Uncertainty in MeasurementUncertainty in Measurement

A A digit that must be digit that must be estimatedestimated is called is called uncertainuncertain. A . A measurementmeasurement always has always has some degree of uncertainty.some degree of uncertainty.

Significant figures lecture

Why Is there Uncertainty?Why Is there Uncertainty? Measurements are performed with instruments No instrument can read to an infinite number of decimal places

The numbers recorded in a measurement ( allcertain digits and the first uncertain digit) arecalled the significant figures

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

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

34563456 hashas

44 sig figs.sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

ZerosZeros-- Leading zerosLeading zeros do not count do not count as as

significant figuressignificant figures..

0.04860.0486 has has

33 sig figs. sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

ZerosZeros-- Captive zeros Captive zeros always always

count ascount assignificant figures.significant figures.

16.07 16.07 hashas

44 sig figs. sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

ZerosZerosTrailing zerosTrailing zeros are significant are significant only if the number contains a only if the number contains a decimal point.decimal point.

9.3009.300 has has

44 sig figs. sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

Exact numbersExact numbers have an infinite have an infinite number of significant figures.number of significant 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

5 sig figs

17.10 kg 4 sig figs

100,890 L 5 sig figs

3.29 x 103 s 3 sig figs

0.0054 cm 2 sig figs

3,200,000 2 sig figs

Rules for Significant Figures in Rules for Significant Figures in Mathematical OperationsMathematical Operations

Multiplication and DivisionMultiplication and Division:: # sig # sig figs in the result equals the number figs in the result equals the number in the least precise measurement in the least precise measurement used in the calculation.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 23 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2

710 m ÷ 3.0 s 236.6666667 m/s 240 m/s

1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft

1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Rules for Significant Figures Rules for Significant Figures in Mathematical Operationsin Mathematical Operations

Addition and SubtractionAddition and Subtraction: The : The number of decimal places in the number of decimal places in the result equals the number of decimal result equals the number of decimal places in the least precise places in the least precise measurement.measurement.

6.8 + 11.934 =6.8 + 11.934 =

18.734 18.734 18.7 ( 18.7 (3 sig figs3 sig figs))

Sig Fig Practice #3Sig Fig Practice #3

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Rules for Significant Figures in Rules for Significant Figures in Mathematical OperationsMathematical Operations

Addition and substractionAddition and substraction:: when when working with whole numbers, the working with whole numbers, the answer should be rounded so that answer should be rounded so that the final significant digit is in the the final significant digit is in the same place as the leftmost same place as the leftmost uncertain digit. uncertain digit.

5400 + 365 =5400 + 365 =

5800 (2 sig figs)5800 (2 sig figs)

Sig Fig Practice #3Sig Fig Practice #3

3.24 m + 7 m

Calculation Calculator says: Answer

10.24 m 10 m

198 g – 20 g 178 g 180 g

4.2 cm + 20 cm 24.2 cm 20 cm

713 L - 3.872 L 709.128 L 709 L

1818.2 lb + 30 lb 1848.2 lb 1850 lb

2030.3 mL - 800 mL 1230.3 mL 1200 mL

Rules for Rounding numbers Rules for Rounding numbers ending in 5ending in 5

If the number you are rounding is 5, then look at the preceding digit

If the preceding digit is even, keep it

If the preceding digit is odd round up

Rounding numbers that end Rounding numbers that end in 5in 5

3.625 m x 4.0 m

Calculation Calculator says: Answer

14.5 m2 14 m2

0.307 m x 50.0 m 15.35 m2 15.4 m2

Precision and AccuracyPrecision and AccuracyAccuracyAccuracy refers to the agreement of a refers to the agreement of a particular value with the particular value with the truetrue value.value.

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

Neither accurate nor

precise

Precise but not accurate

Precise AND accurate