Uncertainty in Measurement
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Transcript of Uncertainty in Measurement
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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
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Why Is there Uncertainty?Why Is there Uncertainty? Measurements are performed with instruments No instrument can read to an infinite number of decimal places
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The numbers recorded in a measurement ( allcertain digits and the first uncertain digit) arecalled the significant figures
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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.
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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.
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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.
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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.
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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
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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
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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)
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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
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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))
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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
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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)
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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
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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
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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
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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