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CHAPTER 2
Measurements and Calculations
Section 2.1
Scientific Method
The scientific method is a logical approach to solving
problems by observing and collecting data, formulating
hypotheses, testing hypotheses, and formulating
theories that are supported by data.
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Section 2.1
Scientific Method
Scientific Method Vocabulary
•  Qualitative data - descriptive data
•  Quantitative data - numerical data
•  Hypothesis - testable statement; often written as an
“if-then” statement
Section 2.1
Scientific Method
Scientific Method Vocabulary
•  A hypothesis must be tested with a controlled experiment
(one that tests only one variable at a time)
•  The variable that is purposefully changed by the
experimenter is called the independent variable
•  The variable that changes as a result is called the
dependent variable; this is what is being measured in the
experiment
•  All other variables are kept constant so that they will have no
effect on the results
•  Results from a controlled experiment are valid; if the
experiment is not controlled, the results will be invalid.
•  The results are reliable if they are repeatable; other
researchers must be able to conduct the same experiment
under the same conditions and get the same results
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Section 2.2
Units of Measurement
•  Measurements are a number plus a unit.
•  Scientists all over the world have agreed on a
single measurement system called Le Système
International d’Unités, abbreviated SI.
•  SI has 7 base units and many derived units.
SI Base Units
Quantity
Length
Mass
Time
Temp.
Amt. of
substance
Quantity
Symbol
l
m
t
T
n
Unit Name
meter
kilogram
second
kelvin
mole
Unit
Abbrev.
m
kg
s
K
mol
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Derived SI Units
Derived units are made of more than one base unit.
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Derived unit – Volume of a liquid
•  The volume of a liquid can be directly measured using a
graduated cylinder
•  Hold the graduated cylinder at eye level and measure at the
bottom of the meniscus
•  The units of liquid volume are Liter (L) or milliliter (mL)
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Derived unit – Volume of a liquid
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Derived unit – Volume of a solid
•  The volume of a regular solid can be calculated with
mathematical formulas:
•  For a square or rectangular cube:
Length x width x height
•  For a cylinder:
π x r2 x h
•  Units of solid volume are m3 or cm3
•  The volume of an irregular solid can be measured by the
water displacement method:
•  1 ml = 1 cm3
•  1 L = 1000 cm3
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Derived unit - Density
A sample of Al metal has a mass of 8.4 g. The volume of the
sample is 3.1 cm3. Calculate the density of the Al.
•  mass (m) = 8.4 g
•  vol. (V) = 3.1 cm3
•  density (D)= ?
What is the density of a sample of ore that has a mass
of 74.0 g and occupies 20.3 cm3 .
•  mass (m) = 74.0 g
•  vol. (V) = 20.3 cm3
•  density (D)= ?
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Find the volume of a sample of wood that has a mass
of 95.1 g and a density of 0.857 g/cm3.
•  mass (m) = 95.1 g
•  density (D)= 0.857 g/cm3
•  vol. (V) = ?
Density
•  Density can be represented with a graph of mass vs.
volume
•  The slope of the line = the density of the substance
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Density
•  When liquids of different densities are mixed, the liquid
with the lowest density sits on top of the others.
Day 2
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Scientific Notation
•  Scientific notation is a way of writing very large or very small
numbers.
In scientific notation, numbers are written in the form
M × 10n
where M is a number between 1 and 10
and
n is a whole number
Scientific Notation
General form: M x 10n
•  M must be an integer between 1 and 10
•  M will indicate the correct number of sig figs
•  n must be an integer
•  Example: These are NOT in scientific notation. What’s
wrong with them?
•  34 x 105
•  4.8 x 100.5
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Scientific Notation
What’s the difference between a positive exponent
and a negative exponent?
•  Positive exponent tells you how many times the number
is multiplied by 10; positive exponents express big
numbers (greater than 10)
•  Negative exponent tells you how many times the
number is divided by 10; negative exponents express
small numbers (less than 1)
Scientific Notation
Converting from standard form to scientific notation
•  Move the decimal to the left or right until you have a
number between 1 and 10. This number is “M”
•  The number of spaces you moved the decimal is the
exponent “n”
•  How do I know if my exponent is positive or negative?
•  If you moved the decimal to the left, your exponent will be
positive
•  If you moved the decimal to the right, your exponent will be
negative
example: 0.000 12 mm = 1.2 × 10−4 mm
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Scientific Notation
Converting from standard form to scientific notation
Scientific Notation
Converting from scientific notation to standard form
•  Remember… M x 10n
•  A positive exponent “n” indicates a large number, so
you should move the decimal to the right
•  A negative exponent “n” indicates a small number, so
you should move the decimal to the left
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Scientific Notation
Converting from scientific notation to standard form
Scientific Notation
How to enter a number in scientific notation into
your calculator:
•  Enter “M”
•  Press the “EXP” or “EE” button
•  Enter “n”
•  Do NOT press the multiply button or enter the number 10
•  “EXP” or “EE” takes the place of this step
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Day 3
SI Prefixes
To Get Manly king hector darinks delicious chocolate milk
µost nights petting furry animals.
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SI Prefixes
Prefix
Abbrev.
Exponent
Tera
Giga
Mega
Kilo
Hecto
Deca
T
G
M
k
h
da
Deci
Centi
Milli
Micro
Nano
Pico
Femto
Atto
d
c
m
µ
n
p
f
a
1012
109
106
103
102
101
100
10-1
10-2
10-3
10-6
10-9
10-12
10-15
10-18
Meaning
1 000 000 000 000
1 000 000 000
1 000 000
1 000
100
10
1
1/10
1/100
1/1000
1/1 000 000
1/1 000 000 000
1/1 000 000 000 000
1/1 000 000 000 000 000
1/1 000 000 000 000 000 000
Factor Label Method (t-chart)
•  A way to solve math problems in chemistry
•  You can use your knowledge of the prefixes and their
exponents to convert from a base unit to a prefix or from a
prefix to the base unit.
•  To use this method we need:
1.  Given quantity (what you’re converting from)
2.  Unknown quantity (what you’re converting to)
3.  Conversion factor (use silly sentence for this)
•  If you are converting from prefix to prefix, you must
convert from the given prefix to the base unit, then from the
base unit to the desired prefix!
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Section 2.3
Using Scientific Measurements
•  Accuracy = closeness of measurements to the correct or
accepted value of the quantity measured
•  Precision = closeness of a set of measurements of the
same quantity made in the same way; the uncertainty of
the measurement
Percent Error
Percent error is a measure of accuracy:
Percent error =
accepted value – experimental value x 100
accepted value
•  Answer = positive if the experimental value is smaller than the accepted value.
•  Answer = negative if the experimental value is larger than the accepted value.
A student measures the mass and volume of a substance and calculates its
density as 1.40 g/mL. The correct, or accepted, value of the density is 1.36 g/mL.
What is the percent error of the student’s measurement?
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Density Lab next time!!!
Significant Figures
•  It is important to realize that any measurement will have
some degree of uncertainty. The uncertainty in a
measurement is an indication of the measurement’s
precision.
•  A common convention used in science to indicate precision is
known as significant figures.
•  Significant figures are all the digits in a measurement that
are known with certainty PLUS the first digit that is uncertain.
•  ONLY ONE estimated digit is allowed to be significant.
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Significant Figures
Even though this ruler is
marked in only centimeters
and millimeters, if you
estimate, you can report
measurements to a
hundredth of a centimeter.
Significant Figure Rules
1. 
2. 
3. 
4. 
All non-zero digits are significant.
Zeros between non-zero digits are significant.
Zeros in front of a number are NEVER significant.
Zeros at the end of a number are significant IF there is
a decimal present. If there is no decimal present, they
are not significant.
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How Many Significant Figures?
•  28.6 g
•  3440. cm
•  910 m
•  0.04604 L
•  0.0067000 kg
•  1.68 x 105 m
•  2.0 x 103 g
Addition/Subtraction with Sig Figs
•  When adding or subtracting decimals, the answer must
have the same number of digits to the right of the decimal
as there are in the measurement having the fewest digits
after the decimal.
•  Example:
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Addition/Subtraction with Sig Figs
•  When adding or subtracting whole numbers (no
decimals), the position of the last significant figure in each
number being added must be compared. The one
farthest to the left is where the last significant figure
should be in the answer.
Multiplication/Division with Sig Figs
•  For multiplication and division, the answer can have no more
significant figures than are in the measurement with the fewest
number of significant figures.
•  Example:
Conversion factors are not measurements, so there is no
uncertainty in them. Therefore you do not count sig figs for
conversion factors when you are working factor label problems.
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Rounding Rules
Once you know how many significant figures your answer needs,
use these rules to round correctly.
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