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9.6 Summary of key concepts

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module reviews the key concepts from the chapter "Measurement and Geometry."

Summary of key concepts

Measurement ( [link] )

Measurement is comparison to some standard.

Standard unit of measure ( [link] )

A quantity that is used for comparison is called a standard unit of measure .

Two types of measurement systems ( [link] )

There are two major types of measurement systems in use today. They are the United States system and the metric system .

Unit fraction ( [link] )

A unit fraction is a fraction that has a value of 1. Unit fractions can be used to convert from one unit of measure to another.

Meter, liter, gram, and associated prefixes ( [link] )

Common units of measure in the metric system are the meter (m), for length, the liter (L), for volume, and the gram (g), for mass. To each of these units, a prefix can be attached.
  • thousand
  • tenth
  • hundred
  • hundredth
  • ten
  • thousandth

Metric conversions ( [link] )

To convert from one metric unit to another:
  1. Determine the location of the original number on the metric scale.
  2. Move the decimal point of the original number in the same direction and the same number of places as is necessary to move to the metric unit you wish to convert to.

Denominate numbers ( [link] )

Numbers that have units of measure associated with them are denominate num­bers . The number 25 mg is a denominate number since the mg unit is associated with the pure number 25. The number 82 is not a denominate number since it has no unit of measure associated with it.

Simplified denominate number ( [link] )

A denominate number is simplified when the number of standard units of measure associated with it does not exceed the next higher type of unit. 55 min is simplified, whereas 65 min is not simplified

Addition and subtraction of denominate numbers ( [link] )

Denominate numbers can be added or subtracted by
  1. writing the numbers vertically so that the like units appear in the same column.
  2. adding or subtracting the number parts, carrying along the unit.
  3. simplifying the sum or difference.

Multiplying a denominate number by a whole number ( [link] )

To multiply a denominate number by a whole number, multiply the number part of each unit by the whole number and affix the unit to the product.

Dividing a denominate number by a whole number ( [link] )

To divide a denominate number by a whole number, divide the number part of each unit by the whole number beginning with the largest unit. Affix the unit to this quotient. Carry the remainder to the next unit.

Polygon ( [link] )

A polygon is a closed plane (flat) figure whose sides are line segments (portions of straight lines).

Perimeter ( [link] )

The perimeter of a polygon is the distance around the polygon.

Circumference, diameter, radius ( [link] )

The circumference of a circle is the distance around the circle. The diameter of a circle is any line segment that passes through the center of the circle and has its endpoints on the circle. The radius of a circle is one half the diameter of the circle.

The number π ( [link] )

The symbol π , read "pi," represents the nonterminating, nonrepeating decimal number 3.14159... . For computational purposes, π is often approximated by the number 3.14.

Formula ( [link] )

A formula is a rule for performing a task. In mathematics, a formula is a rule that directs us in computations.

Circumference formulas ( [link] )

C = π ⋅ d size 12{C=π cdot d} {} C ≈ ( 3 . 14 ) d size 12{C approx \( 3 "." "14" \) d} {}
C = 2 ⋅ π ⋅ r size 12{C=2 cdot π cdot r} {} C ≈ 2 ( 3 . 14 ) r size 12{C approx 2 \( 3 "." "14" \) r} {}

Area ( [link] )

The area of a surface is the amount of square length units contained in the surface.

Volume ( [link] )

The volume of an object is a measure of the amount of cubic length units contained in the object.

Area formulas ( [link] )

Triangle : A = 1 2 ⋅ b ⋅ h size 12{A= { {1} over {2} } cdot b cdot h} {}
Rectangle : A = l ⋅ w size 12{A=1 cdot w} {}
Parallelogram : A = b ⋅ h size 12{A=b cdot h} {}
Trapezoid : A = 1 2 ⋅ ( b 1 + b 2 ) ⋅ h size 12{A= { {1} over {2} } cdot \( b rSub { size 8{1} } +b rSub { size 8{2} } \) cdot h} {}
Circle : A = π ⋅ r 2 size 12{A=π cdot r rSup { size 8{2} } } {}

Volume formulas ( [link] )

Rectangle solid : V = l ⋅ w ⋅ h size 12{V=l cdot w cdot h} {}
Sphere : V = 4 3 ⋅ π ⋅ r 3 size 12{V= { {4} over {3} } cdot π cdot r rSup { size 8{3} } } {}
Cylinder : V = π ⋅ r 2 ⋅ h size 12{V=π cdot r rSup { size 8{2} } cdot h} {}
Cone : V = 1 3 ⋅ π ⋅ r 2 ⋅ h size 12{V= { {1} over {3} } cdot π cdot r rSup { size 8{2} } cdot h} {}

Questions & Answers

what's Thermochemistry
rhoda Reply
the study of the heat energy which is associated with chemical reactions
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explain please
Victory
First twenty elements with their valences
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asue
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what is the change of matter from one state to another
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what is isolation of organic compounds
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what is atomic radius
ThankGod Reply
Read Chapter 6, section 5
Dr
Read Chapter 6, section 5
Kareem
Atomic radius is the radius of the atom and is also called the orbital radius
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atomic radius is the distance between the nucleus of an atom and its valence shell
Amos
Read Chapter 6, section 5
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Bohr's model of the theory atom
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is there a question?
Dr
when a gas is compressed why it becomes hot?
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It has no oxygen then
Goldyei
read the chapter on thermochemistry...the sections on "PV" work and the First Law of Thermodynamics should help..
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an increase in the pressure of a gas results in the decrease of its
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definition of the periodic table
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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