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Section 2.1 Units and Measurements
• Define SI base units for time, length, mass, and
temperature.
• Explain how adding a prefix changes a unit.
• Compare the derived units for volume and density.
mass: a measurement that reflects the amount of
matter an object contains
Section 2.1 Units and Measurements
base unit
kelvin
second
derived unit
meter
liter
kilogram
density
Chemists use an internationally
recognized system of units to
communicate their findings.
(cont.)
Units
• Système Internationale d'Unités (SI) is an
internationally agreed upon system of
measurements.
• A _______________is a defined unit in a
system of measurement that is based on an
object or event in the physical world, and is
independent of other units.
Units (cont.)
• The SI base unit of time is the second (s),
based on the frequency of radiation given
off by a cesium-133 atom.
• The SI base unit for length is the meter (m),
the distance light travels in a vacuum in
1 / 299,792,458th of a second.
• The SI base unit of mass is the kilogram
(kg), about 2.2 pounds
Units (cont.)
Units Temperature:
• The SI base unit of temperature is the kelvin (K).
• Temperature: Measure of the average kinetic energy
of particles in matter.
• What is kinetic energy?
• Zero kelvin is the point where there is no particle
motion or kinetic energy, also known as
_________________.
• Two other temperature scales are Celsius and
Fahrenheit.
• Temperature conversions:
• Celsius : Kelvin
C + 273 = K
• Celsius : Fahrenheit
°C x 9/5 + 32 = °F
(°F - 32) x 5/9 = °C
Important temps
273 K = 0C = 32 F
373 K = 100 C = 212 F
• Heat vs Temperature
– Heat is the sum total of the kinetic energy,
temperature is the average.
– Units
• Joules
• Calories
• BTU’s
• Prefixes
– We can adapt the base units to fit larger or
smaller measurements by adding prefixes.
• Where do we put prefixes?
– How large is a gram?
– How many grams do you weigh?
– Is there a better unit to measure your weight
Units (cont.)
Derived Units
• Not all quantities can be measured with SI
base units.
• A unit that is defined by a combination of
base units is called a ____________ unit
Derived Units (cont.)
• Volume is measured in cubic meters (m3), but
this is very large. A more convenient measure
is the _______, or one cubic decimeter (dm3).
Derived Units (cont.)
• ___________ is a derived unit, g/cm3, the
amount of mass per unit volume.
• A cm3 or cubic centimeter, or cc, is equal
to 1 milliliter of water.
• density = mass/volume
• D=m/V
Section 2.2 Scientific Notation and
Dimensional Analysis
• Express numbers in scientific notation.
• Convert between units using dimensional analysis.
quantitative data: numerical information
describing how much, how little, how big, how
tall, how fast, and so on
Section 2.2 Scientific Notation and
Dimensional Analysis (cont.)
scientific notation
dimensional analysis
conversion factor
Scientists often express numbers in
scientific notation and solve problems
using dimensional analysis.
Scientific Notation
• ___________________________ can be used to
express any number as a number between 1 and
10 (the coefficient) multiplied by 10 raised to a
power (the exponent).
• Step 1:
Count the number of places the decimal point must
move to make coefficient between 1 and 9.99999
• 0.000067 becomes 6.7 x 10 ?
• 12,345 becomes 1.2345 x 10 ?
Scientific Notation (cont.)
• Step 2: 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.
• Or if the original number was greater than 1.0,
it is positive, if it is less than 1.0, it is negative
800. = 8.0  102
0.0000343 = 3.43  10–5
• 2,359 =
• 0.000258
• 2.34 x 106
• 9.08 x 10 - 9
Scientific Notation (cont.)
• Addition and subtraction
– Exponents must be the same.
– Rewrite values with the same exponent.
– Add or subtract coefficients.
– 6.4 x 109 - 1.3 x 109 =
Scientific Notation (cont.)
• Multiplication and division
– To multiply, multiply the coefficients, then
add the exponents.
– To divide, divide the coefficients, then
subtract the exponent of the divisor from the
exponent of the dividend.
– 4.0 x 109 x 3.0 x 103 =
– 3.0 x 104 ÷ 1.5 x 109 =
Dimensional Analysis
• _________________________is a
systematic approach to problem solving
that uses conversion factors to move, or
convert, from one unit to another.
• The overall value is the same, but the units
change
• $10 bill = 2 $5 bills
• A ______________________is a ratio of
equivalent values having different units.
Dimensional Analysis
(cont.)
• Writing conversion factors
– Conversion factors are derived from equality
relationships, such as 1 dozen = 12
– 1 dozen / 12 eggs or 12 eggs / 1 dozen
– Percentages can also be used as
conversion factors. They relate the number
of parts of one component to 100 total parts.
– 30% = 30 / 100
Dimensional Analysis
(cont.)
• Using conversion factors
– A conversion factor must cancel one unit
and introduce a new one.
– If there are 32 people going on a trip, and
each will want 2 bottles of water, how many
eight-packs of water will need to be
purchased?
– Multiply across the top, divide by whats on
bottom
Section 2.3 Uncertainty in Data
• Define and compare accuracy and precision.
• Describe the accuracy of experimental data using
error and percent error.
• Apply rules for significant figures to express
uncertainty in measured and calculated values.
experiment: a set of controlled observations that
test a hypothesis
Section 2.3 Uncertainty in Data (cont.)
accuracy
percent error
precision
significant figures
error
Measurements contain uncertainties
that affect how a result is presented.
Accuracy and Precision
• _____________refers to how close a
measured value is to an accepted value.
• _____________refers to how close a series
of measurements are to one another.
Measuring Accuracy
• ________________________________ is
defined as the difference between an
experimental value and an accepted value.
Measuring Accuracy
• The error equation is:
error = experimental value – accepted value.
• ________________________expresses error
as a percentage of the accepted value.
• So if the density of water is supposed to
be 1.0 g / ml, and you calculate it to be
1.29 g / ml
• What is the error?
• What is the percent error?
Significant Figures: measuring precision
• Often, precision is limited by the tools
available.
• ______________________include all known
digits plus one estimated digit. These tell us
how precise the measurements were.
Significant Figures (cont.)
• Rules for significant figures
– Rule 1: Nonzero numbers are always significant.
– 2.34 = 3 s.f.
– Rule 2: Zeros between nonzero numbers are
always significant.
– 1.003 = 4 s.f.
– 4,000, 006 = 7 s.f.
– Rule 3: All final zeros to the right of the decimal
are significant.
– 1.300 = 4 s.f.
– Rule 4: Placeholder zeros or introductory zeroes, are not
significant. To remove placeholder zeros, rewrite the
number in scientific notation.
– 0.00054 = 2 s.f.
– 5.4 x 10 - 4
– Rule 5: Counting numbers and defined constants have an
infinite number of significant figures.
– 1 dozen = 12 eggs….. infinite s.f.
– Rule 6: A decimal point makes zeroes before it become
significant.
– 12,000. = 5 s.f.
– 12,000 = 2 s.f.
Significant figures: Rounding
• Calculators are not aware of significant
figures.
• Answers should not have more significant
figures than the original data with the fewest
figures, and should be rounded.
Significant Figures: Rounding
• Addition and subtraction
– Round numbers so all numbers have the same
number of digits to the right of the decimal.
– 6.4 + 3.79 =
• Multiplication and division
– Round the answer to the same number of significant
figures as the original measurement with the fewest
significant figures.
– 2.1 x 2 =
Section 2.4 Representing Data
• Create graphics to
reveal patterns in data.
• Interpret graphs.
independent variable:
the variable that is
changed during an
experiment
graph
Graphs visually depict data, making it
easier to see patterns and trends.
Graphing (cont.)
• A circle graph, or pie chart, has wedges
that visually represent percentages of a
fixed whole.
Graphing (cont.)
• Bar graphs are often used to show how a
quantity varies across categories.
Graphing (cont.)
• On line graphs, independent variables are
plotted on the x-axis and dependent
variables are plotted on the y-axis.
Graphing (cont.)
• If a line through the points is straight, the
relationship is linear and can be analyzed
further by examining the slope.
Interpreting Graphs
• Interpolation is reading and estimating
values falling between points on the graph.
• Extrapolation is estimating values outside the
points by extending the line.