than the experiment supports.
Random error causes measurements to scatter above and below the true value, while systematic error shifts results in one direction. Accuracy describes closeness to an accepted or true value, and precision describes how closely repeated measurements agree with each other. Percent error compares an experimental value with an accepted value, while uncertainty propagation estimates how measurement limits affect a calculated result.
In a lab report, a complete result includes both a value and its uncertainty, such as 24.63 ± 0.05 mL.
Key Facts
- Percent error = |experimental value - accepted value| / |accepted value| × 100%
- Absolute uncertainty is written in the same units as the measurement, such as 12.50 ± 0.02 g.
- Relative uncertainty = absolute uncertainty / measured value.
- Percent uncertainty = relative uncertainty × 100%.
- For addition or subtraction, add absolute uncertainties: Δq = Δa + Δb.
- For multiplication or division, add relative uncertainties: Δq / q = Δa / a + Δb / b.
Vocabulary
- Random error
- Random error is unpredictable variation that makes repeated measurements scatter around an average value.
- Systematic error
- Systematic error is a consistent bias that shifts measurements in the same direction away from the true value.
- Accuracy
- Accuracy is how close a measured or calculated value is to the accepted or true value.
- Precision
- Precision is how closely repeated measurements agree with one another.
- Uncertainty
- Uncertainty is the estimated range around a measured value within which the true value is reasonably expected to lie.
Common Mistakes to Avoid
- Reporting too many digits after a calculation, because the final answer cannot be more precise than the measurements used to produce it.
- Confusing accuracy with precision, because a set of measurements can be tightly grouped but still far from the accepted value.
- Ignoring systematic error, because repeating the same biased method many times does not remove a constant offset such as an uncalibrated balance.
- Adding percent uncertainties for addition or subtraction, because absolute uncertainties should be added when quantities are added or subtracted.
Practice Questions
- 1 A student measures a mass as 5.82 g, while the accepted mass is 5.75 g. Calculate the percent error.
- 2 A volume is measured as 24.60 ± 0.05 mL and a mass is measured as 19.68 ± 0.02 g. Calculate the density and estimate its percent uncertainty using relative uncertainties.
- 3 A class repeats a titration five times and gets very similar volumes, but every calculated concentration is higher than the known standard value. Identify whether this pattern suggests random error or systematic error, and explain how accuracy and precision apply.