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Summary of Key Concepts

Module by: Denny Burzynski, Wade Ellis. E-mail the authorsEdited By: Math Editors

Summary: 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 ((Reference))

Measurement is comparison to some standard.

Standard Unit of Measure ((Reference))

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

Two Types of Measurement Systems ((Reference))

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

Unit Fraction ((Reference))

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 ((Reference))

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.

  • kilo —  thousand
  • deci —  tenth
  • hecto —  hundred
  • centi —  hundredth
  • deka —  ten
  • milli —  thousandth

Metric Conversions ((Reference))

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 ((Reference))

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 ((Reference))

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 ((Reference))

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 ((Reference))

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 ((Reference))

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 ((Reference))

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

Perimeter ((Reference))

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

Circumference, Diameter, Radius ((Reference))

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 ππ ((Reference))

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

Formula ((Reference))

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

Circumference Formulas ((Reference))

C = π d C = π d size 12{C=π cdot d} {}

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

Area ((Reference))

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

Volume ((Reference))

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

Area Formulas ((Reference))

Triangle: A=12bhA=12bh size 12{A= { {1} over {2} } cdot b cdot h} {}
Rectangle: A=lwA=lw size 12{A=1 cdot w} {}
Parallelogram: A=bhA=bh size 12{A=b cdot h} {}
Trapezoid: A=12(b1+b2)hA=12(b1+b2)h size 12{A= { {1} over {2} } cdot \( b rSub { size 8{1} } +b rSub { size 8{2} } \) cdot h} {}
Circle: A=πr2A=πr2 size 12{A=π cdot r rSup { size 8{2} } } {}

Volume Formulas ((Reference))

Rectangle solid: V=lwhV=lwh size 12{V=l cdot w cdot h} {}
Sphere: V=43πr3V=43πr3 size 12{V= { {4} over {3} } cdot π cdot r rSup { size 8{3} } } {}
Cylinder: V=πr2hV=πr2h size 12{V=π cdot r rSup { size 8{2} } cdot h} {}
Cone: V=13πr2hV=13πr2h size 12{V= { {1} over {3} } cdot π cdot r rSup { size 8{2} } cdot h} {}

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Definition of a lens

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A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

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Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

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