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UNCERTAINTY IN MEASUREMENTS
Different measuring devices have different uses
and different degrees of precision
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ESTIMATING UNCERTAINTY
• To estimate a measuring devices
uncertainty, read to ½ the
smallest scale division.
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INDICATING UNCERTAINTY IN A MEASUREMENT
• Indicate using + after the recorded measurement
stating the ½ beyond the smallest scale division
followed by the units
•
Example:
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INDICATING UNCERTAINTY IN A MEASUREMENT
For digital devices, uncertainty is
always +/- .1 of the smallest
scale
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SIGNIFICANT FIGURES - COUNTING
• Counting Significant Figures – Atlantic Pacific Method
• Decimal point absent (Atlantic) – begin on right side
of number and cross out all zero digits until first non
– zero digit, remaining digits are significant
• Decimal point present (Pacific) - begin on left side of
number and cross out all zero digits until first non –
zero digit, remaining digits are significant
• Exact numbers – have infinite number of significant
figures
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EXAMPLES: COUNTING SIG. FIGS
234 cm
67000 cm
45000 cm
560. cm
0.5630 cm
1.0034 cm
0.00467 cm
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SCIENTIFIC NOTATION
• Used to shorten large or small numbers
• Standard Form
Base - one number to the left of the decimal
place, with all the significant figures shown
Exponent – is the number of places the decimal
point must be shifted to give the number in
standard form
Negative Exponent – value less than 1
Positive Exponent – value greater than 1
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EXAMPLES: SCIENTIFIC NOTATION
124300 =
0.00362 =
1300000 =
1.23E-5 =
5.61 x 10^6 =
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SIGNIFICANT FIGURES IN MATHEMATICAL
OPERATIONS
• Addition/Subtraction – the answer will have the
same number of decimal places as the
measurement with the fewest decimal places
• Multiplication/Division – the answer will have the
same number of significant figures as the
measurement with the fewest significant figures
• Mixed operations – follow the order of operations,
determining s.f. for each step, do not round until
the end!
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EXAMPLE OF SIG. FIGS IN CALCULATIONS
33.5 cm + 7.88 cm + 0.977 cm =
23000 km + 8.7 km =
67.23 cm x 9.22 cm =
(200 cm x 3.333) + (300 x 1.35) cm =
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CALCULATORS AND SCIENTIFIC NOTATION
• Calculators handle scientific notation by only
inputting the exponent, using an EXP or EE key
enter the base as you would a regular
number, then press EXP or EE, then enter the
exponent
• Display – the calculator used E to show
exponent ( E means x 10 )
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RANDOM ERRORS - PRECISION
• Random errors - Precision
•A random error makes the measured value
both smaller and larger than the true value
(this happens by chance alone)
•Reduce random errors- repeat the
experiment
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SYSTEMATIC ERRORS
• Systematic error - Accuracy
• Errors due to "incorrect" use of
equipment or poor experimental design
• Makes the measured value always smaller or
larger than the true value, but not both.
• An experiment may involve more than one
systematic error and these errors may nullify
one another
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CATEGORIES OF SYSTEMATIC ERRORS
• Personal errors – the result of ignorance,
carelessness, prejudices, or physical limitations on
the experimenter.
• Instrumental Errors - attributed to imperfections in
the tools with which the analyst works.
• Method Errors - results when you do not consider
how to control an experiment.
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DETERMINATION OF ERROR
• Accuracy - how close a
measurement is to the true value of
a quantity.
• Precision - how close several
measurements are to each other.
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PRECISION VS. ACCURACY
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EVALUATING ACCURACY AND PRECISION IN DATA
• When evaluating whether data is accurate or precise
you could look at
Accuracy
Precision
Single Data Point
A single data point is accurate if
it is close the literature value
A single data point is
precise if it has many
decimal places/significant
figures. Meaning, you
used a very precise tool or
method for measuring the
value.
Set of Data Points
A set of data points are accurate
if the average or mean is close
to the literature value. This is
the reason we do multiple trials.
Any random errors cancel out
when the average is taken, thus
random error is reduced.
A set of data points are
precise if they are all very
close together. This
definition refers to the
consistency of the data.
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PERCENT UNCERTAINTIES AND ERRORS
• Percent Error
(accepted value – experimental value) x 100
accepted value
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CH. 3 - MEASUREMENT
TEMPERATURE
CONVERSIONS
A. TEMPERATURE
Temperature
measure of the average KE of
the particles in a sample of
matter
Kelvin  oC  273.15
9o
Fahrenheit 
C  32
5
5 o
Celsius  ( F  32)
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A. TEMPERATURE
Convert these temperatures:
1)
25oC = ______________K
2)
-15oF = ______________ K
3)
315K = ______________ oC
4)
288K = ______________ oF
CH. 3 - MEASUREMENT
DIMENSIONAL ANALYSIS
CONVERSION FACTORS
PROBLEMS
A. PROBLEM-SOLVING STEPS
1. Analyze
2. Plan
3. Compute
4. Evaluate
B. DIMENSIONAL ANALYSIS
Dimensional Analysis
A tool often used in science for converting units within
a measurement system
Conversion Factor
A numerical factor by which a quantity expressed in
one system of units may be converted to another
system
B. DIMENSIONAL ANALYSIS
The “Factor-Label” Method
Units, or “labels” are canceled, or “factored” out
g
g
cm 

3
cm
3
B. DIMENSIONAL ANALYSIS
Steps to solving problems:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each
bottom number.
4. Check units & answer.
C. CONVERSION FACTORS
Fractions in which the numerator and
denominator are EQUAL quantities
expressed in different units
Example:
1 in. = 2.54 cm
Factors: 1 in.
and
2.54 cm
2.54 cm
1 in.
HOW MANY MINUTES ARE IN 2.5
HOURS?
Conversion factor
2.5 hr x
1
cancel
60 min
1 hr
= 150 min
By using dimensional analysis / factor-label method,
the UNITS ensure that you have the conversion right
side up, and the UNITS are calculated as well as the
numbers!
C. CONVERSION FACTORS
Learning Check:
Write conversion factors that relate
each of the following pairs of units:
1. Liters and mL
2. Hours and minutes
3. Meters and kilometers
E. DIMENSIONAL ANALYSIS
PRACTICE
You have $7.25 in your pocket in quarters.
How many quarters do you have?
$7.25
1
X
4 quarters
1 dollar
E. DIMENSIONAL ANALYSIS PRACTICE
How many seconds are in 1.4
days?
1.4
24 hr 60
days
min
60 s
1
day
1
min
1 hr
= 12000 s
E. DIMENSIONAL ANALYSIS PRACTICE
How many milliliters are in 1.00 quart of milk?
E. DIMENSIONAL ANALYSIS PRACTICE
You have 1.5 pounds of gold. Find its volume in cm 3 if
the density of gold is 19.3 g/cm3.
E. Dimensional Analysis Practice
Your European hairdresser wants to cut your hair 8.0
cm shorter. How many inches will he be cutting off?
E. Dimensional Analysis Practice
Roswell football needs 550 cm for a 1st down.
How many yards is this?
E. Dimensional Analysis Practice
A piece of wire is 1.3 m long. How many 1.5-cm
pieces can be cut from this wire?
E. DIMENSIONAL ANALYSIS PRACTICE
How many liters of water would fill a container
that measures 75.0 in3?
BASE UNITS
In the SI (Le Système International
d'Unités) system of measurement there
are seven base units
These units are used in the measurement
of different quantities and independent
of each other
BASE UNIT
Quantity
Unity
Symbol
Mass
Grams
g
Length
Meter
m
Amount of
Substance
Mole
mol
Time
Second
s
Electric Current
Ampere
A
Kelvin
K
candela
cd
Temperature
Luminous Intensity
D. SI PREFIX CONVERSIONS
1. Memorize the following chart. (next slide)
2. Find the conversion factor(s).
3. Insert the conversion factor(s) to get to the
correct units.
4. When converting to or from a base unit, there will
only be one step. To convert to or from any other
units, there will be two steps.
A. SI PREFIX CONVERSIONS
move right
move left
Prefix
Symbol
Factor
tera-
T
1012
gigamegakilohectodekaBASE UNIT
decicentimillimicronanopico-
G
M
k
h
da
--d
c
m

n
p
109
106
103
102
101
100
10-1
10-2
10-3
10-6
10-9
10-12
D. SI PREFIX CONVERSIONS
Tera-
1 T(base) = 1 000 000 000 000(base) = 1012 (base)
Giga-
1 G(base) = 1 000 000 000 (base) = 109 (base)
Mega-
1 M(base) = 1 000 000 (base) = 106 (base)
Kilo-
1 k(base) = 1 000 (base) = 103 (base)
Hecto-
1 h(base) = 100 (base) = 102 (base)
Deka-
1 da(base) = 101 (base)
Base
1 (base) = 1 (base)
Deci-
10 d(base) = 1(base)
Centi-
100 c(base) = 1 (base)
Milli-
1000 m (base) = 1(base)
Micro-
1 (base) = 1 000 000 µ = 10-6(base)
Nano-
1 (base) = 1 000 000 000 n = 10-9(base)
Pico-
1 (base) = 1 000 000 000 000 p = 10-12(base)
D. SI PREFIX CONVERSIONS
a. cm to m
b. m to µm
c. ns to s
d. kg to g
D. SI PREFIX CONVERSIONS
1)
20 cm =
______________ m
2) 0.032 L =
______________ mL
3) 45 m =
______________ m
D. SI PREFIX CONVERSIONS
4) 805 Tb = ______________ b
Terabytes
bytes
D. SI PREFIX CONVERSIONS
1) 400. g = ______________ kg
1) 57 Mm = ______________ nm
MATTER
Matter is defined as anything that has mass and takes up space.
Volume is the amount of space matter occupies.
The smallest building block of matter is the atom.
STATES OF MATTER
Solid- definite volume
and definite shape;
vibrate at fixed points
Liquid- has a definite
volume but an
indefinite shape;
particles can move
past one another and
will take the shape of
its container
Gas- Neither a definite
volume nor a definite
shape; particles move
rapidly and will take
the shape of its
container
Plasma- high
temperature state in
which atoms lose
electrons (Sun and
stars)
UNITS FOR MATTER
Volume is measured in mL, L, or cm3 and is done so
by using a metric ruler or graduated cylinder.
Mass, the amount of matter in an object, is
measured by using a scale. The units for mass
are the gram (g) or kilogram (kg).
Weight is the measure of the pull of gravity on an
object. It is measured in Newtons (N) by using a
spring scale.
Mass does not change with location; however,
weight does change with location.
PURE SUBSTANCES
Element- The simplest type of a pure substance
made of only one kind of atom. The smallest
particle of an element is an atom.
Compounds- Pure substances that are made of
two or more elements that are chemically
bonded. Examples are sugar, carbon dioxide,
ammonia, baking soda, and vinegar.
COMPOUNDS
Compounds can be broken down into simpler
substances while elements cannot. Heat and
electricity are often used to break apart
compounds.
The properties of a compound are very different
from the elements that make up the compound.
Ex.- Salt is a compound made from sodium ( a
silvery metal) and chlorine ( a greenish poisonous
gas)
COMPOUNDS
The smallest particle of a compound is a
molecule. Molecules of a compound are all
alike. Water in the ocean is like water that
comes from the faucet.
Atoms are represented by symbols and
molecules are represented by formulas.
Every element and compound has chemical
properties that are used for classification.
CLASSIFYING MATTER
Matter is classified into one of two groups: Pure Substances or Mixtures
Pure substances include compounds and elements and they have a definite
composition.
Mixtures contain more than one substance; therefore, the composition varies.
MIXTURES
A mixture is a blend of two or more kinds of
matter which retains its own identity and
properties.
Mixtures that have a uniform composition are
called homogeneous mixtures or solutions.
Mixtures that do not have uniform compositions
are called heterogeneous mixtures.
In Chemistry, the amount of substance present
in a mixture is referred to by percent by mass
of the substance.
PROPERTIES
Physical properties
can be observed
without changing
the identity of the
substance.
 Melting Point
 Boiling Point
 Freezing Point
 Color
 Mass
Chemical
Properties can be
observed when
new substances
are produced.
 Ability to Burn
 Ability to Tarnish
 Ability to Rust
TYPES OF PHYSICAL PROPERTIES
Extensive properties
depend on the amount
of matter present.
 Volume
 Mass
 Amount of Energy
Intensive properties
do not depend on
the amount of
matter present.
 Melting Point
 Boiling Point
 Density
 Conductivity
PHYSICAL CHANGE
A change is a substance that does not involve a
change in the identity of the substance
Examples include
 Breaking
 Tearing
 Changes of state
 Grinding
 Cutting
CHEMICAL CHANGE
Chemical Reactions- changing of a substance into something else
Examples include
 Burning, Rusting, Tarnishing, Reacting
Reactants- substances that react
Products- Substances that are produced
CHEMICAL REACTIONS
Evidence that a chemical reaction has taken place includes:
 Heat
 Light
 Production of a gas
 Production of a precipitate (solid substance)
LAW OF CONSERVATION OF MATTER
Matter can be neither created nor destroyed but can be transformed from one form to
another
The same will happen for energy as well. It is conserved during reactions.
Kinetic energy- energy in motion
Potential energy- stored energy
ENERGY IN A CHEMICAL REACTION
Endothermic- heat is absorbed
Exothermic- heat is released
Endergonic- energy is absorbed
Exergonic- energy is released
PERIODIC TABLE OF ELEMENTS
Groups or Families- vertical columns on periodic
table
Periods, row, or series- horizontal rows on
periodic table
Periodic table is divided into three main sections
 Metals
 Nonmetals
 Metalloids
METALS
Found on left side
of periodic table
Good conductors of
heat and
electricity
Tend to have 3 or
fewer valence
electrons
Malleable
Ductile
High Luster
Most are solids at
room
temperature
NONMETALS
Located on the right
side of periodic
table with the
exception of
Hydrogen
Poor conductors of
heat and electricity
Tend to have 5 or
more valence
electrons
Non-malleable
Non-ductile
Brittle
Dull
Most are gases at
room temperature
Group 8- Noble gases
are inert
METALLOIDS
Elements that have characteristics of both metals and nonmetals
Semiconductors
Used in computers, calculators, watches, televisions, and radios
Include B, Si, Ge, As, Sb, Te