accuracy and precision

Accuracy and PrecisionAccuracy and PrecisionWhy 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 in Degree of exactness or refinement in

a measurement.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 the Estimation skill of the person taking the

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

measurement is indicated by the measurement is indicated by the place value of the last measureable place value of the last measureable digit. digit.

Significant Figures (Digits)Significant Figures (Digits) The certainty of any measurement is The certainty of any measurement is

communicated by the number of communicated by the number of significant figures in the measurement.significant figures in the measurement.

In a measured or calculated value, In a measured or calculated value, significant figures are the digits that are significant figures are the digits that are known to be certain.known to be certain.

More digits there are, the more certain More digits there are, the more certain you are about the measurement.you are about the measurement.

How Many Significant How Many Significant Figures?Figures?

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

245 m245 m

3 sig figs3 sig figs


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

1074 kg 1074 kg 4 sig figs4 sig figs


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.

0.00345 s0.00345 s



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

2.00345 s2.00345 s



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.

0.275000 m0.275000 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 m275 000 m3 sig figs3 sig figs


275 000.275 000.6 sig figs6 sig figsRule: 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.


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.

20 students20 students Sig figsSig figs


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 (decimal places).precision (decimal places).

375.4 m + 2.54 m = ?375.4 m + 2.54 m = ?Answer = 377.9 mAnswer = 377.9 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.

(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

HomeworkHomework Read page 258Read page 258 Page 257 #7, 11-15Page 257 #7, 11-15

accuracy and precision

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