Chapter 1:
Matter, Measurements,
and Calculations
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Part 1: Matter
Sections 1.1-1.4
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MATTER
• Matter is anything that has mass and occupies space.
MASS
• Mass is a measurement of the amount of matter in an
object.
• Mass is independent of the location of an object.
• An object on the earth has the same mass as the same
object on the moon.
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WEIGHT
• Weight is a measurement of the gravitational force acting
on an object.
• Weight depends on the location of an object.
• An object weighing 1.0 lb on earth weighs about 0.17 lb on
the moon.
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PHYSICAL PROPERTIES OF MATTER
• Physical properties can be observed or measured without
attempting to change the composition of the matter being
observed.
• Examples of physical properties are color, shape and
mass.
CHEMICAL PROPERTIES OF MATTER
• Chemical properties can be observed or measured only by
attempting to change the composition of the matter being
observed.
• Examples of chemical properties are flammability and the
ability to react (e.g. when vinegar and baking soda are
mixed).
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PHYSICAL CHANGES OF MATTER
• Physical changes take place without a change in
composition.
• Examples of physical changes are the freezing, melting, or
evaporation of a substance (e.g. water).
CHEMICAL CHANGES OF MATTER
• Chemical changes are always accompanied by a change
in composition.
• Examples of chemical changes are the burning of paper
and the fizzing of a mixture of vinegar and baking soda.
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THE PARTICULATE MODEL OF MATTER
• All matter is made up of tiny particles called molecules
and atoms.
MOLECULES
• A molecule is the smallest particle of a pure substance that
is capable of a stable independent existence.
ATOMS
• Atoms are the particles that make up molecules.
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DIATOMIC MOLECULES
• Diatomic molecules contain two atoms.
TRIATOMIC MOLECULES
• Triatomic molecules contain three atoms.
POLYATOMIC MOLECULES
• Polyatomic molecules contain more than three atoms.
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HOMOATOMIC MOLECULES
• The atoms contained in homoatomic molecules are of the
same kind.
HETEROATOMIC MOLECULES
• The atoms contained in heteroatomic molecules are of two
or more kinds.
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CLASSIFICATION OF MATTER
• Matter can be classified into several categories based on
chemical and physical properties.
PURE SUBSTANCES
• Pure substances have a constant composition and a fixed
set of other physical and chemical properties.
• An example is pure water that always contains the same
proportions of hydrogen and oxygen, and freezes at a
specific temperature.
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MIXTURES
• Mixtures can vary in composition and properties.
• An example is a mixture of table sugar and water which
can have different proportions of sugar and water.
•A glass of water could contain one, two, three, etc.
spoons of sugar.
•Properties such as sweetness would be different for
the mixtures with different proportions.
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HETEROGENEOUS MIXTURES
• The properties of a sample of a heterogeneous mixture
depends on the location from which the sample was taken.
• A pizza pie is a heterogeneous mixture. A piece of crust
has different properties than a piece of pepperoni taken
from the same pie.
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HOMOGENEOUS MIXTURES
• Homogeneous mixtures are also called solutions. The
properties of a sample of a homogeneous mixture are the
same regardless of where the sample was obtained from
the mixture.
• Samples taken from any part of a mixture made up of one
spoon of sugar mixed with a glass of water will have the
same properties such as the same taste.
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ELEMENTS
• Elements are pure substances that are made up of
homoatomic molecules or individual atoms of the same
kind.
• Examples are oxygen gas made up of homoatomic
molecules and copper metal made up of individual copper
atoms.
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COMPOUNDS
• Compounds are pure substances that are made up of
heteroatomic molecules or individual atoms (ions) of two or
more different kinds.
• Examples are pure water made up of heteroatomic
molecules and table salt made up of sodium atoms (ions)
and chlorine atoms (ions).
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MATTER CLASSIFICATION SUMMARY
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Part 2: Measurement & Problem
Solving
Sections 1.5-1.11
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MEASUREMENTS AND MEASUREMENT UNITS
• Measurements consist of two parts, a number and a unit or
label such as feet, pounds, or gallons.
• Measurement units are agreed upon by those making and
using the measurements.
• Measurements are made
using measuring devices
(e.g. rulers, balances,
graduated cylinders, etc.).
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THE METRIC SYSTEM OF MEASUREMENT
• The metric system is a decimal system in which larger and
smaller units are related by factors of 10.
TYPES OF METRIC SYSTEM UNITS
• Basic or defined units [e.g. 1 meter (1 m)] are used to
calculate derived units [e.g. 1 square meter (1 m2)].
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THE USE OF PREFIXES
•Prefixes are used to relate basic and derived units.
•The commonly-used prefixes are given in the following table:
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TEMPERATURE SCALES
• The three most commonlyused temperature scales are
the Fahrenheit, Celsius and
Kelvin scales. The Celsius
and Kelvin scales are used in
scientific work.
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RELATIONSHIPS BETWEEN THE TEMPERATURE
SCALES
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CONVERSIONS FROM ONE TEMPERATURE SCALE
TO ANOTHER
• Readings on one temperature scale can be converted to
the readings on the other scales by using mathematical
equations.
• Converting Fahrenheit to Celsius.
C  59  F  32
• Converting Celsius to Fahrenheit.
F  95  C  32
• Converting Kelvin to Celsius.
C  K  273
• Converting Celsius to Kelvin
K  C  273
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COMMONLY-USED METRIC UNITS
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SCIENTIFIC NOTATION
• Scientific notation provides a convenient way to express
very large or very small numbers.
• Numbers written in scientific notation consist of a product
of two parts in the form M x 10n, where M is a number
between 1 and 10 (but not equal to 10) and n is a positive
or negative whole number.
• The number M is written with the decimal in the standard
position.
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STANDARD DECIMAL POSITION
• The standard position for the decimal is to the right of the
first nonzero digit in the number M.
SIGNIFICANCE OF THE EXPONENT n
• A positive n value indicates the number of places to the
right of the standard position that the original decimal
position is located.
• A negative n value indicates the number of places to the
left of the standard position that the original decimal
position is located.
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MULTIPLICATION OF NUMBERS WRITTEN IN
SCIENTIFIC NOTATION
• Multiply the M values of each number to give a product
represented by M'.
• Add together the n values of each number to give a sum
represented by n'.
• Write the final product as M' x 10n'.
• Move decimal in M' to the standard position and adjust n'
as necessary.



3.0  108 4.0  102  3.0  4.0  10
8    2
 12  106
 1.2  107
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DIVISION OF NUMBERS WRITTEN IN SCIENTIFIC
NOTATION
• Divide the M values of each number to give a quotient
represented by M'.
• Subtract the denominator (bottom) n value from the
numerator (top) n value to give a difference represented by
n'.
• Write the final quotient as M' x 10n'.
• Move decimal in M' to the standard position and adjust n'
as necessary.
3.0  108 3.0
 8   2

 10
2
4.0  10
4.0
 0.75  1010
 7.5  109
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SIGNIFICANT FIGURES
• Significant figures are the numbers in a measurement that
represent the certainty of the measurement, plus one
number representing an estimate.
COUNTING ZEROS AS SIGNIFICANT FIGURES
• Leading zeros are never significant figures.
• Buried zeros are always significant figures.
• Trailing zeros are generally significant figures.
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NUMBER OF SIGNIFICANT FIGURES TO USE IN A
PRODUCT OR QUOTIENT OF NUMBERS
•
The answer obtained by multiplication or division must
contain the same number of significant figures (SF) as
the quantity with the fewest number of significant figures
used in the calculation.
4.325  4.5  19.4625  19
 4 SF   2 SF  
2 SF
4.325  4.5  0.961  0.96
 4 SF    2 SF  
2 SF
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NUMBER OF SIGNIFICANT FIGURES TO USE IN A
SUM OR DIFFERENCE OF NUMBERS
•
The answer obtained by addition or subtraction must
contain the same number of places to the right of the
decimal (prd) as the quantity in the calculation with the
fewest number of places to the right of the decimal.
5.325  5.5  10.825  10.8
 3 prd  1prd 
1prd
5.325  5.5  0.175  0.2
 3 prd  1prd 
1prd
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ROUNDING RULES FOR NUMBERS
• If the first of the nonsignificant figures to be dropped from
an answer is 5 or greater, all the nonsignificant figures are
dropped and the last remaining significant figure is
increased by one.
• If the first of the nonsignificant figures to be dropped from
an answer is less than 5, all nonsignificant figures are
dropped and the last remaining significant figure is left
unchanged.
Round 10.825 to 1place to the right of the decimal.
 10.8
Round  0.175 to 1place to the right of the decimal.
 0.2
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EXACT NUMBERS
• A number used as part of a defined relationship between
quantities is an exact number (e.g. 100 cm = 1 m).
• A counting number obtained by counting individual objects
is an exact number (e.g. 1 dozen eggs = 12 eggs).
• A reduced simple fraction is an exact number (e.g. 5/9 in
equation to convert ºF to ºC).
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USING UNITS IN CALCULATIONS
• The factor-unit method for solving numerical problems is a
four-step systematic approach to problem solving.
•Step 1: Write down the known or given quantity. Include
both the numerical value and units of the quantity.
•Step 2: Leave some working space and set the known
quantity equal to the units of the unknown quantity.
•Step 3: Multiply the known quantity by one or more factors,
such that the units of the factor cancel the units of the known
quantity and generate the units of the unknown quantity.
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•Step 4: After you generate the desired units of the unknown
quantity, do the necessary arithmetic to produce the final
numerical answer.
• Please see Example 1.15 and 1.16 for an example. I also
suggest that you try “Learning Check 1.16 on the bottom of
page 27 in your textbook. If you have problems, please bring it
up on the discussion board.
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PERCENTAGE
• The word percentage means per one hundred. It is
the number of items in a group of 100 such items.
PERCENTAGE CALCULATIONS
• Percentages are calculated using the equation:
In this equation, part represents the number of specific
items included in the total number of items.
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EXAMPLE OF A PERCENTAGE CALCULATION
• A student counts the money she has left until pay day
and finds she has $36.48. Before payday, she has to
pay an outstanding bill of $15.67. What percentage
of her money must be used to pay the bill?
• Solution: Her total amount of money is $36.48, and
the part is what she has to pay or $15.67. The
percentage of her total is calculated as follows:
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DENSITY
• Density is the ratio of the mass of a sample of matter
divided by the volume of the same sample.
or
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EXAMPLE OF A DENSITY CALCULATION
• A 20.00 mL sample of liquid is put into an empty beaker
that had a mass of 31.447 g. The beaker and contained
liquid were weighed and had a mass of 55.891 g.
Calculate the density of the liquid in g/mL.
• The mass of the liquid is the difference between the mass
of the beaker with contained liquid, and the mass of the
empty beaker or 55.891g -31.447 g = 24.444 g. The
density of the liquid is calculated as follows:
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