Measurement

Measurement Definitions

Accuracy & Precision

• Accuracy refers to the largest allowable error that occurs under specific operating conditions.

– Example: A digital voltmeter with ±2% accuracy will read 100V anywhere between 98V and 102V

• Precision refers to an instrument’s ability to provide the same measurement repeatedly.

Significant Digits

• If a number expressing the result of a measurement has more digits than the measurement resolution, those digits are unreliable and useless.

-> Consider adding two length measurements, one from a tape measure (resolution = 1mm) and one using calipers (resolution = 10𝜇m=0.01mm). -> 102mm + 8.07mm = 110mm ✅

• The following are not significant figures:

-> Leading zeros (e.g. 0.056 only has 2 significant figures)

-> Trailing zeros used as placeholders (e.g. 1500m if the 0s are not actually certain)

• Arithmetic: 

  • Addition and subtraction: the last significant figure position in the result should be the same as the largest digit position of the measured quantities in the calculation.

  • Multiplication and division: result should have as many significant figures as the least number of significant figures among the measured quantities used in the calculation

–> Exceptions: multiplications by integers or constants with infinite precision

• •  In multiple-stage calculations, you should retain full computational accuracy and only round off to the appropriate # of significant digits at the very end.