What a learner can do afterwards
- Estimates an uncertainty from repeated readings and states the number of readings used
- Estimates an uncertainty from a manufacturer's tolerance when repeating is not possible
- Distinguishes a random contribution from a systematic one and names an experiment that would reveal each
- Quotes a result with a matched number of significant figures in the value and its uncertainty
1 · Read
You never get to report a bare number. Every measurement carries a small range, and you must quote it, or nobody can tell whether two results agree. Precision means your repeats agree with each other. Accuracy means they sit near the truth.
You measure a table five times and get 120.1, 120.3, 120.2, 120.3 and 120.1 cm. Order them, then subtract the lowest from the highest: 120.3 minus 120.1 is 0.2 cm. Report half of that range, plus or minus 0.1 cm, and always state that it came from 5 readings.
Some things you can measure only once, like a flask you may fill a single time. Then your uncertainty comes from the tolerance the maker printed on the glassware. Learn the two kinds of error: scatter around the middle is random and repeats reveal it, while a steady push one way is systematic, like a scale that always reads 2 kg heavy, and only a known standard reveals that.
Quote the value and its uncertainty so their digits stop together, as in 120.2 cm plus or minus 0.1 cm. Extra digits claim knowledge your readings never gave you.
Quote every result with its range, and let repeats, tolerances and a known standard each play their part.
2 · Watch
Take it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.