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Accuracy, precision and measurement resolution

A measurement is not just a number; it is a statement about an unknown physical quantity made through an instrument and procedure. Three different ideas describe its quality.

Accuracy is closeness to the quantity's true or accepted value. Precision is the degree to which repeated measurements agree with one another. Resolution is the smallest change an instrument can distinguish or display. These properties are related but not interchangeable.

Suppose a calibrated reference is $10.000,\mathrm{V}$. Instrument A repeatedly reads $9.52,9.51,9.52,\mathrm{V}$. The readings are precise because they cluster tightly, but inaccurate because they are systematically displaced. Instrument B reads $9.8,10.2,10.0,\mathrm{V}$: its mean is accurate but its individual readings are less precise. A digital meter that reports only tenths of a volt additionally has a resolution of $0.1,\mathrm{V}$, regardless of whether its calibration is accurate.

Resolution should not be confused with uncertainty. A display step of $0.01,\mathrm{mm}$ does not prove that the measurement is known to $0.01,\mathrm{mm}$: calibration, alignment, environmental drift, sampling, and the measurement model can contribute larger uncertainty. Likewise, reporting many digits does not create information that the experiment did not measure.

A useful measurement report therefore distinguishes the measured estimate from claims about its quality. Precision can often be assessed through repetition; accuracy requires comparison with a trustworthy reference or a validated measurement model; resolution is a property of how the instrument discriminates values. Keeping these concepts separate prevents false confidence in experimental data.