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, 1st number (non-zero)
and anything after it is significant
0.001 ml
4.7200 mL
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
6.02x1023
Accuracy with Measurements
• Significant Figures
• Practice:
http://science.widener.edu/svb/tutorial/sigfigure
s.html
• Rounding to Significant Figures
314.7
314.721 (four)
8800
8792 (two)
87.1
87.073 (three)
0.001775
0.0018 (two)
-5 -5
4.36x10
4.3622x10
(three)
3
1.0x10
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: 3.126x10-6 x 2.8x10-7 =
8.8x10-13
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 = 3.51x10-8
2) 9.62 x 105 x 5.4 x 106 = 5.2x1012
3) 2.62x10-4 ÷ 3.14x10-8 = 8344= 8.34x103
4) 7.72x10-2 x 5.74x10-2 = .004431= 4.43x10-3
-9
-5
4
3x10
5) 8.22x10 ÷ 3 x10 =
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) 9.27x10-4 + 9.237x10-5 = 1.019x10-3 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) 5.8465x102 + 1.2x103 = 1.8x103
4) 9x102 + 5x102 = 1.4x103
5) 46.8 – 41.4 = 5.4
WebAssign 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)
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/cm3. What
is the percent error of the following experimental
measurements?
a) 20.1 g/cm3
4.04 % error
b) 19.51 g/cm3
0.9834 % error
c) 19.7 g/cm3
1.97 % error
d) 18.90 g/cm3
2.174 % error
Accuracy with Measurements
• Practice Problems
Due tomorrow