Presentation on theme: "Uncertainty and Significant Figures"— Presentation transcript:
1 Uncertainty and Significant Figures Cartoon courtesy of Lab-initio.com
2 Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.
3 Why Is there Uncertainty? Measurements are performed with instrumentsNo instrument can read to an infinite number of decimal placesWhich of these balances has the greatest uncertainty in measurement?
4 Types of Data:Qualitative Data – data collected that does NOT include numbersExamples: red precipitate, beaker felt warmQuantitative Data – data collected that does include numbersExamples: g, C
5 Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value.how close a measurement is to the actual/ accepted valuePrecision refers to the degree of agreement among several measurements made in the same manner.the repeatability of measurements; how close multiple measurements (of the same sample) are to each otherNeither accurate nor precisePrecise but not accuratePrecise AND accurate
6 Precision and Accuracy Bulls eye = analogy for actual/accepted valueArrows = analogy for measurementsaccuracy: highprecision: NAb. accuracy: lowprecision: high
7 Percent ErrorPercent Error – a quantitative expression of accuracy.Percent Error = __Experimental Value-Accepted Value__Accepted ValueJulie measured an object to be 7.89 mm long. When she checked with the actual value of the object, she was supposed to measure 8.91 mm long. What is her percent error?100
8 Types of ErrorRandom Error (Indeterminate Error) - measurement has an equal probability of being high or low.Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration.
9 Rules for Counting Significant Figures - Details Nonzero integers always count as significant figures.3456 has4 significant figures
10 Rules for Counting Significant Figures - Details Zeros- Leading zeros do not count assignificant figures.has3 significant figures
12 Rules for Counting Significant Figures - Details ZerosTrailing zeros are significant only if the number contains a decimal point.9.300 has4 significant figures
13 Sig Fig Practice #1 1.0070 m 5 sig figs 17.10 kg 4 sig figs How many significant figures in each of the following?m 5 sig figs17.10 kg 4 sig figs100,890 L 5 sig figs3.29 x 103 s 3 sig figscm 2 sig figs3,200,000 2 sig figs
14 Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation.6.38 x 2.0 =12.76 13 (2 sig figs)
15 Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m 100.0 g ÷ 23.7 cm3g/cm34.22 g/cm30.02 cm x cmcm20.05 cm2710 m ÷ 3.0 sm/s240 m/slb x 3.23 ftlb·ft5870 lb·ft1.030 g ÷ 2.87 mLg/mL2.96 g/mL
16 Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement.= 18.7 (3 sig figs)
17 Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 100.0 g g76.27 g76.3 g0.02 cm cm2.391 cm2.39 cm713.1 L LL709.2 Llb lblblb2.030 mL mL0.16 mL0.160 mL