Precision, accuracy and significant figures
Distinguish precision, agreement between repeated readings, from accuracy, closeness to a true or accepted reference value. Round measurements to stated decimal places or significant figures, and choose instruments using their capacity and scale divisions.
What a learner can do afterwards
- Explains the distinction between precision and accuracy with examples
- Rounds measurements to an appropriate number of significant figures
- Selects and uses a measuring instrument with suitable capacity and scale divisions for the quantity being measured
1 · Read
You have compared repeat readings before. Precision describes how closely readings agree under the same conditions. A smaller spread means greater precision in the same task. Accuracy describes closeness to a true or accepted reference value. Compare each reading with that reference. One reading can be close to a reference, but you need repeats to judge their agreement.
Measure the same object under the same conditions when checking repeats. A mean can reduce the effect of random variation, but cannot remove an offset shared by every reading. Check the zero setting, equipment and method against a trusted reference. A shared offset does not identify its cause by itself. Keep unusual readings, investigate them and explain any later exclusion.
Choose a tool that holds the required volume and shows suitably small scale divisions. Resolution is the smallest change its scale or display shows. Finer divisions can reduce reading uncertainty, but do not prove accuracy. Inspect the actual markings rather than judging by capacity. For water, place a cylinder upright on a level surface. Read the bottom of the curved water surface at eye level.
Report the detail your method supports. Nearest 0.1 cm means one decimal place, the tenths place. To round 16.27 cm, keep the tenths digit, 2, and inspect the next digit, 7. This lesson uses the rule: 5 or more rounds up; less than 5 leaves the kept digit unchanged. The result is 16.3 cm.
Significant figures report a measurement's detail; its last digit may still be uncertain. Start counting at the first nonzero digit. Ignore zeros before it. Count zeros between nonzero digits and final zeros in a decimal measurement. For example, 0.0304 m has three significant figures: 3, 0 and 4. The measurement 4.500 cm has four. Writing extra digits does not improve accuracy.
To round to a stated number of significant figures, count from the first nonzero digit. Keep the required digits and inspect the next digit. Use this lesson's rounding rule: 5 or more rounds up; less than 5 leaves the last kept digit unchanged. For 27.84 g to three significant figures, keep 2, 7 and 8. The next digit is 4, so report 27.8 g.
Compare repeats for precision and a reference for accuracy. Check the tool and method, choose suitable divisions, and report only supported detail.
This lesson, its questions and its flashcards were written for this dataset.
These readings and additional questions were written for this dataset. The linked video, What's the difference between accuracy and precision?, is by Matt Anticole for TED-Ed and is hosted on YouTube.
More to read
Agreement and reference checks
Repeat readings let you compare agreement. Use the same object and conditions when checking precision. A tight group has a smaller spread than a scattered group in the same task.
To check accuracy, compare readings with a true or accepted reference value. Several matching readings can all differ from that reference. Taking more readings with the same setup might repeat the difference.
Investigate the equipment and the method. A balance might need its zero setting checked. A ruler might have been aligned at the wrong starting mark. A shared offset alone does not tell you which cause applies.
Record any change you make before taking new readings. Keep earlier results so another person can follow what happened.
Choosing the digits to report
A measurement method supports a limited amount of detail. Extra calculator digits do not make the original observation more accurate.
Decimal places count positions after the decimal point. Significant figures count from the first nonzero digit. Earlier zeros locate the decimal point. Zeros between nonzero digits count, as do final zeros in a decimal measurement.
Read the reporting instruction before rounding. Keep the requested places or significant digits, inspect the next digit and round once. This lesson uses the school rule that a next digit of 5 or more rounds up.
Some sources use a different convention for exact halfway cases. Follow the convention specified for the task. Rounding changes the reported number, not the equipment or the observation.
Reading uncertainty and repeated results
Uncertainty describes doubt about a measurement. A scale's divisions or display limit the differences it can show. Reading position and the measurement method also matter.
Choose a tool with enough capacity and suitable divisions. For water in a cylinder, keep the cylinder upright on a level surface and read the bottom of the curved surface at eye level. A fine scale does not remove the need for correct use or calibration checks.
Repeated results show the variation you observed. Their smallest-to-largest interval does not guarantee that the true value lies inside it. Every reading could share an offset.
A mean can reduce the effect of random variation, but it cannot remove a shared offset. Preserve unusual readings while investigating them. Explain any decision to exclude one.
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