Transcript Introduction Day 1, Monday 24 August, 2009

Day 8, Friday, 4 September, 2015
Uncertainty and Significant Figures
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Unit Analysis
Lecture
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Uncertainty
Significant Figures
Dimensional Analysis
Unit Analysis
you wish
Given units
Given
= Unknown units
(1) _ Unknown = Unknown
(Given)
(1)
actually does
Day 8, Friday, 4 September, 2015
New Stuff
Good things to know
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2.54 cm/in
2.2 lbs/kg
39.5 in/m
1,000 kg/ton
(2,200 lbs/ton)
Water’s density is 1 ton/m3 or 1 g/cc
Uncertainty
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Instruments always have flaws
Measurements always involve
estimation
Take measurements from
the perpendicular
Meter stick demo
The last digit is estimated
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The certain digits and the estimated
digit of a measurement together are
significant digits.
Reliability
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Precision
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Repeatability of a measurement
Accuracy
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Agreement with an accepted value
Lucky Duck
High Accuracy
Low Precision
Lucky Duck 2
Low Accuracy
High Precision
Unlucky Duck
High Accuracy
High Precision
When is Zero significant?
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As a measured value zero is significant
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A zero between two other non zero numbers is
always significant
As a placeholder zero is not significant
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Leading zeros before decimal point are meaningless
Leading zeros are not significant
Unmeasured trailing zeros are not significant
The two uses of zero
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1. As an actual value
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The number between 1 and -1
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significant
2. As a placeholder
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The value of a column
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Not significant
0.0023405670000
0.0023405670000
not significant
0.0023405670000
significant*
0.0023405670000
significant
0.0023405670000
totally useless
* If measured (They bothered to write it
so it is assumed to be significant)
Multiplying and dividing Sig Figs
A chain is only as strong as its weakest link.
A nice paint job on a sloppily built car looks sloppy
A sloppy paint job on a nicely built car looks sloppy
If I give $137.58 to 972 people then I have given away $133,727.76.
If I give away $137.58 to about 1,000 people have I given away $133,727.76?
NO, I have given away about $140,000.
If I give away about $140 to 972 people have I given away $133,727.76?
NO, I have given away about $140,000.
Multiplying or Dividing
Use the least number of Sig Figs given
(regardless of where the decimal point is).
1.23456789 x 1.2 = 1.5
1.23456789 x 1.20000000 = 1.48148147
1.23456789 / 1.2 = 1.0
1.23456789 / 1.20000000 = 1.028806575
Adding and Subtracting Sig Figs
Use the smallest decimal column that is
common to both numbers (counted from the
decimal point).
1.23456789 + 1.2 = 2.4
1.23456789 + 1.23456789 = 2.46913578
1.23456789 - 1.2 = 0.0
1.23456789 - 1.20000000 =0.03456789
Format for Homework Problems
Credits
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Dartboard graphics
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www.mathsisfun.com