Significant Figures, Precision, and Accuracy

Significant Figures• Significant figures are numbers that mean

something when reporting a value.• Just because your calculator gives out the

value 0.5384615 when 7.00 is divided by 13.0, to a scientist not all of the numbers in 0.5384615 have meaning.

• Significant figures reflect the significance of the measurements upon which the scientific calculation is based.

Rules for Counting Rules for Counting Significant Figures - Significant Figures -

DetailsDetailsNonzero integersNonzero integers always count always count as significant figures. as significant figures.

34563456 hashas

4 4 sig figs.sig figs.

Rules for Counting Rules for Counting Significant Figures - Significant Figures -

DetailsDetailsZeros Zeros Leading zerosLeading zeros do not count as do not count as

significant figures. significant figures.

0.04860.0486 has has

33 sig figs. sig figs.

Rules for CountingRules for CountingSignificant Figures - Significant Figures -

DetailsDetails

Zeros Zeros Captive zerosCaptive zeros always always

count as count as significant figures. significant figures.

16.07 16.07 hashas

4 4 sig figs.sig figs.

Rules for CountingRules for CountingSignificant Figures - Significant Figures -

DetailsDetailsZeros Zeros Trailing zerosTrailing zeros are significant are significant onlyonly if the number contains a if the number contains a decimal point.decimal point.

9.3009.300 has has

44 sig figs. sig figs.

Rules for CountingRules for CountingSignificant Figures - Significant Figures -

DetailsDetails

• Exact numbersExact numbers (such as those (such as those in conversion factors) have an in conversion factors) have an infinite number of significant infinite number of significant figures.figures.

11 inch = inch = 2.542.54 cm, exactlycm, exactly

Sig Fig Practice #1Sig Fig Practice #1How many significant figures in each of the following?

1.0070 m 17.10 kg

100,890 L

3.29 x 103 s

0.0054 cm

3,200,000

Use the Rounding Poem to Round Numbers CorrectlyFind your numberLook right next door4 or less, just ignore5 or greater add one more!

Round 4.167 to the closest hundredths4.167 Find your

numberLook right next door4.17

Rules for Significant Rules for Significant Figures in Mathematical Figures in Mathematical

OperationsOperations

Multiplication and DivisionMultiplication and Division:: the the # # of sig. figs. in the result equals of sig. figs. in the result equals the number in the the number in the leastleast precise precise measurement (lowest # of sig. measurement (lowest # of sig. figs.) used in the calculation. figs.) used in the calculation.

6.38 x 2.0 = 6.38 x 2.0 =

12.76 12.76 13 (2 sig figs)13 (2 sig figs)

Sig Fig Practice #2Sig Fig Practice #2

3.24 m x 7.0 m

Calculation Calculator says: Answer:

22.68 m2 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 g/cm3

0.02 cm x 2.371 cm 0.04742 cm2 cm2

710 m ÷ 3.0 s 236.6666667 m/s m/s

1818.2 lb x 3.23 ft 5872.786 lb·ft lb·ft

1.030 g ÷ 2.87 mL 2.9561 g/mL g/mL

Precision and AccuracyPrecision and AccuracyAccuracyAccuracy refers to the agreement of a particular value with refers to the agreement of a particular value with the the true true value.value. If the true value were 5.00 and three If the true value were 5.00 and three measured values 2.0, 6.0, and 7.0 average out to 5.0 (as measured values 2.0, 6.0, and 7.0 average out to 5.0 (as they do), then that they do), then that set of measurementsset of measurements would be accurate. would be accurate.

Precision Precision refers to the degree of agreement among several refers to the degree of agreement among several measurements made in the same manner.measurements made in the same manner.

Neither accurate nor

precise

Precise but not accurate

Precise AND accurate