Science of Physics
Metric Prefixes
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SI Units
Rules for Significant Figures
Rules for Calculating with
Significant Figures
Determining Individual and Overall Percent Error
• Error is identified as +/- half the smallest increment of
measurement per device.
• In the image above the smallest increment of the ruler is 0.1 cm.
Therefore the error when measuring would be +/- 0.05 cm.
• Hence, the diameter of the block would be 0.55 cm +/- 0.05 cm.
Carrying Error throughout the Calculations
• When multiplying or dividing:
– Convert all +/- errors into a % error.
– Add % errors together.
– Convert total % error back to +/- error for the final
calculation.
Density Cube Example
Equations
Recorded Data
•
Volume = side x side x side
•
Density =
Mass
Volume
•
•
Side Length = 2.50 cm +/- 0.05 cm
Mass = 17.10 g +/- 0.05 g
Percent Error for Each Measurement
0.05
2.50
x 100 = 2.0%
0.05
17.10
x 100 = 0.29%
Calculate out Answer
D = Mass =
17.10 g
= 1.0944 g/cm3
Volume
(2.50 cm)(2.50 cm)(2.50 cm)
Add Percent Errors
0.29% + 2.0% + 2.0% + 2.0% = 6.29%
Final Answer
1.09 g/cm3 +/- 6.29%
or
1.09 g/cm3 +/- 0.07 g/cm3
Double Checking Answers
• Dimensional Analysis – utilize the units to
determine if your answer makes sense. If the
answer is asking for the amount of time
required to run a race, the final unit should be
in seconds, minutes, hours, etc.
• Order of Magnitude – Does the answer make
any sense?
Energy Order of Magnitude
Links for Order of Magnitude
• http://www.flixxy.com/science-education-universedocumentary.htm
• http://primaxstudio.com/stuff/scale_of_universe/
• http://www.youtube.com/watch?v=qysS9xThKXc
Sources
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http://www.scienceteacherprogram.org/physics/Image3.gif
http://www.spiraxsarco.com/images/resources/steam-engineering-tutorials/2/1/table_2_1_1.gif
http://whs.wsd.wednet.edu/Faculty/Busse/MathHomePage/busseclasses/physics/studyguides/chapter
1/Significant-Digits.jpg
http://whs.wsd.wednet.edu/Faculty/Busse/MathHomePage/busseclasses/physics/studyguides/chapter
1/adding-significant.jpg
http://www.chs.k12.nf.ca/science/s1206/physics/sigfigcalc.gif
http://talklikeaphysicist.com/wp-content/uploads/2009/01/energy-scale-100-orders-of-magnitude.jpg
http://www.beginnerphysics.net/images/Fig.1.29.gif