Chapter 2
Analyzing Data
Chapter 2 Introduction
• 2.1 Units & Measurements
• 2.2 Scientific Notation &
Dimensional Analysis
– “Factor-Label” Method a.k.a.
Conversion Factors or Dimensional
Analysis
• 2.3 Uncertainty in Data
– Sig Figs, Sig Digs
Chapter 2 Learning Targets
By the end of Chapter 2 I am able to…
Identify the SI base units of
measurements for mass, time, length,
temperature & volume (2.1)
Distinguish between qualitative &
quantitative observations and give
examples of each. (2.1)
Explain the meanings of the SI prefixes
(2.1)
Compare & contrast mass and weight
(2.1)
State the derived units used to represent
speed, area & density. (2.1)
Analyze a problem, solve for an unknown
and evaluate my answer (2.1)
Chapter 2 Learning Targets
Express numbers in scientific notation
(2.2)
Convert between units using dimensional
analysis/factor-label method (2.2)
Define & compare accuracy & precision
(2.3)
Describe the accuracy of experimental
data using error & percent error (2.3)
Apply the rules of “Sig Figs” to express
uncertainty in measured & calculated
values (2.3)
2.1 Units & Measurements
Learning Targets
 Identify the SI base units of measurements for
mass, time, length, temperature & volume (2.1)
 Distinguish between qualitative & quantitative
observations and give examples of each. (2.1)
 Explain the meanings of the SI prefixes (2.1)
 Compare & contrast mass and weight (2.1)
 State the derived units used to represent speed,
area & density. (2.1)
 Analyze a problem, solve for an unknown and
evaluate my answer (2.1)
2.1 Units & Measurements
• Système Internationale d'Unités (SI)
is an internationally agreed upon
system of measurements.
• Chemistry involves both measuring
and calculating
• Two types of observations in science
– Qualitative (no measurements, no
numbers)
– Quantitative (actual measurements)
2.1 Units & Measurements
• There are 7 base
units in SI
• Measurements
based on an object
or event (a physical
standard).
• See p. 33 in text.
• YOU NEED TO
KNOW THESE!
2.1 Units & Measurements
• To better
describe the
range of
possible
measurements,
scientists add
prefixes to base
units
• Based on
factors of 10 –
metric system
** KNOW THESE… p 33 in text
2.1 Units & Measurements
• Mass vs. Weight
– Weight is a measure of force of gravity
between two objects (wt. changes
w/respect to gravity)
• Scales are for weighing
– Mass is a measure of the amount of
matter an object contains
• A balance is used for finding mass
• The SI unit for mass is the Kilogram (kg)
The Physical Standard for
Mass (FYI…)
• The international
prototype of the
kilogram is inside
three nested bell
jars at the Bureau
International des
Poids et Mesures
in Paris.
http://www.npr.org/templates/story/story.php?storyId=112003322
In search of a new
Standard…
• Physicist Richard
Steiner adjusts
the watt balance.
This extremely
sensitive scale
can detect
changes as small
as ten-billionths of
a kilogram.
2.1 Units & Measurements
• Temperature: quantitative
measurement of the average kinetic
energy of the particles w/in an
object.
• A thermometer is used to measure
temperature
• Three temperature scales:
– Fahrenheit, Celsius, Kelvin
• SI base unit - Kelvin
2.1 Units & Measurements
• Kelvin scale developed by William
Thomson (a.k.a. Lord Kelvin)
• Zero Kelvin is the point at which all
molecular motion stops – “Absolute Zero”
• The size of the Celsius degree (oC) is the
same as a Kelvin (K)
• To convert between the two:
K  C -273
C  K +273
Water boils at 100 oC, to convert to Kelvin add
273. What is water’s BP in K?
373 K
2.1 Units & Measurements
• Derived Units: combination of base
units
• Volume – SI unit is cubic meter (m3)
– Usually the liter (L) is used
– 1 L equals 1 dm3
– For laboratory use the cubic centimeter
is often used (cm3 or cc)
– 1 cm3 = 1 mL (See Figure 2.4 p. 36)
Figure 2.4 p. 36
The three cubes show volume relationships
between m3 dm3 & cm3. as you move from
left to right, the volume of each cube gets
10 x 10 x 10, or 1000 (103) times smaller.
2.1 Units & Measurements
• Derived Units… continued
• Density – a physical property of
matter
– defined as amount of mass per unit
volume (density = mass/volume)
Common units:
– g/cm3 for solids
– g/ml for liquids & gases
Application
Question: 116 g of sunflower oil is used in a recipe. The density
of the oil is 0.925 g/ml. What is the volume of the sunflower oil
in ml?
What are you being asked to solve for?
volume of sunflower oil
What do you know, what are you given?
Density = mass/volume
Density = 0.925 g/ml
Mass = 116 g
What is the unknown?
volume
Write the equation and isolate the unknown factor.
density = mass/volume
rearrange to solve for unknown: volume = mass/density
Substitute known quantities into equation & solve.
volume = 116g/0.925g/ml
volume = 125 ml
2.1 HW problems
• #2-6 (p.38-39) , #66-67 (p. 62)
• Due :
– Next class
2.2 Scientific Notation &
Dimensional Analysis
Learning Targets
Express numbers in scientific
notation (2.2)
Convert between units using
dimensional analysis/factor-label
method (2.2)
2.2 Scientific Notation &
Dimensional Analysis
• Scientific notation used for short-handing
very large and very small measurements.
• Very large number - the number of atoms
in a sample might be something like
124,500,000,000,000 atoms.
• Very small number - the size of an
molecule in meters might be something
like 0.0000000000238
meters.
2.2 Scientific Notation &
Dimensional Analysis
• The number of places moved equals the
value of the exponent.
• The exponent is positive when the
decimal moves to the left and negative
when the decimal moves to the right.
• Example:
Exponent
800 = 8.0  102
0.0000343 = 3.43  10–5
Coefficient
2.2 Application
• Question: Each cell in the human body
contains a complete genome which is
composed of base pairs. Each base
pair is 0.000,000,034m in length. There
are 6,000,000,000 base pairs in each
human cell. Change the above
information into scientific notation.
a.) 3.4 x 10-8 m
b.) 6 x 109 base pairs
2.2 Scientific Notation &
Dimensional Analysis
• Addition & Subtraction of numbers in
scientific notation:
– Exponents must be the same.
– Add or subtract coefficients.
(7.35 x 102 m) + (2.43 x 102 m) = 9.78 x 102 m
Application
• Add 3.5 x 103 m to 6.8 x 103 m
NO, you
can’t write it
like this!
(3.5 x 103) + (6.8 x 103) = 10.3 x 103m
Why??? Answer must be 1.03 x 104
because proper scientific notation
states that you must have one whole
number to the left of the decimal
2.2 Scientific Notation &
Dimensional Analysis
• What if the exponents are NOT the same?
– Rewrite values with the same exponent.
– Example: Consider amounts of energy produced by
renewable energy sources in the U.S. in 2004:
•
•
•
•
•
Hydroelectric
Biomass
Geothermal
Wind
Solar
What is the Total ?
2.840 x 1018 J
3.146 x 1018 J
3.60 x1017 J
1.50 x 1017 J
6.9 x 1016 J
0.360 x 1018 J
0.150 x 1018 J
0.069 x 1018 J
6.565 x 1018 J
Application
• Subtract 7.9 x 102 km from 1.0 x 103 km
Move decimal place to the Left to
make exponents the same, 103
NO, you
can’t write it
like this!
(1.0 x 103) – (0.79 x 103) = 0.21 x 103
Remember you must write as 2.1 x 102
(one whole number to the left of the
decimal!!)
2.2 Scientific Notation &
Dimensional Analysis
• Multiplication and division, exponents do NOT
need to be the same:
– To multiply, multiply the coefficients, then add the
exponents.
(4.6 x 1023 atoms) (2x10-23 g/atom) =
9.2 x 100 g = 9.2 g
– To divide, divide the coefficients, then subtract the
exponent of the divisor from the exponent of the
dividend.
(9 x 108) / (3 x 10-4)
Divide coefficients: 9/3 = 3
Subtract the exponents: 8 – (-4) = 8+4 = 12
Combine the parts: 3 x 1012
Math Skill Review
•
1.
2.
3.
4.
5.
Can you multiply these fractions?
Complete the following in your
notebook. Remember… MATH IN
PENCIL! 
2/3 x 5/7
2/3 x 3/9
a/b x c/d
a2/b x b3/a
5 x 2/15
2.2 Scientific Notation &
Dimensional Analysis
•
•
“Factor-Label Method” (Dimensional
Analysis & Conversion factors – book
name)
Problem solving consists of three
parts:
Known  Conversion Factor  Desired
Answer
2.2 Scientific Notation &
Dimensional Analysis
• Conversion factors are ratios with a
value equal to one
• Example: $1 = 4 quarters
1km = 1000m
• The ratios are written as follows:
$1
and
4 quarters
4 quarters
$1
1 km
1000 m
and
1000 m
1 km
2.2 Application
• An object is traveling at a speed of 7500
centimeters per second. Convert the value to
kilometers per minute.
 Known: 7500 cm /sec
 Desired: ? km/min
• What relationships are known between cm &
km? Between sec & min? Write them down
 100 cm = 1m; 1000 m = 1 km; 60 s = 1 min
• Use these relationships as ratios in such a way
that s, cm, & m all divide out:
• km =
min
Open Note Quiz
1. How many seconds in a class at
SKHS? Class periods are 98
minutes.
2. Convert 78 seconds to hours
3. Convert 2.5 x 106 g to kg
4. Convert 37.5g/ml to kg/L
5. Convert 7.56 mm3/s to dm3/min
6. Convert 9.06 km/hr to m/s
2.2 HW – Due Next Class
•
•
•
•
#11-16 (p. 41-43)
#19-20 (p. 45)
#25 (p. 46)
#76-80 (p. 62)
2.3 Uncertainty in Data
Learning Targets
Define & compare accuracy &
precision (2.3)
Describe the accuracy of
experimental data using error &
percent error (2.3)
Apply the rules of “Sig Figs” to
express uncertainty in measured &
calculated values (2.3)
2.3 Uncertainty in Data
• Accuracy & Precision
– Accuracy refers to how close a
measured value is to an accepted
value
– Precision refers to how close
measurements are to one another.
2.3 Uncertainty in Data
Figure 2.10 on p. 47
2.3 Uncertainty in Data
Application
• Open your books and consider the
data table, p. 48.
2.3 Uncertainty in Data
Application - continued
• Students were asked to determine
the density of an unknown white
powder.
• Each student measured the volume
and mass of three samples.
• They calculated the densities and
averaged the three.
2.3 Uncertainty in Data
Application - continued
• Which student collected the most
accurate data?
• Student A
• Why?
– closest to the accepted value.
•
•
•
•
Who collected the most precise data?
Student C
Why?
closest to one another.
2.3 Uncertainty in Data
• Error & Percent Error
– Error is defined as the difference
between an experimental value (values
measured during an experiment) and
an accepted value
– Error Equation:
Error = experimental value – accepted value
Absolute value… only concerned about how
far away from the target you were, so sign
doesn’t matter
2.3 Uncertainty in Data
• Error & Percent Error (cont…)
– Percent Error expresses error as a
percentage of the accepted value.
– Percent Error Equation:
Absolute value is used because
only the size of the error
matters; it does not matter
whether the experimental value
is larger or smaller than the
accepted value.
2.3 Application – do this in
your notebook as part of
your notes
•
The melting point of paradichlorobenzene is
53oC. In a laboratory activity two students
tried to verify this value.
Student #1 records: 51.5oC, 53.5oC, 55.0oC,
52.3oC, and 54.2oC
Student #2 records: 52.3oC, 53.2oC, 54.0oC,
52.5oC, and 53.5oC
a. Calculate the average value for the two
students
b. Calculate the percent error for each student
c. Which of the students is most precise?
Accurate? Explain.
Calculate the average value
for the two students
Student #1: 51.5oC + 53.5oC + 55.0oC +
52.3oC + 54.2oC = 266.5/5 = 53.3oC
Student #2 : 52.3oC + 53.2oC + 54.0oC +
52.5oC + 53.5oC = 53.1oC
Calculate the percent error
for each student
• Student #1:
Percent error =
• Student #2:
Percent error =
(53.3oC - 53.0oC) X100 = 0.566 % error
53.0oC
(53.1oC - 53.0oC) X100 = 0.189 % error
53.0oC
Which of the students is
most precise?
Accurate? Explain.
• Student 2 is the most precise with a
range of values from 52.3 to 54.0.
• Student 2 is also most accurate with
a 0.189 % error.
2.3 Uncertainty in Data
• Significant Figures: include all known
digits plus one estimated digit.
• Often precision is limited by the tools
available.
5.00 cm
Figure 2.12 p. 50 The
markings on the ruler
represent the known
digits plus the estimated
digit. The measure is
5.23 cm. What is the
estimated digit if the
length of the object fell
directly on the 5 cm
mark?
2.3 Uncertainty in Data
• Rules for Significant Figures:
–Rule 1: Nonzero numbers are always
significant.
•Example: 72.3 g How many sig figs? 3
•
9.4567 How many sig figs? 5
–Rule 2: Zeros between nonzero numbers
are always significant.
•Example: 60.5 g How many sig figs? 3
•
5005.05 How many sig figs? 6
–Rule 3: All final zeros to the right of the
decimal are significant.
•Example: 6.2000 How many sig figs? 5
2.3 Uncertainty in Data
• Rules for Significant Figures:
– Rule 4: Placeholder zeros are not
significant. To remove placeholder zeros,
rewrite the number in scientific notation.
• Example: 0.0253g and 4320 (3 sig figs each)
Rewritten in Scientific notation:
2.53 x 10-2
4.32 x 103
0.000601 How many sig figs? 3 6.01 x 10-4
50000 How many sig figs? 1 5 x 104
2.3 Uncertainty in Data
• Rules for Significant Figures:
–Rule #5: Counting numbers
and defined constants have an
infinite number of significant
figures.
–Example: 6 molecules
60s = 1 min
2.3 Uncertainty in Data
Examples using the
4 Rules:
5465
0.60750
0.020020
500.0
300
How many Sig Figs
4 – Rule #1
5 – Rules #2 & 3
5 – Rules #2 & 3
4 – Rules #2 & 3
1 – Rule #4
2.3 Uncertainty in Data
• Rules for Significant Figures:
– What happens when your calculator gives you a
funky number, how do you know how many sig
figs to report in your answer?
– Rule 6: Addition & Subtraction, answer will have
the number of sig figs from the number with the
least amount of decimal places in the problem.
Example:
Decimal Places
10.21
2
0.2
1
+ 256
266.41
So… my answer should
have 0 decimal places
0
266
2.3 Uncertainty in Data
• Rules for Significant Figures:
– Rule 7: Multiplication & Division The
answer will have the number of sig figs from
the number with the least amount of sig figs.
Example:
**YOU WILL
USE THIS RULE
4675 x 625 = ________
A LOT!!!!!
Which has the least # of sig figs?
625 has 3, so your answer must have 3
4675 x 625 = 2921875  2920000 = 2.92 x 106
3 sig figs
Rule 4
2.3 Homework
•
•
•
•
#32-36 p. 49-51
#40 p. 53
# 42-43, 47 & 51 p. 54
#87, 91, 93-94 p. 63