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1.3 Significant Figures and
Scientific Notation
Types of Uncertainty
• Error - the difference
between the true
value and our
estimation
– Random
– Systematic
• Accuracy - the
degree of agreement
between the true
value and the
measured value
• Precision - a
measure of the
agreement of replicate
measurements
1.3 Significant Figures and
Scientific Notation
Significant Figures in Calculation of
Results
Rules for Addition and Subtraction
• The result in a calculation cannot have greater
significance than any of the quantities that
produced the result
• Consider:
37.68
6.71862
108.428
152.82662
liters
liters
liters
liters
correct answer 152.83 liters
1.3 Significant Figures and
Scientific Notation
Rules for Multiplication and Division
• The answer can be no more precise than the least
precise number from which the answer is derived
• The least precise number is the one with the
fewest significant figures
4.2 103 (15.94)
8

2
.
9688692

10
(on calculator)
4
2.255 10
Which number has the fewest
significant figures? 4.2 x 103 has only 2
The answer is therefore, 3.0 x 10-8
1.3 Significant Figures and
Scientific Notation
Rules for Multiplication and Division
Use in unit conversion
1.3 Significant Figures and
Scientific Notation
Exact and Inexact Numbers
• Inexact numbers have uncertainty by
definition
• Exact numbers are a consequence of
counting
• A set of counted items (beakers on a
shelf) has no uncertainty
• Exact numbers by definition have an
infinite number of significant figures
1.3 Significant Figures and
Scientific Notation
Rules for Rounding Off Numbers
• When the number to be dropped is less than 5 the
preceding number is not changed
• When the number to be dropped is 6 or larger, the
preceding number is increased by one unit
• When the number to be dropped is 5 and is
followed by non-zero numbers, the last figure kept
should be unchanging if the last figure is even, and
increased by one if the last figure is odd.
• Round to 3 significant figures: 3.34966 x 104
=3.35 x 104
1.3 Significant Figures and
Scientific Notation
Rules for Rounding Off Numbers
• When the number to be dropped is less than 5 the
preceding number is not changed
• When the number to be dropped is 6 or larger, the
preceding number is increased by one unit
• When the number to be dropped is 5 and is
followed by non-zero numbers, the last figure kept
should be unchanging if the last figure is even, and
increased by one if the last figure is odd.
6.65 to 2 figures ….6.6
6.55 to 2 figures ….6.6
6.45 to 2 figures ….6.4
but 6.4501 to to figures …6.5
1.3 Significant Figures and
Scientific Notation
How Many Significant Figures?
Round off each number to 3 significant
figures:
1. 61.40
2. 6.171
3. 0.066494
1.3 Significant Figures and
Scientific Notation
How Many Significant Figures?
Round off each number to 3 significant
figures:
1. 61.40
61.4
2. 6.171
6.17
3. 0.066494 0.0665
1.4 Units and Unit Conversion
Data, Results, and Units
• Data - each piece is an individual result of a
single measurement or observation
– mass of a sample
– temperature of a solution
• Results - the outcome of the experiment
• Data and results may be identical, however
usually related data are combined to
generate a result
• Units - the basic quantity of mass, volume or
whatever quantity is being measured
– A measurement is useless without its
units
1.4 Units and Unit
Conversion
English and Metric Units
• English system - a collection of
functionally unrelated units
– Difficult to convert from one unit to another
– 1 foot = 12 inches = 0.33 yard = 1/5280
miles
• Metric System - composed of a set of
units that are related to each other
decimally, systematic
– Units relate by powers of tens
– 1 meter = 10 decimeters = 100 centimeters
= 1000 millimeters
1.4 Units and Unit
Conversion
Basic Units of the Metric System
Mass
Length
Volume
gram
meter
liter
g
m
l
• Basic units are the units of a quantity
without any metric prefix
1.4 Units and Unit
Conversion
1.4 Units and Unit
Conversion
UNIT CONVERSION
• You must be able to convert
between units
- within the metric system
- between the English system and metric system
• The method used for conversion is
called the factor-label method or
dimensional analysis
!!!!!!!!!!! VERY IMPORTANT !!!!!!!!!!!
1.4 Units and Unit
Conversion
• Let your units do the work for you by
simply memorizing connections
between units.
– For example: How many donuts are in
one dozen?
– We say: “Twelve donuts are in a dozen.”
– Or: 12 donuts = 1 dozen donuts
• What does any number divided by
itself equal?
• ONE!
12 donuts
1
1 dozen
1.4 Units and Unit
Conversion
12 donuts
1
1 dozen
• This fraction is called a unit factor
• What does any number times one
equal?
• That number
• Multiplication by a unit factor does
not change the amount – only the unit
1.4 Units and Unit
Conversion
• We use these two mathematical facts to
use the factor label method
– a number divided by itself = 1
– any number times one is the same number
• Example: How many donuts are in 3.5
dozen?
• You can probably do this in your head
but try it using the factor-label method.
1.4 Units and Unit
Conversion
Start with the given information...
12 donuts
3.5 dozen 
1 dozen
= 42 donuts
Then set up your unit factor...
See that the units cancel...
Then multiply and divide all numbers...
1.4 Units and Unit
Conversion
If you screw up, and some of you will,
and use the reciprocal conversion factor
1dozen
instead of
12 donuts
12 donuts
you get
1dozen
dozen 2
1dozen
 0.29
3.5 dozen 
donuts
12 donuts
1.5 Experimental Quantities
• Mass - the quantity of matter in an object
– not synonymous with weight
– standard unit is the gram
• Weight = mass x acceleration due to gravity
• Mass must be measured on a balance (not a
scale)
1.5 Experimental Quantities
• Units should be chosen to suit the
quantity described
– A dump truck is measured in tons or
tons
– A person is measured in kg or pounds
– A paperclip is measured in g or
ounces
– An atom?
• For atoms, we use the atomic mass
unit (amu)
– 1 amu = 1.661 x 10-24 g
1.5 Experimental Quantities
• Length - the distance between two
points
– standard unit is the meter
– long distances are measured in km
– distances between atoms are measured
in nm, 1 nm = 10-9 m
• Volume - the space occupied by an
object
– standard unit is the liter
– the liter is (closely) the volume occupied
by 1000 grams of water at 4 oC
– 1 ml = 1/1000 l = 1 cm3
1.5 Experimental Quantities
The milliliter
(ml) and the
cubic centimeter
(cm3) are
equivalent
1.5 Experimental Quantities
• Time
- metric unit is the second
• Temperature - the degree of “hotness”
of an object
1.5 Experimental Quantities
Kelvin Temperature Scale
• The Kelvin scale is another temperature
scale.
• It is of particular importance because it is
directly related to molecular motion.
• As molecular speed increases, the Kelvin
temperature proportionately increases.
K = oC + 273
1.5 Experimental Quantities
Energy
• Energy - the ability to do work
• kinetic energy - the energy of motion
• potential energy - the energy of
position (stored energy)
• Energy is also categorized by form:
•
•
•
•
•
light
heat
electrical
mechanical
chemical
1.5 Experimental Quantities
Characteristics of Energy
• Energy cannot be created or destroyed
• Energy may be converted from one form
to another
• Energy conversion always occurs with
less than 100% efficiency
• All chemical reactions involve either a
“gain” or “loss” of energy
1.5 Experimental Quantities
Units of Energy
• Basic Units:
• joule or calorie
• 1 calorie (cal) = 4.184 joules (J)
• A kilocalorie (kcal) also known as the
large Calorie. This is the same
Calorie as food Calories.
• 1 kcal = 1 Calorie = 1000 calories
• 1 calorie = the amount of heat energy
required to increase the temperature
of 1 gram of water 1oC.
1.5 Experimental Quantities
Concentration
Concentration:
– the number of particles of a substance
– the mass of those particles
– that are contained in a specified volume
Often used to represent the mixtures of
different substances
– Concentration of oxygen in the air
– Pollen counts
– Proper dose of an antibiotic
1.5 Experimental Quantities
Density and Specific Gravity
• Density
– the ratio of mass to volume
– an extensive property
– use to characterize a substance
as each substance has a unique
density
– Units for density include:
• g/ml
• g/cm3
• g/cc (cc - cubic centimeter, do not
use)
mass
m
d 

volume V
1.5 Experimental Quantities
cork
water
brass nut
liquid mercury
Brass 8.4 - 8.73
Cork 0.24
1.5 Experimental Quantities
Calculating the Density of a
Solid
• 2.00 cm3 of aluminum are found to weigh
5.40 g. Calculate the density of
aluminum in units of g/cm3.
– Use the formula
– Substitute our values
5.40 g
2.00 cm3
= 2.70 g/cm3
mass
m
d 

volume V
1.5 Experimental Quantities
Air has a density of 0.0013 g/ml. What
is the mass of 6.0-l sample of air?
Calculate the mass in grams of 10.0 ml
if mercury (Hg) if the density of Hg is
13.6 g/ml.
Calculate the volume in milliliters, of a
liquid that has a density of 1.20 g/ml and
a mass of 5.00 grams.
1.5 Experimental Quantities
Specific Gravity
• Values of density are often related to a standard
• Specific gravity - the ratio of the density of the
object in question to the density of pure water at
4oC
• Specific gravity is a unitless term because the 2
units cancel [measurement without unit!]
• Often the health industry uses specific gravity
to test urine and blood samples
density of object (g/ml)
specific gravity 
density of water (g/ml)
Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Chapter 2
The Structure of the
Atom and the
Periodic Table
Denniston
Topping
Caret
6th Edition
2.1 Composition of the Atom
• Atom - the basic structural unit of
an element
• The smallest unit of an element
that retains the chemical
properties of that element
2.1 Composition of the Atom
Electrons, Protons and
Neutrons
• Atoms consist of three primary particles
• electrons
• protons
• neutrons
• Nucleus - small, dense, positively
charged region in the center of the
atom
- protons - positively charged
particles
- neutrons - uncharged particles
2.1 Composition of the Atom
Characteristics of Atomic
Particles
• Electrons are negatively charged particles
located outside of the nucleus of an atom
• Protons and electrons have charges that are
equal in magnitude but opposite in sign
• A neutral atom that has no electrical charge
has the same number of protons and
electrons
• Electrons move very rapidly in a relatively
large volume of space while the nucleus is
small a dense
2.1 Composition of the Atom
Symbolic Representation
of an Element
Charge of
particle
Mass
Number
Atomic
Number
A
Z
X
C
Symbol of
the atom
• Atomic number (Z) - the number of
protons in the atom
• Mass number (A) - sum of the
number of protons and neutrons