Transcript No Slide Title
DATA
There is no such thing as absolute certainty of a scientific claim.
The validity of a scientific conclusion is always limited by:
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the experiment
design, equipment, etc...
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the experimenter
human error, interpretation, etc...
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our limited knowledge
ignorance, future discoveries, etc...
developed in France in 1795 a.k.a. “SI” International System of Units The U.S. was (and still is) reluctant to “go metric.”
• •
very costly to change perception of “Communist” system
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natural resistance to change
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American pride
The SI unit of:
• length is the
meter , m
• time is the
second , s
• mass is the
kilogram , kg.
• electric charge is the
Coulomb , C
• temperature is the degree
Kelvin , K
• an amount of a substance is the
mole , mol
• luminous intensity is the
candle , cd
•
The second is defined in terms of atomic vibrations of Cesium-133 atoms.
•
The meter is defined in terms of the speed of light .
•
The kilogram is still defined by an official physical standard .
“Derived units” are combinations of these “fundamental units”
Examples include speed in
m/s
, area in
m 2
, force in
kg .
m/s 2
, acceleration volume in
m 3
, energy in
kg .
in
m 2 m/s /s 2 2
,
10 18 10 15 10 12 10 9 10 6 10 3 10 2 10 1 exa peta tera giga mega kilo hecto deka E P T G M k h da 10
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18 10
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15 10
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12 10
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9 10
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6 10
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3 10
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2 10
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1 atto femto pico nano micro milli centi deci f a p n
m
m c d
Explore the metric system at link1 , link2 , and link3 .
See definitions of metric units here .
Click here to do conversions.
All measurements have some degree of uncertainty.
Precision
single measurement exactness, definiteness group of measurements agreement, closeness together
Accuracy
closeness to the accepted value
% error
= accepted observed accepted x 100%
Example of the differences between precision and accuracy for a set of measurements: Four student lab groups performed data collection activities in order to determine the resistance of some unknown resistor (you will do this later in the course). Data from 5 trials are displayed below.
Group 1 2 3 4 Trial 1 34 126 20 502 Trial 2 612 127 500 501 Trial 3 78 126 62 503 Trial 4 126 128 980 498 Trial 5 413 125 938 499 Suppose the accepted value for the resistance is 500 Ω. Then we would classify each groups’ trials as: avg 132.6
126.4
500 500.6
Group 1: neither precise nor accurate Group 2: precise, but not accurate Group 3: accurate, but not precise Group 4: both precise and accurate
1.
2.
All non-zero digits are significant .
Zeros between other significant digits are significant .
3.
4.
Leading zeros are not significant . Final zeros before the decimal are not significant .
Operations with Significant Digits
Addition and Subtraction round the sum or difference to the least precise decimal place Multiplication and Division round so that the product or quotient has a total number of significant digits equal to the total number of significant digits of the least precise quantity
Learn more about significant digits here and here .
Check your understanding here and here .
The “bottom line” is that the precision to which a measured or calculated amount is written provides valuable information as to the precision (certainty) of that value and the device used to measure it.