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P2 (H) Make measurements with accuracy and precision and
record data using scientific notation and International System
(SI) units.
P2 (I) Identify and quantify causes and effects of uncertainties
in measured data.
P2 (J) Organize and evaluate data and make inferences from
data, including the use of tables, charts, and graphs.
P2 (K) Communicate valid conclusions supported by the data
through various methods such as lab reports, labeled
drawings, graphic organizers, journals, summaries, oral
reports, and technology-based reports.
P2 (L) Express and manipulate relationships among physical
variables quantitatively, including the use of graphs, charts,
and equations.
After studying this unit, the students should be able to
 Give the basic quantities of physics and their units
 Convert quantities from one set of units to another
 Perform dimensional analysis (metric and english
units)
 Use scientific notation
 Report answers with a reasonable amount of precision,
given the measurements provided
 Use basic trigonometric functions (SOH CAH TOA)
 Identify and give the relationships between quantities
using sentence, symbols, formula and graphs
Contents
•Base quantities and their units
•Definition of SI base units
•Prefixes used in SI system
•Mass and weight
•Density
•Temperature
•Uncertainty in measurements
•Scientific notation
Systems of Measurement
1. English System – FPS- foot, pound, second
2. Metric System
a) MKS – meter, kilogram, second
b) CGS – centimeter, gram, second
Base physical
quantity
Symbol for
quantity
Name for SI unit
Symbol for SI
unit
Length
l
Meter
m
Mass
m
Kilogram
Kg
Time
t
Second
s
Electric current
I
Ampere
A
Thermodynami
c temperature
T
Kelvin
K
Amount of
substance
n
Mole
mol
Luminous
intensity
I
Candela
cd
DATA
SCIENCE is…
the search for
relationships
that explain
and predict the
behavior of the
universe.
PHYSICS is…
the science
concerned with
relationships
between matter,
energy, and its
transformations.
There is no such thing as
absolute certainty
of a scientific claim.
The validity of a scientific conclusion is always limited by:
• the experiment
design, equipment, etc...
• the experimenter
human error, interpretation, etc...
• our limited knowledge
ignorance, future discoveries, etc...
Scientific Law
a statement describing a natural event
Scientific Theory
an experimentally confirmed explanation
for a natural event
Scientific Hypothesis
an educated guess (experimentally untested)
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
• natural resistance to change
• 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 m2,
force in kg.m/s2, acceleration in m/s2,
volume in m3, energy in kg.m2/s2
1018
1015
1012
109
106
103
102
101
exa
peta
tera
giga
mega
kilo
hecto
deka
E
P
T
G
M
k
h
da
10-18
10-15
10-12
10-9
10-6
10-3
10-2
10-1
atto
a
femto
f
pico
p
nano
n
micro m
milli
m
centi
c
deci
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
x
100%
accepted
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
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
avg
1
34
612
78
126
413
132.6
2
126
127
126
128
125
126.4
3
20
500
62
980
938
500
4
502
501
503
498
499
500.6
Suppose the accepted value for the resistance is 500 Ω.
Then we would classify each groups’ trials as:
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. All non-zero digits are significant.
2. Zeros between other significant
digits are significant.
3. Leading zeros are not significant.
4. Final zeros before the decimal
are not significant.
Operations with Significant Digits
Addition and Subtraction
(link)
round the sum or difference
to the least precise decimal place
Multiplication and Division
(link)
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.
Practice on significant figures,
scientific notation, precision vs
accuracy, metric system prefixes.