Accuracy v Precision Quality of Data Precision Wellgrouped

Accuracy v. Precision • Quality of Data • Precision: • Well-grouped together • Results are repeatable • Compare to other repeated measurements • Accuracy: • Close to actual value • Compare to correct value

Accuracy v. Precision Precise – all the hits are close together Not accurate – the hits are not close to bulls eye Not precise – none of the hits are close together Not accurate – none of the hits are close to bulls eye Precise – all the hits are close together Accurate – all the hits are near the bulls eye

2 ways to show accuracy & precision Significant Figures Percent Error

Accuracy with Measurements • Significant Figures : numbers that show precision in measurements • Key question: Is there a decimal? YES: come from left, 1 st number (non-zero) and anything after it is significant 0. 001 ml 4. 7200 m. L 82. 0 sec

Accuracy with Measurements • Significant Figures : numbers that show precision in measurements • Key question: Is there a decimal? NO: come from right, until you hit a number and everything past it is significant 5090 dm 7000 meters * Scientific Notation: don’t count it 6. 02 x 1023

Accuracy with Measurements • Significant Figures • Practice: http: //science. widener. edu/svb/tutorial/sigfigure s. html • Rounding to Significant Figures 314. 721 (four) 0. 00180. 001775 (two) 8800 8792 (two) 4. 36 x 10 -5 4. 3622 x 10 -5 (three)87. 1 1. 0 x 103 87. 073 (three) 1040 (two)

Accuracy with Measurements • Practical Applications: Estimating in Measurements • Always estimate one decimal place past the actual accuracy of the measuring device’s scale

Accuracy with Measurements • Practical Applications: Estimating in Measurements

Accuracy with Measurements • Significant Figures in Calculations • Multiplication and Division • Answer’s sig figs = least sig figs • Example: 3. 126 x 10 -6 x 2. 8 x 10 -7 = 8. 8 x 10 -13

Accuracy with Measurements • Practice! Use your calculator to find the following answers. Report it in scientific notation. Round to the proper amount of sig figs 1) 5. 231 x 10 -4 ÷ 1. 49 x 104 = 3. 51 x 10 -8 2) 9. 62 x 105 x 5. 4 x 106 = 5. 2 x 1012 3) 2. 62 x 10 -4 ÷ 3. 14 x 10 -8 = 8344= 8. 34 x 103 4) 7. 72 x 10 -2 x 5. 74 x 10 -2 =. 004431= 4. 43 x 10 -3 -9 -5 4 3 x 10 5) 8. 22 x 10 ÷ 3 x 10 =

Accuracy with Measurements • Significant Figures in Calculations • Addition & Subtraction • Answer’s decimal places = least decimal places • Examples: a) 128. 112 g – 18. 92 g = 109. 19 g b) 100 g +. 01 g = 100 g c) 9. 27 x 10 -4 + 9. 237 x 10 -5 = 1. 019 x 10 -3 g. 000927 +. 00009237 =. 001019 g

Accuracy with Measurements • Practice! Use your calculator to find the following answers. Report it in scientific notation. Round to the proper amount of sig figs 1) 39. 64 + 1. 3 = 40. 9 2) 195. 4 – 193 = 2 3) 5. 8465 x 102 + 1. 2 x 103 = 1. 8 x 103 4) 9 x 102 + 5 x 102 = 1. 4 x 103 5) 46. 8 – 41. 4 = 5. 4

Web. Assign Hint • Just assume that you should use sig figs from here on out. Also, on the Web. Assign, you will see this: This symbol means you must put the correct number of significant figures on web assign (not always 4)

Data Analysis • Percent error: shows how accurate experimental values are by determining how much error they have Actual = correct answer Experimental = what you got

Data Analysis • Practice: The density of silver is 10. 49 g/ml. If I measured it to be 11. 1 g/ml, what is my percent error? 5. 82% error

Data Analysis • Practice: The density of gold is 19. 32 g/cm 3. What is the percent error of the following experimental measurements? a) 20. 1 g/cm 3 4. 04 % error c) 19. 7 g/cm 3 1. 97 % error b) 19. 51 g/cm 3 0. 9834 % error d) 18. 90 g/cm 3 2. 174 % error

Accuracy with Measurements • Practice Problems Due tomorrow