Uncertainty in Measurement © 2012 Pearson Education, Inc.

Uncertainty in Measurements Different measuring devices have different uses and different degrees of accuracy. © 2012 Pearson Education, Inc.

ESTIMATE THE LAST PLACE! Figure 1.24 Uncertainty and significant figures in a measurement.

© 2012 Pearson Education, Inc. Significant Figures The term significant figures refers to digits that were measured. When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers. © 2012 Pearson Education, Inc.

© 2012 Pearson Education, Inc. Significant Figures All nonzero digits are significant. Zeroes between two significant figures are themselves significant. Zeroes at the beginning of a number are never significant. Zeroes at the end of a number are significant if a decimal point is written in the number. © 2012 Pearson Education, Inc.

Significant Figures Rule 1: 123 grams (three significant figures) Rule 2: 103 grams (three significant figures) Rule 3: 0.1 or 0.01 gram (one significant figures) 1 x 10 -1 or 1 x 10 -2 g Rule 4: End of number with decimal point 10300 g Chapter 1, Unnumbered Table, Page 23

7.6 cm = 2 significant figures Chapter 1, Unnumbered Figure 3, Page 32 7.6 cm = 2 significant figures

115 km/hr = 3 significant figures Chapter 1, Unnumbered Figure 4, Page 42

What is “wrong” with the measurements? Chapter 1, Unnumbered Figure 5, Page 32 How many significant figures in the volume?

Chapter 1, Unnumbered Figure 1, Page 34

Always estimate the LAST DIGIT- even if it is a zero! 14.45 mL If on the LINE 14.40 mL Chapter 1, Unnumbered Figure 2, Page 34

© 2012 Pearson Education, Inc. Significant Figures When addition or subtraction is performed, answers are rounded to the least significant decimal place. When multiplication or division is performed, answers are rounded to the number of digits that corresponds to the least number of significant figures in any of the numbers used in the calculation. © 2012 Pearson Education, Inc.

Addition/Subtraction “POSITION” Chapter 1, Unnumbered Table, Page 24 Multiplication/Division “least amount/number”

Unit Conversions: Dimensional Analysis Convert 8.00 m to inches Chapter 1, Unnumbered Figure 2, Page 26

Determining Accuracy Percent Error Accuracy is how close an experimental measurement is to the accepted value. This is usually reported as percent error, defined by the equation: Percent error = |your result- accepted value| x 100% accepted value Negative number- experimental value too low Positive number = experimental value too high

How are you going to do this? Measurements needed? Determining Thickness of Aluminum Foil and determine percent error in your measurements Pre-Lab How are you going to do this? Measurements needed? Additional information necessary? What should go in data table? Materials needed Accepted Value 22 microns (mm) Chapter 1, Unnumbered Figure 2, Page 27

Lab Notebook- IN INK ONLY Title: Purpose/Problem: Materials: Numbered procedure (include SAFETY concerns) Data Table (measurements AND calculated values) Calculations (with significant figures) Percent Error(HOW did your error in measurement affect your calculated value?) Error Analysis Conclusion

  Pts Self Peer Tchr Format Includes title, members in group, 1 sentence purpose or problem identified, 2 Materials Include list of materials needed (only necessary when you are designing the procedure) Procedure Procedures were outlined in a step-by-step fashion that could be followed by anyone without additional explanations. No adult help was needed to accomplish this. Must include SAFETY. Data Collection Measurements and calculated values with labels are in your data table. Data are entered in table(s) during class time. Graphs and tables are labeled and titled (when applicable). 3 Calculations ONE sample calculation is shown; the results are labeled, and included correct number of significant figures. Value should appear in your data table. Error Analysis Predictions are made about your error in measurement. How did your error in measurement affect your calculated value? Conclusion Conclusion is a grammatically correct, one-to two- sentence summary of results, and is a separate section of the report. (Include any calculated error in statement(s)). 15