Date post: | 03-Jan-2016 |
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• 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
Accuracy v. Precision
Not accurate – the hits are not close to bulls eye
Not precise – none of the hits are close togetherNot accurate – none of the hits are close to
bulls eye
Precise – all the hits are close togetherAccurate – all the hits are near the bulls eye
Precise – all the hits are close togetherPrecise – all the hits are close together
2 ways to show 2 ways to show accuracy & precisionaccuracy & precision
Significant FiguresPercent Error
• Significant Figures : numbers that show precision in measurements
• Key question: Is there a decimal?
YES: come from left, 1st number (non-zero) and anything after it is significant
0.001 ml 4.7200 mL 82.0 sec
Accuracy with Measurements
Accuracy with Measurements
• Significant Figures
• Practice: http://science.widener.edu/svb/tutorial/sigfigures.html
• Rounding to Significant Figures
314.721 (four) 0.001775 (two)
8792 (two) 4.3622x10-5 (three)
87.073 (three) 1040 (two)
Accuracy with Measurements
314.7
8800
87.1
0.00184.36x10-5
1.0x103
• 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 MeasurementsAccuracy with Measurements
• Significant Figures in Calculations
• Multiplication and Division
• Answer’s sig figs = least sig figs
• Example: 3.126x10-6 x 2.8x10-7 =
8.8x10-
13
Accuracy with Measurements
• Practice!
Accuracy with Measurements
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 =2)9.62 x 105 x 5.4 x 106 =3)2.62x10-4 ÷ 3.14x10-8 =4)7.72x10-2 x 5.74x10-2 =5)8.22x10-5 ÷ 3 x104 =
3.51x10-
85.2x1012
8344.00443
1
= 8.34x103
3x10-9
= 4.43x10-
3
Accuracy with Measurements
• Practice!
Accuracy with Measurements
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 = 2)195.4 – 193 = 3)5.8465x102 + 1.2x103 = 4)9x102 + 5x102 = 5)46.8 – 41.4 =
40.92
1.8x103
1.4x103
5.4
WebAssign HintWebAssign Hint• Just assume that you should use sig figs from here on
out. Also, on the WebAssign, you will see this:
This symbol means you must put the correct number of significant figures on web assign (not always 4)
• Percent error: shows how accurate experimental values are by determining how much error they have
Data Analysis
Actual = correct answer
Experimental = what you got
• 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?
Data Analysis
5.82% error
• Practice: The density of gold is 19.32 g/cm3. What is the percent error of the following experimental measurements?
a) 20.1 g/cm3 c) 19.7 g/cm3
b) 19.51 g/cm3 d) 18.90 g/cm3
Data Analysis
4.04 % error
0.9834 % error
1.97 % error
2.174 % error
• Practice Problems
Accuracy with Measurements
Due tomorrow