### Chapter 2 – Measurement and Calculations Taken from Modern Chemistry written by Davis, Metcalfe, Williams & Castka Scientific Method Section 1 - Objectives – Describe the purpose.

```Chapter 2 – Measurement and
Calculations
Taken from Modern Chemistry
written by Davis, Metcalfe, Williams
& Castka
Scientific Method
Section 1 - Objectives
– Describe the purpose of the scientific method.
– Distinguish between qualitative and quantitative
observations.
– Describe the differences between:
– Hypotheses
– theories
– and models
Section 2-1
The Scientific method is a logical approach to
solving problems by observing and collecting
data, creating a hypothesis, testing the same,
and formulating theories that are supported by
data.
1. Not sleeping at night , something, before I go to bed is impacting my
sleep
2. List the foods I eat and activities I take part in
3. Hypothesis that by eliminating something I will get a better nights sleep
4. Test the same
5. Come up with theory supported by data
Section 2-1 (continued)
Observing and Collecting Data
Observing is using our senses to obtain
information (data).
The data fall into to categories:
– Qualitative – descriptive (the ore has a red-brown
color)
– Quantitative - numerical (the ore has a mass of
25.7 grams)
A system is a specific portion of matter in a given region of
space that has been selected for study during an
experiment or observation
Section 2-1 (continued)
Formulating Hypothesis
A hypothesis is a testable statement.
“if...then”
•If I raise the temperature of a cup of water, then the amount of sugar that can
be dissolved in it will be increased.
•If the size of the molecules is related to the rate of diffusion as they pass
through a membrane, then smaller molecules will flow through at a higher rate.
Section 2-1 (continued)
Testing Hypothesis
Testing a hypothesis requires
experimentation.
•If I raise the temperature of a cup of water, then the amount of sugar that can
be dissolved in it will be increased.
(The scientist will use 10 separate cups of water and increase the temperature
in each by 5° C and then measure how much sugar will go into solution.)
•If the size of the molecules is related to the rate of diffusion as they pass
through a membrane, then smaller molecules will flow through at a higher rate.
•(The scientist will use 1 membrane and 5 different size molecules and then
measure how the diffusion rate through the membrane.)
Section 2-1 (continued)
Theorizing
A model in science is often
used as an explanation
of how phenomenon
occur and how data or
events are related. 
A theory is a broad
generalization that
explains a body of facts
or phenomena.

Section 2-1 (continued)
Experimental Design – POGIL
Units of Measurement
Section 2 - Homework
Notes on section 2.2 only pages 33-38.
Units of Measurement
Section 2 - Objectives
– Distinguish between:
– A quantity
– A unit
– And a measurement standard.
– Identify SI units for:
–
–
–
–
–
Length
Mass
Time
Volume
Density
– Distinguish between mass and weight
– Perform density calculations
– Transform a statement of equality to a conversion
factor.
Section 2-2
Measurements represent quantities.
A quantity is something that has a magnitude and a
size or amount.
My mass and
height
Section 2-2 (continued)
SI Measurements
Le Systeme International d’Unites or SI
Different  75 000 is what we in the U.S. would know
as 75,000
Commas in other countries represent decimal points.
Section 2-2 (continued)
SI Base Units - Mass
Mass is a measure of the quantity of matter.
SI Standard is the kilogram (kg).
~2.2 pounds
The gram (g) which is 1/1000th of a
kilogram is more commonly used for
smaller objects.
Section 2-2 (continued)
SI Base Units – Mass (continued)
Mass should not be confused with weight.
Weight is a measure of the gravitational pull on matter
Mass is measured with a
balance.
Weight is measured with a
spring scale..
Section 2-2 (continued)
SI Base Units – Length
SI standard is the meter (m).
1 meter = 39.3701 inches
To express longer
distances the
kilometer (km) is
used, = 1000 meters
Section 2-2 (continued)
Derived SI units
Combinations of SI base units form derived units.
EXAMPLES
2
m
= length x width
Others are given there own name…
kg/m∙s2
This is a pascal (Pa) and it is
used to measure pressure.
Section 2-2 (continued)
Derived SI Units (continued) – Volume
Volume is the amount of space occupied by an object.
The derived SI unit for volume
would be a m3
Instead scientist often us a non-SI unit called
the liter (L) which is equal to one cubic
decimeter.
1 L = 1.05669 quarts
Section 2-2 (continued)
Derived SI Units (continued) – Density
Density is the ratio of mass to volume, written as mass
divided by volume..
D=
m/
v
Earth based reference
The density of H2O
@ 4 ° C = 1 g/cm3
Section 2-2 (continued)
Derived SI Units– Density (continued)
We are going to practice by finding the
Section 2-2 (continued)
Derived SI Units– Density (continued)
Section 2-2 (continued)
Conversion Factors
A conversion factor is a ratio derived from the equality
between two different units that can be used to
convert from one unit to another.
General equation
Section 2-2 (continued)
Conversion Factors - Deriving Conversion Factors
We can deriver a conversion factor when we know the
relationship between the factors we have and the
units we what.
Section 2-2 (continued)
Conversion Factors - Deriving Conversion Factors
Practice
HW / Classwork (depends) – Section review bottom
of page 42 questions 2-5 all
Section 2-2 (continued)
Conversion Factors – Metrics (step method)
The next slide will teach you about:
King henry died by drinking chocolate milk under no pressure
Kilo- (k)
Decimal Moves to left
103
Hecto(h)
Deka102
(da)
Base
10
________
Remember
The decimal moves
the way you are
stepping
____
Liters
Deci(d)
Meters 10-1
Grams
Larger
Units
Smaller
Units
Centi(c)
10-2
Milli(m)
10-3
Micro
(µ)
10-6
nano-
(n)
Decimal Moves to right
10-9
pico
(p)
10-12
Kilo- (k)
Decimal Moves to left
103
Hecto(h)
Deka102
(da)
Base
10
________
Remember
The decimal moves
the way you are
stepping
____
Liters
Deci(d)
Meters 10-1
Grams
Larger
Units
Smaller
Units
Centi(c)
10-2
Step Practice
HW
Milli(m)
10-3
Micro
(µ)
10-6
nano-
(n)
Decimal Moves to right
10-9
pico
(p)
10-12
Using Scientific Measurements
Section 3 - Objectives
HW Notes on this section with
these objectives in mind
– Distinguish between accuracy and precision.
– Determine the number of significant figures in
measurements.
– Perform mathematical operations involving
significant figures.
– Convert measurements into scientific notation.
– Distinguish between inversely and directly
proportional relationships
Section 2-3
Accuracy and Precision
Accuracy refers to the closeness of measurements to the
correct or accepted value.
Precision refers to the closeness of a set of measurements
made in the same way.
Section 2-3 (continued)
Accuracy and Precision (continued) – Percent Error
( VALUEACCEPTED – VALUEEXPERIMENTAL)
Percent error = ----------------------------------------------------- x 100
VALUEACCEPTED
% error is positive (+) when the VALUEACCEPTED is greater than VALUEEXPERIMENTAL
% error is negative (-) when the VALUEACCEPTED is less than VALUEEXPERIMENTAL
Section 2-3 (continued)
Accuracy and Precision (continued) – Percent Error
( VALUEACCEPTED – VALUEEXPERIMENTAL)
Percent error = ----------------------------------------------------- x 100
VALUEACCEPTED
EXAMPLE 1
(time estimation)
EXAMPLE 2
(penny density)
Section 2-3 (continued)
Accuracy and Precision (continued) – Error in Measurement
Some error or uncertainty always exists in any
measurement.
Reasons
Skill of measurer
conditions (temperature, air pressure,
humidity etc)
Instruments themselves
Section 2-3 (continued)
Accuracy and Precision – Error in Measurement
(continued)
ONLY NEED TO COPY THE RED
Ways to Improve Accuracy in Measurement
1. Make the measurement with an instrument that has the highest level of
precision. The smaller the unit, or fraction of a unit, on the measuring device,
the more precisely the device can measure. The precision of a measuring
instrument is determined by the smallest unit to which it can measure.
2. Know your tools! Apply correct techniques when using the measuring
instrument and reading the value measured. Avoid the error called "parallax" -always take readings by looking straight down (or ahead) at the measuring
device. Looking at the measuring device from a left or right angle will give an
incorrect value.
3. Repeat the same measure several times to get a good average value.
4. Measure under controlled conditions. If the object you are measuring could
change size depending upon climatic conditions (swell or shrink), be sure to
measure it under the same conditions each time. This may apply to your measuring
instruments as well.
Using Scientific Measurements
Section 2.3 (second) - Objectives
– Determine the number of significant figures in
measurements.
– Perform mathematical operations involving
significant figures.
HW Notes on this
section with
these objectives
in mind
Pgs 46-50
Section 2-2 (continued)
Accuracy and Precision – POGIL
Up to Problem # 22
Section 2-3
Significant figures (‘Sig figs’) in a measurement consist
of all the digits known with certainty plus one final digit,
which is uncertain or is estimated.
Section 2-3
Significant Figures – Determining the number of significant
digits
EXAMPLES
1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are
ALWAYS significant.
2) ALL zeroes between non-zero numbers are
ALWAYS significant.
3) ALL zeroes which are SIMULTANEOUSLY to
the right of the decimal point AND at the end of
the number are ALWAYS significant.
4) ALL zeroes which are to the left of a written
decimal point and are in a number >= 10 are
ALWAYS significant.
12 eggs
2001 Dalmations
172.00 Kg
10000. L
Section 2-3
Significant Figures – Determining the number of
significant digits (continued)
Number
48,923
3.967
900.06
0.0004 (= 4 E-4)
8.1000
501.040
3,000,000 (= 3 E+6)
10.0 (= 1.00 E+1)
# Significant Figures
5
4
5
1
5
6
1
3
Rule(s)
1
1
1,2,4
1,4
1,3
1,2,3,4
1
1,3,4
Section 2-3
Significant Figures – Rounding (continued)
Digit following
Last digit
Example
Round to 3 Sig Figs
greater than 5
Increased by 1
42.68 g  42.7 g
Less than 5
Stay the same
42.32 m  42.3 m
5, followed by nonzero
Increased by 1
2.7851 cm  2.79 cm
5, not followed by
nonzero
AND preceded by an
odd digit
Increased by 1
4.635 kg  4.64 kg
5, not followed by
nonzero
AND preceded by an
even digit
Stay the same
78.65 mL  78.6 mL
Section 2-3
Significant Figures – Sig Figs & Rounding (continued)
PRACTICE # 1
(only front side)
PRACTICE # 2
(only front side)
Section 2-3
Significant Figures (continued) – Addition or subtraction with
Significant Figures
When adding or subtracting decimals, the
answer must have the same number of digits
to the right of the decimal point as there
are in the measurement having the FEWEST
digits to the right of the decimal point.
Example
25.1 g
2.03 g
______
27.13 g as seen on a calculator, BUT using the above rule
you would round the answer to  27.1 g
Section 2-3
Significant Figures (continued) – Multiplication & Division
with Significant Figures
For multiplication or division the answer can
have no more significant figures than are in
the measurement with the fewest number of
significant digits.
Example
Density = mass ÷ volume
3.05 g
_______
8.47 mL
= 0.360094451 g/mL
CALCULATOR
But using the rule we go to 3 sig figs giving us  0.360 g/mL
WARNING: do not let your friend the calculator screw up your
Section 2-3
Significant Figures (continued) – Conversion Factors &
Significant Digits
When using conversion factors there is no
uncertainty – the conversion are exact.
Example
100 cm
_______
m
x 4.608 m = 460.8 cm
Practice Break
Practice break (the other sides & more)
PRACTICE # 1
(only back side)
PRACTICE # 2
(only back side)
TONIGHT’S HW
HW in advance: Notes to the end of the
chapter for Friday
Section 2-3
Scientific Notation
In scientific notation, numbers are written
in the form M x 10n, where M is a number
greater than or equal to 1 but less than 10
and n is a whole number.
Examples
149 000 000 km  1.49 x 108 km
1.49e8
0.000181 m  1.81 x 10-4 m
1.81e-4
Section 2-3
Scientific Notation (continued) – Mathematical Operations
using Scientific Notation – addition & subtraction
To add or subtract you must make the
exponents the same
1.49 x 104 km
1.81 x
103
OR
EITHER
km
14.9 x 103 km
1.49 x 104 km
km
0.181 x 104 km
16.71 x 103 km
1.671 x 104 km
1.81 x
103
16.7 x 103 km Remember rounding 1.67 x 104 km
Section 2-3
Scientific Notation (continued) – Mathematical Operations
using Scientific Notation – addition & subtraction
UNITS TOO (don’t get
tripped up on this)
Examples
1.49 x 105 km
Becomes 1.49 x 108 m
5.02 x 104 m Becomes 0.00502 x 108 m
Becomes 1.49502 x 108 m
Rounding Becomes 1.50 x 108 m
Section 2-3
Scientific Notation (continued) – Mathematical Operations
using Scientific Notation – Multiplication
M factors are multiplied and ns are added
Remember general form M x 10n
Examples
1.49 x 108 m
1.81 x 10-4 m
2.969 x 104 m
2.97 x 104 m Rounded
Section 2-3
Scientific Notation (continued) – Mathematical Operations
using Scientific Notation – Division
M factors are divided and ns are subtracted
denominator from numerator
Examples
7 g
5.44
x
10
_____________
8.1 x 104 mol
= 0.6716049383 x 103 g/mol
= 6.7 x 102 g/mol
Section 2-3
Scientific Notation - Practice
PRACTICE
PRACTICE KEY
Joke Break
A man jumps into a NY City cab and asks the cab
driver, “Do you know how to get to Carnegie
Hall?”
The cabbie turns around and says , “Practice,
practice , practice!”
PRACTICE
PRACTICE
Multiplying & Dividing
PRACTICE
Sig Figs
 Key to Sig Figs
Section 2-2 (continued)
Significant Figures – POGIL
HW
Chapter Review
 Key
Section 2-3
Direct & Inverse Proportions
Graphing Practice
What the results should look like:
Chapter Summary Questions
HW – pages 60-61
27, 31, 34, 36, 43, 48 & 57
Supplemental Scientific
Notation Material
Back
27
Density = Mass / Volume
5.03 g / 3.24 mL
= 1.552496...... g/mL
Rounded = 1.55 g/mL
31
0.603 L x 1000 ml/L
= 6.03 x 102 mL
34
( VALUEACCEPTED – VALUEEXPERIMENTAL)
Percent error = ----------------------------------------------------- x 100%
VALUEACCEPTED
((1.54 g/cm3 – 1.25 g/cm3) / 1.54 g/cm3) x 100%
= 18.8311.....%
Rounded = 18.8 %
36
a)
b)
c)
d)
Four
One
Six
Three
43
a) 8.278 x 104 mg
b) 2.5766 x 10-2 kg
c) 6.83 x 10-2 m3
d) 8.57 x 108 m2
48
Density = Mass / Volume
57.6 g / 40.25 cm3
= 1.4310559....... g/cm3
Rounded = 1.43 g/cm3
57
a) 2 g fat = 15 calories
1g = 7.5 Cal
8 Cal/g
a) 0.6 kg
b) 2 x 105 μg
c) One; the value 2 g limits the number of
significant figures for these data.
Supplemental Scientific Notation
Approximately, how much further
from the sun is Saturn than Earth.
Earth is approximately 9.3 × 107
miles from the sun and Saturn is
approximately 8.87 × 108 miles
from the sun.
(8.87 × 108) – (9.3 × 107)
= (8.87 × 101 × 107) – (9.3 × 107)
= (88.7 × 107) – (9.3 × 107)
= (88.7 – 9.3) × 107
= 79.4 × 107
= 7.94 × 101 × 107
= 7.9 × 108
PRACTICE