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MR. SURRETTE
VAN NUYS HIGH SCHOOL
CHAPTER 1: MEASUREMENT and THE SCIENTIFIC METHOD
CONVERSIONS CLASS NOTES
(PHYSICS)
WHAT IS PHYSICS?
Physics is the study of the universe. The universe is everything we can observe and measure.
PHYSICS AND CHEMISTRY
Like all the sciences, chemistry is governed by the laws of physics. Physical laws and examples will
occasionally appear in this course. They are meant to complement and reinforce the chemistry content.
STANDARDS OF LENGTH, MASS, AND TIME
The universe can be described by using certain physical quantities like length, mass, and time. The
metric unit of length is the meter (about 39 inches), the metric unit of mass is the kilogram (about 2.2
pounds), and the metric unit of time is the second.
REVIEW OF TRIGONOMETRY
REVIEW OF TRIGONOMETRY
The three most basic trigonometric functions of a right triangle are the sine, cosine, and tangent:
Example 1. If a submarine on the surface dives at an angle of 15 degrees with respect to the horizontal
and follows a straight line path for a distance of 40.00 m, how far below the surface will it be (measured
in m)?
1A.
(1) y = (sin 15o)(40 m)
(2) y = (0.2588)(40 m)
(3) y = 10.35 m
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CHEMISTRY
MR. SURRETTE
VAN NUYS HIGH SCHOOL
ORDER OF MAGNITUDE
Sometimes you need to make “hip pocket” estimates of numbers (usually when no calculator is
available!). These estimates are called order of magnitude calculations and are usually done in your
head.
ORDER OF MAGNITUDE
In order to perform an order of magnitude calculation, you round all numbers to the nearest power of ten
and then multiply the terms together.
Example 2. On planet Q, quash is a popular beverage among the natives. The average person on Q
consumes 3 guppies of quash per month. There are 8 months per year on Q and an estimated population
of 200 million. Provide an order of magnitude estimate value for the total value of quash consumed per
year (in guppy units).
2A.
(1) Start: 3 x 8 x 200,000,000
(2) Round: 100 x 101 x 108
(3) 109 guppy units
DIMENSIONAL ANALYSIS
Sometimes it is necessary to convert from one unit of measurement to another. This conversion process
is called dimensional analysis.
Example 3. On planet N, the standard unit of length is the nose. If a 6.1 foot height astronaut travels to
planet N and is measured to have a height of 94 noses, what would be the height in noses of another
astronaut who measures 5.5 feet in height?
3A.
(1) h = (5.5 foot) 94 nose = 84.8 noses
6.1 foot
(2) h = 84.8 noses
Example 4. A gallon of paint (volume = 3.78 x 10-3 m3) covers 25 m2. What is the thickness of the
paint on the wall (in millimeters)?
4A.
(1) V = A T
(2) T = V / A
(3) T = (3.78 x 10-3 m3) / 25 m2
(4) T = 1.51 x 10-4 m
(5) T = 0.15 mm
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CHEMISTRY
MR. SURRETTE
VAN NUYS HIGH SCHOOL
CHAPTER 1: MEASUREMENT and THE SCIENTIFIC METHOD
SCIENTIFIC METHOD CLASS NOTES
CHEMISTRY
Chemistry studies the composition, structure, properties, and reactions of matter. In particular, it
examines matter at the atomic and molecular levels.
MATTER
Matter is anything that has mass and takes up space.
BRANCHES OF CHEMISTRY
Chemistry is a very broad science. It includes these and many other branches:
Biochemistry
Biochemistry studies the chemistry of organisms. Topics include the Krebs cycle and the formation of
hemoglobin.
Organic Chemistry
Organic chemistry is the study of carbon-based molecules. Many of these molecules form DNA to
gasoline also contain hydrogen, oxygen, and nitrogen.
Inorganic Chemistry
Inorganic chemistry mostly studies the colorful transition metals like chromium and manganese.
Physical Chemistry
Physical chemistry studies the extremes of matter like super-cooled water and liquid hydrogen.
SCIENTIFIC METHOD
Most chemists follow the scientific method. It is a process they follow when they go to a lab and
explore.
SCIENTIFIC METHOD
There are five general steps to the scientific method:
1. OBSERVATION
An observation is a thought or idea.
2. HYPOTHESIS
A hypothesis attempts to explain the observation.
3. EXPERIMENT
Scientists design experiments to disprove a hypothesis.
4. THEORY
A hypothesis that survives many experiments becomes a theory.
5. LAW
A law is a theory that withstands the test of time, like Newton’s law of gravity.
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CHEMISTRY
MR. SURRETTE
VAN NUYS HIGH SCHOOL
CHAPTER 1: MEASUREMENT AND THE SCIENTIFIC METHOD
MEASUREMENT CLASS NOTES
UNITS OF MEASUREMENT
When making measurements, it is important to define both the numbers and the units that are used. For
example, it is more accurate to write about the greenhouse effect: “the temperature has increased 2o
Celsius per decade” than “the temperature has increased 2o per decade.”
PRECISION
Precision improves the data that is collected. For example, it is more precise to write, “the temperature
has increased 2.1o C/decade” than “the temperature has increased 2 o C/decade.”
UNCERTAINTY
The last digit of any number has the highest uncertainty, and can lead to confusion. For example, what
is “1.0 x 20”? Is it 20? Is it 20.0? The rules of scientific notation address the issue of uncertainty.
SCIENTIFIC NOTATION
Scientific notation is a way to clearly report numbers and eliminate confusion. Scientific notation
makes use of exponents and rules to determine significant figures (“sig figs”).
EXPONENTS
Exponents express numbers as powers of 10. They are especially useful for very large or very small
numbers:
10o = 1
101 = 10
10-1 = 0.1
103 = 1,000
10-3 = 0.001
6
10 = 1,000,000
10-6 = 0.000001
109 = 1,000,000,000
10-9 = 0.000000001
SIGNIFICANT FIGURES
Significant figures address the uncertain digits found in numbers. They follow six rules:
1. All nonzero digits are significant. For example: 10.007 and 0.0490
2. Interior zeros are significant. For example: 5.309
3. Trailing zeros are significant. For example: 3.780 and 6.00
4. Leading zeros are not significant. For example: 0.0097
5. Zeros at the end of a number are ambiguous. For example: 3100
6. Exact numbers have unlimited number of significant figures. They include:
(a) Counts of discrete objects. For example: 7 pieces of paper
(b) Defined quantities. For example: 12 inches = 1 foot
(c) Numbers that are presented in formulas. For example: Surface area of sphere = 4r2
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CHEMISTRY
MR. SURRETTE
VAN NUYS HIGH SCHOOL
Example 5. Convert 4397 into scientific notation.
5A.
4397 = 4.397 x 103
Example 6. Convert 0.00756 into scientific notation.
6A.
0.00756 = 7.56 x 10-3
Example 7. Convert 1,404,219 into scientific notation.
7A.
1,404,219 = 1.404219 x 106
MULTIPLICATION AND DIVISION RULE
Sometimes numbers are multiplied and divided. Products and quotients match the number with the
fewest significant figures.
Example 8. What is the area of a rectangular piece of wood 5.3 inches long and 2.97 inches wide?
8A.
(1) 5.3 x 2.97 = 15.741
(2) inches x inches = in2
(3) 15.741 in2(5.3 has the fewest sig. figs.)
(4) 16 in2
ADDITION AND SUBTRACTION RULE
When quantities are added or subtracted, the number with the fewest decimal places determines the
significant figures in the answer.
Example 9. What is the sum of:
106.7 + 0.25 + 0.195?
9A.
(1) 106.7 + 0.25 + 0.195
(2) 107.145 (106.7 has the fewest decimal places)
(3) 107.1
MULTIPLE STEP PROBLEMS
Sometimes problems involve both multiplication/division and addition/subtraction. They may also
include parentheses and partial operations. In these cases, compute the operations in parentheses first,
followed by multiplication/ division, then, finally, addition/subtraction.
KEEP TRACK OF UNCERTAINTY
As seen in the following examples, it is good practice to underline uncertain digits throughout multiple
step problems. To avoid errors, retain all decimal places and only round off numbers at the end of
problems.
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CHEMISTRY
MR. SURRETTE
VAN NUYS HIGH SCHOOL
Example 10. Compute 6.78 x 5.903 (5.489 – 5.01)
10A.
(1) 6.78 x 5.903 (5.489 – 5.01)
(2) 6.78 x 5.903 (0.479)
(3) 19.17070086 (0.479 only has 2 sig. figs. and determines the round off in the answer)
(4) 19
Example 11. Compute 3.10 x 7.8 + 5.32
11A.
(1) 3.10 x 7.8 + 5.32
(2) (24.18) + 5.32 (24.18 only has 2 sig. figs. because of the multiplication rule)
(3) 29.50 (29.50 has two decimal places because of the addition rule)
(4) 2.950 x 101 (Notice how the second digit remains underlined. It determines the 2 sig. figs. in the
final answer)
(5) 3.0 x 101
METRIC SYSTEM
Scientists use the “SI” or metric system. Standard units for the metric system are:
Length is measured in meters [m]
Time is measured in seconds [s]
Volume is measured in liters [L]
Mass is measured in kilograms [kg]
Temperature is measured in Kelvin [K]
PREFIXES IN THE METRIC SYSTEM
Prefixes are often placed in front of measurements in the metric system. These prefixes make
measurements bigger or smaller. Some common prefixes are:
centi = 10-2
kilo = 103
milli = 10-3
mega = 106
micro () = 10-6
giga = 109
-9
nano = 10
tera = 1012
TEMPERATURE SCALES
1. The degree Fahrenheit (oF) non-metric temperature scale was devised so that the freezing and
boiling temperatures of water are whole numbers.
2. The degree Celsius (oC) scale was devised by dividing the range of temperature between the freezing
and boiling temperatures of pure water into 100 equal parts.
3. The Kelvin (K) temperature scale is an extension of the degrees Celsius scale down to absolute zero,
a hypothetical temperature characterized by a complete absence of heat energy.
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CHEMISTRY
MR. SURRETTE
VAN NUYS HIGH SCHOOL
TEMPERATURE SCALE COMPARISONS
TEMPERATURE EQUATIONS
TC is the Celsius temperature and T is the Kelvin temperature. The size of a degree on the Kelvin scale
is identical to the size of a degree on the Celsius scale:
TC = T – 273
TEMPERATURE EQUATIONS
Other temperature equations:
TF = (9/5)TC + 32
TC = 5/9 (TF – 32)
Example 12. Oxygen condenses into a liquid at approximately 90o Kelvin (90 K). What temperature,
in degrees Fahrenheit, does this correspond to?
12A.
(1) TF = 9/5TC + 32
(2) TF = 9/5(T – 273) + 32
(3) TF = 9/5(90 – 273) + 32
(4) TF = - 297.4o
CONVERSIONS
It is common to convert from one set of units to another. Some common conversion factors are:
1 inch = 2.54 cm
12 inches = 1 foot
1 meter = 100 cm = 1000 mm
1 mL = 1 cm3
Note: Conversion factors are exact numbers and have an unlimited amount of significant figures.
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CHEMISTRY
MR. SURRETTE
VAN NUYS HIGH SCHOOL
DIMENSIONAL ANALYSIS
Dimensional analysis uses reversible fractions to convert numbers from one set of units to another. For
example, “1 inch = 2.54 cm” can be written as:
(1 inch / 2.54 cm) or
(2.54 cm / 1 inch)
Example 13. Convert 14.78 cm to inches.
13A.
14.78 cm x 1 inch = 5.819 in
2.54 cm
Example 14. Convert 4.72 feet into meters.
14A.
4.72 ft x 12 in x 2.54 cm x 1 m
=
1 ft
1 in
100 cm
1.438656 m = 1.44 m
DENSITY
The density  of a substance is mass per unit volume. It has units of kilograms per cubic meter (or
grams per cubic centimeter) in the metric system:
=m/V
Example 15. A cylinder ( = 3.05 g/cm3) is 1.25 cm long and 0.50 cm in diameter. What is the mass of
the cylinder? (Vcyl = r2L)
15A.
(1) V = r2L
(2) V = (0.25 cm)2(1.25 cm)
(3) V = 0.2454369261 cm3
(4) V = 0.25 cm3
(5)  = m / V
(6) m = V
(7) m = (3.05 g/cm3)(0.25 cm3)
(8) m = 0.7625 g
(9) m = 0.76 g
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CHEMISTRY