MEASUREMENTS AND
CALCULATIONS
Chapter 2
2.1
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Scientific Method
A scientific method is a way to logically approach a
problem by making observations, testing a
hypothesis, gathering and analyzing data, and
forming conclusions.
There are many scientific methods
observations
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Using your senses to gather information
Qualitative: descriptive
Quantitative: numerical
Most science experiments utilize quantitative
observations
hypothesis
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A hypothesis is a testable statement
Often written as “if-then” statements (Ex: if
marigold flowers are watered with miracle grow,
then their plant growth will be enhanced)
Tested through experiments to determine if
accepted or rejected
data analysis
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This crucial step is used to determine if the
hypothesis is accepted or rejected through statistical
analysis (t-test, ANOVA, Mann-Whitney, etc)
Both outcomes can be an important contribution to
science since they can be used as a stepping stone
for future experiments
Graphs and charts that depict the results are often
incorporated into a lab report
conclusions
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Based on the results of the experiment, conclusions
can be made
Results can then be published and shared with
colleagues
models
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A visual, verbal, conceptual, or mathematical
explanation for something abstract or difficult to
explain
Ex: model of an atom
theory
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DON’T USE THE WORD THEORY INCORRECTLY!!!!
A theory is a broad generalization that explains a
body of facts or phenomenon and is supported by
experimental evidence
Theories can change as new advancements in science
take place
Ex: the Big Bang Theory
law
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A generalized rule that is used to explain a body
of observations in the form of a verbal or
mathematical statement.
Imply a cause and effect between the observed
elements and must always apply under the same
conditions
Ex: Law of Gravity
Science is……
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Testable- Predictions are tested through
experiments and the results either support or do not
support the hypothesis or theory. NOTHING IS
PROVEN IN SCIENCE!
Tentative- Science CHANGES! All scientific
explanations are the best we can do now. Through
investigation and technological advancements, we
understand more all the time
2.2 Units of Measurement
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Scientific Notation: a method to make writing and
handling very large or very small numbers easy
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34000000 = 3.4 x 107
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.000000076 = 7.6 x 10-7
Operations with Scientific Notation
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Exponents must match with addition and subtraction
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Exponents are added for multiplication
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Exponents are subtracted for division
measurements
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Chemistry is qualitative and quantitative
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Measurements are used to represents quantities
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A quantity has magnitude, size or amount
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Ex: a liter is a unit of measurement while volume is a
quantity
SI Measurements
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SI units are used in science (7 base units)
Mass-kilogram (kg)
Length- meter (m)
Temperature-Kelvin (K)
Amount of a substance- mole (mol)
All SI units can be modified by using prefixes
Ex: kilo = 1000 = 1 x 103
1 kilometer = 1000 meters = 1 x 103 meters
SI Prefixes
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Mega
Kilo
Base units
Centi
Milli
Micro
Nano
Pico
M
K
(m, L, g)
c
m
µ
n
p
106
103
10-2
10-3
10-6
10-9
10-12
Derived units
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Formed by combinations of SI units
Ex: meters/second
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Density = mass/volume
Density is important for identifying substances
Given in kg/m3
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Density of water = 1 kg/m3
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Conversions
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Conversion factors express an equality between two
different units
Quantity given x conversion factor = quantity
sought
Remember:
X
1
= 1
Factor Label Method
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Based on the number of equalities and multiplication
and division in series
Ex: convert 250,000 mg to kg
2.5 x 105mg
1
1 x 10-3 g 1kg = 2.5 x 105-3 x 1
1 mg
1x103g 1x1x1x103
2.5 x 102 kg =
1 x 103
2.5 x 10-1kg
2.3 Using Scientific Measurements
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Accuracy vs Precision
Accuracy is the closeness of measurements to the
true value or correct answer
Precision refers to the closeness of a set of
measurements to one another. (precision is more
related to the way in which the measurements are
made)
Accuracy vs Precision
Calculating Percent Error
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Percent error = valueaccepted – valueexperimental X 100
valueaccepted
percent error will have a positive value if the
accepted value is greater than the experimental
value
Will be negative if the accepted value is less than
the experimental value
Example #1
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What is the percent error if the length of a wire is
4.25 cm if the correct value should be 4.08 cm?
% error = va – ve X 100
va
% error = 4.08 – 4.25 X 100 = - 4.2 %
4.08
Example #2
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The actual density of a material is 7.44 g/cm3. A
student measures density to be 7.30 g/cm3. What is
the percent error?
% error = 7.44 g/cm3 – 7.30 g/cm3 x 100
7.44 g/cm3
= 1.88 %
Significant Figures
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Sig figs consist of all the digits known with certainty
plus one final digit which is somewhat uncertain or
estimated
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If the number has no zeroes, all digits are significant
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Follow the rules in the table!
Rules for Determining Sig Figs
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1. Always count nonzero digits
Example: 21 has two significant figures, while 8.926 has four
2. Never count leading zeros
Example: 021 and 0.021 both have two significant figures
3. Always count zeros which fall somewhere between two nonzero digits
Example: 20.8 has three significant figures, while 0.00104009 has six
4. Count trailing zeros if and only if the number contains a decimal point
Example: 210 and 210000 both have two significant figures, while
210. has three and 210.00 has five
5. For numbers expressed in scientific notation, ignore the exponent and
apply Rules 1-4 to the number
Example: -4.2010 x 1028 has five significant figures
Direct Proportions
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Two quantities are directly proportional to each
other if dividing one by the other gives a constant
value
Example: doubling the mass of a sample doubles
the volume
Inverse Proportions
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Two quantities are inversely proportional if their
product is constant
Example: doubling the speed cuts the required time
in half