Accuracy and Precision

Accuracy and PrecisionAccuracy and Precision

Why do we bother with Why do we bother with significant figures, anyway?significant figures, anyway?

AccuracyAccuracy

Extent to which a reported Extent to which a reported measurement approaches the true measurement approaches the true value of the quantity measuredvalue of the quantity measured

Accuracy is affected by Accuracy is affected by errorerror:: Method errorMethod error occurs due to the occurs due to the

method used.method used. Instrument errorInstrument error is due to poorly is due to poorly

calibrated or damaged instrumentscalibrated or damaged instruments Human errorHuman error includes mistakes in includes mistakes in

reading or recording measurements.reading or recording measurements.

PrecisionPrecision Degree of exactness or refinement Degree of exactness or refinement

in a measurement.in a measurement. Precision can be affected by:Precision can be affected by:

Limitations of the instrument.Limitations of the instrument. Estimation skill of the person taking Estimation skill of the person taking

the measurement.the measurement. The degree of precision in a The degree of precision in a

measurement is shown by using measurement is shown by using significant figuressignificant figures..

How Many Significant How Many Significant Figures?Figures?

245 m245 m

3 sig figs3 sig figs

Rule: All non-zero digits are significantRule: All non-zero digits are significant


1074 kg 1074 kg


Rule: zeros between non-zero digits are Rule: zeros between non-zero digits are significantsignificant


0.00345 s0.00345 s


Rule: Zeros to the left of the first non-zero digit Rule: Zeros to the left of the first non-zero digit are NOT significant.are NOT significant.


2.00345 s2.00345 s


Rule: Zeros between non-zero digits are Rule: Zeros between non-zero digits are significant.significant.


0.275000 m0.275000 m


Rule: Zeros at the end of a measurement that Rule: Zeros at the end of a measurement that are to the right of the decimal point are are to the right of the decimal point are significant. significant.


275 000 m275 000 m


Rule: Zeros at the end of a measurement are Rule: Zeros at the end of a measurement are NOT significant UNLESS you know that they NOT significant UNLESS you know that they were measured OR the decimal point makes were measured OR the decimal point makes them significant.them significant.


275 000.275 000.


Rule: Zeros at the end of a measurement are Rule: Zeros at the end of a measurement are NOT significant UNLESS you know that they NOT significant UNLESS you know that they were measured OR the decimal point makes were measured OR the decimal point makes them significant.them significant.


20 students20 students

RULE: Counted quantities and quantities that RULE: Counted quantities and quantities that have no uncertainty do not involve have no uncertainty do not involve significant figures.significant figures.


375.4 m + 2.54 m = ?375.4 m + 2.54 m = ?

Answer = 377.9 mAnswer = 377.9 m

RULE:RULE: For addition and subtraction, For addition and subtraction, the answer has the same precision the answer has the same precision as the measurement with the LEAST as the measurement with the LEAST precision.precision.


(20.0 m)(3.0 m) = ?(20.0 m)(3.0 m) = ?

Answer = 60. m or 6.0 x 10 Answer = 60. m or 6.0 x 10 11 m m

RULE: RULE: For multiplication and division, For multiplication and division, the answer has the same number of the answer has the same number of significant figures as the significant figures as the measurement with the measurement with the FEWESTFEWEST significant figures.significant figures.

Accuracy and Precision

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