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MAT081 :: Lecture Note :: Week 11
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MerriamWebster Online
[http://wm.com]
defines measurement as follows.1 : the act or process of measuring 2 : a figure, extent, or amount obtained by measuring : DIMENSIONMeasurements are used to measure stuff like time, temperature, length, weight, speed, money, power, and so on.
There are two primary measurement systems: US and Metric.
Each measurement system consists of many different units. For example, in the US, lengths are measured using units of inches, feet, yards, and miles. The metric system uses length units based on the meter (kilometer, millimeter, centimeter, and so on). [UNC.edu:: metric prefixes]
Let's use inch as a starting point. An inch is about the width of a man's thumb at the base of the nail and it is used to measure length.
Inches work well when measuring short lengths. Longer lengths are usually measured using other units of measurements such as feet and yards. Example: A football field is
3600 inches
in length, but we usually say it is100 yards
.Ratios have been established to convert from one unit of measure to another. The following are some US length ratios.
12 inches equals 1 foot 3 feet equals 1 yard 1760 yards equals 1 mileExercise: Convert
36 inches
tofeet
. We are given thatone foot
equalstwelve inches
.Setup two proportions and solve for the unknown. 1 ft. n ft.  =  12 in. 36 in. 1) multiply both sides by 36 in. 1 ft. n ft. 36 in. *  =  * 36 in. 12 in. 36 in. 2) solve for 'n' 1 ft. n ft. 36in.*  =  *36 in.12in.36 in.36 * 1 ft.  = n ft. 12 36 ft.  = n ft. 12 3 ft. = n ft. 36 inches equals 3 feet.Units of Measurement Resources
NIST.gov:: General Tables of Units of Measurement
National Institute of Standards and Technology
http://ts.nist.gov/WeightsAndMeasures/Publications/appxc.cfm
UNC.edu:: How Many?
University of North Carolina
http://www.unc.edu/~rowlett/units
Time
60 seconds per 1 minute 60 minutes per 1 hour 24 hours per 1 dayLet's compute how many seconds are in a day.
We want to solve the following. ? seconds  1 day We are given the following. 60 seconds 60 minutes 24 hours    1 minute 1 hour 1 day Multiply the three fractions together. The units of measurement "cancel" each other out. 60 seconds 60minutes24hours *  *  1minute1hour1 day 60 * 60 * 24 = 86,400 Answer. 86,400 seconds  1 dayA couple time and money quotes...
"Remember that time is money."
Benjamin Franklin"Minutes are worth more than money. Spend them wisely."
Thomas P. MurphyMoney
5 pennies per 1 nickel 2 nickels per 1 dime 5 nickels per 1 quarter 4 quarters per 1 dollarA penny is
one hundreth
of a dollar (i.e.$0.01
) and a dime isone tenth
of a dollar (i.e.$0.10
).A nickel is
%5
of a dollar (i.e.$0.05
) and a quarter is%25
of a dollar (i.e.$0.25
).Temperature (measure of molecular motion)
Degrees Fahrenheit are used to record surface temperature measurements by meteorologists in the United States. Most of the rest of the world uses degrees Celsius. Most of the scientific world uses Kelvin. [The word "degrees" is not used with Kelvin. In addition, Kelvin starts at "absolute zero;" therefore, there are no negative values. "Absolute zero" is the point at which all molecular motion stops.]
Formula: Fahrenheit to Celsius
°C = (°F  32) / 1.8 or Tc = (5/9) * (Tf  32) where Tc is temperature in degrees celsius Tf is temperature in degress fahrenheitFormula: Fahrenheit to Kelvin
K = (°F + 459.67) / 1.8The boiling point of sea water is
100 °C
.The freezing point of water at sea level is
0 °C
.The average room temperature is
20 °C
.The average human body temperature approximates
37 °C
.
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On 8 January 2007, NASA announced that the Moon will be metric leaving only the "United States, Liberia, and Burma still primarily using English units."
The metric system is also called the International System of Units (denoted by SI).
The following are base metric units of measurement.
length................ meter...... m mass.................. kilogram... kg time.................. second..... s electric current...... ampere..... A temperature........... Kelvin..... K amount of substance... mole....... mol luminous intensity.... candela.... cd volume................ liter...... L [nonSI]Metric Prefixes
10^{1} deka da 10^{2} hecto h 10^{3} kilo k 10^{6} mega M 10^{9} giga G 10^{12} tera T 10^{15} peta P 10^{18} exa E 10^{21} zeta Z 10^{24} yotta Y 10^{1} deci d 10^{2} centi c 10^{3} milli m 10^{6} micro u 10^{9} nano n 10^{12} pico p 10^{15} femto f 10^{18} atto a 10^{21} zepto z 10^{24} yocto y1 dekameter...... 10 meters 1 hectometer..... 100 meters 1 kilometer...... 1000 meters ... 1 gigameter...... 1,000,000,000 meters 1 decimeter...... 0.1 meter 1 centimeter..... 0.01 meter 1 millimeter..... 0.001 meter ... 1 nanometer...... 0.000000001 meterThe metric prefixes work on other base metric units.
1 kilogram....... 1000 grams 1 milligram...... 0.001 gram ... 1 nanogram....... 0.000000001 gram 1 hectoliter..... 100 liters 1 milliliter...... 0.001 liter ... 1 nanoliter...... 0.000000001 liter[nanovery, very, very small]
Update::2008.11.13
From nanotech...
"Sculpted using nanolithography by University of Michigan mechanical engineer, John Hart, each Obama face is composed of 150 million carbon nanotubes and measures half a millimeter across."NanoObama.com::Vote for Science
to hightech...
"Cisco predicts IP traffic will nearly double every two years, increasing at a combined annual growth rate of 46 percent from 2007 to 2012. That growth would result in an annual bandwidth demand on the world's IP networks of approximately 522 exabytes, or more than half a zettabyte. This demand on networks is equivalent to downloading 125 billion DVD movies per month." [...] "On the scalability front, the Cisco ASR 9000 offers up to six times the capacity of comparable edgerouter solutions, with up to 6.4 terabits per second of total capacity and up to four times the linecard speed available on the market, with 400 gigabits per slot."NewsFactor.com::Cisco Unveils 'ZettabyteEra' Router for Online Video
at Scottsdale Community College (SCC).
MathBabbler did not have a MAT082 class during the Spring 2008 semester, but during that semester, Dr. Art Decabooter stepped down as president of SCC. Notice how Decabooter's name starts with the metric prefix deca.BAB::Metric Prefixes: Is it Deca or Deka?
Drugs have taught an entire generation of Americans the metric system.  P. J. O'Rourke
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NIST.gov:: General Tables of Units of Measurement
National Institute of Standards and Technology
http://ts.nist.gov/ts/htdocs/230/235/appxc/appxc.htm
UNC.edu:: How Many?
University of North Carolina
http://www.unc.edu/~rowlett/units
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Tempe and Show Low are
163
miles apart. Calculate this distance inkilometers
.Given: 1 mi = 1.609344 km Solve: ??? kilometers  163 miles 1) setup a proportion ??? kilometers 1.61 kilometers  =  163 miles 1 mile 2) solve for ??? by multiplying both sides by 163 miles ??? kilometers 1.61 kilometers 163 miles x  =  x 163 miles 163 miles 1 mile ??? kilometers 1.61 kilometers163milesx  =  x 163miles163miles1mile1.61 x 163 equals 262.43 Answer: 163 miles is approximately equal to 262.43 kilometers[check answer] Google.com::Calculator:: 163mi to km
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Tempe and Superior are appoximately
52 miles
apart. Compute how many inches this is.Solve. ? inches  52 miles Given. 1 mile = 1760 yards 1 yard = 3 feet 1 foot = 12 inches 1) Convert 52 miles into yards. 1760 yards ? yards  =  1 mile 52 miles 52 miles equals 91,520 yards 2) Convert 91,520 yards into feet. 3 feet ? feet  =  1 yard 91,520 yards 91,520 yards equals 274,560 feet 3) Convert 274,560 feet into inches. 12 inches ? inches  =  1 foot 274,560 feet 3,294,720 inches equals 274,560 feet Answer. 52 miles equals 3,294,720 inches.
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Given.
60 seconds per 1 minute 60 minutes per 1 hour 24 hours per 1 dayLet's compute how many seconds are in a day.
We want to solve the following. ? seconds  1 day We are given the following. 60 seconds 60 minutes 24 hours    1 minute 1 hour 1 day Multiply the three fractions together. The units of measurement "cancel" each other out. 60 seconds 60minutes24hours x  x  1minute1hour1 day 60 * 60 * 24 = 86,400 Answer. 86,400 seconds  1 dayA couple time and money quotes...
"Remember that time is money."
Benjamin Franklin"Minutes are worth more than money. Spend them wisely."
Thomas P. Murphy
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The first definition for money given by MerriamWebster Online is as follows.
"1 : something generally accepted as a medium of exchange, a measure of value, or a means of payment: as a : officially coined or stamped metal currency"Here is only one of many good money quotes...
Money can't buy you happiness, but it does bring you a more pleasant form of misery.
 Spike Milligan (0191802002) { British actor and comic; more... } [money/happiness]In the United States of America we deal with monetary units of measurement such as pennies, nickels, dimes, quarters and dollars ($1, $5, $10, $20, $50, $100, ...; what about $2?).
Conversion ratios.
5 pennies per 1 nickel ( 5 cents; $0.05) 2 nickels per 1 dime ( 10 cents; $0.10) 5 nickels per 1 quarter ( 25 cents; $0.25) 4 quarters per 1 dollar (100 cents; $1.00)A penny is
one hundreth
of a dollar (i.e.1/100
or$0.01
) and a dime isone tenth
of a dollar (i.e.1/10
or$0.10
).A nickel is
%5
of a dollar (i.e.$0.05
) and a quarter is%25
of a dollar (i.e.$0.25
).Finance.Yahoo.com:: Currency Converter
Currency conversion examples.
 GDT::BAB:: Domain Names by the Euro
 GDT::BAB:: Scottsdalebased Canadian CompanyIsotechnika
 GDT::BAB:: U.K. Allocates Funds For Hector [04 April 2006]
That's my .02 cents on the subject.
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Temperature is a measure of molecular motion.
Here is a quote about temperature.
A Harvard Medical School study has determined that rectal thermometers are still the best way to tell a baby's temperature. Plus, it really teaches the baby who's boss.
 Tina Fey (1970???) { Saturday Night Live comedian; pic }Degrees Fahrenheit are used to record surface temperature measurements by meteorologists in the United States. Most of the rest of the world uses degrees Celsius. Most of the scientific world uses Kelvin. [The word "degrees" is not used with Kelvin. In addition, Kelvin starts at "absolute zero;" therefore, there are no negative values. "Absolute zero" is the point at which all molecular motion stops.]
Formula: Fahrenheit to Celsius
°C = (°F  32) / 1.8 or Tc = (5/9) * (Tf  32) where Tc is temperature in degrees celsius Tf is temperature in degress fahrenheitFormula: Fahrenheit to Kelvin
K = (°F + 459.67) / 1.8The boiling point of sea water is
100 °C
.The freezing point of water at sea level is
0 °C
.The average room temperature is
20 °C
.The average human body temperature approximates
37 °C
.The hottest recorded temperature in the United States is
56.7 °C (134 °F)
in Death Valley, California on 10 July 1913. The hottest temperature ever recorded on Earth is136 °F
at Al' Aziziyah, Libya in September of 1922.The coldest recorded temperature on earth was
128.6 °F
on 31 July 1983 at a Russian research station at Vostok, Antarctica.The following was copied from ClassZone.com
"The Vostok ice core provides the longest continuous record of Antarctic climatic history. Analysis of the core has been completed to a depth of 3350 meters, representing approximately 440,000 years of climate history."YouTube.com::How Hot Can It Get?
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Geometry is a "branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids."
When Moses was alive, these pyramids were a thousand years old.
Here began the history of architecture. Here people learned to
measure time by a calendar, to plot the stars by astronomy and
chart the earth by geometry. And here they developed that most
awesome of all ideas  the idea of eternity.
 Walter Cronkite (0191602009) {"the most trusted man in America"; more...} [geometry][update::2012.04.16] CBS News marks historic Cronkite anniversary
Terminology
The following terms are used extensively in geometry.
point: location (no dimensions, no length, no width, no depth) space: set of all points plane: set of points on one surface line: set of points (at least two) that has only one dimension, length line segment: line having two endpoints ray: line with one endpoint angle: two lines that intersect form an angle vertex: point where two lines intersectAccording to Euclid, an plane angle is "the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line."
Points
Points are typically labeled.
Lines
A line segment is a line that has a starting and ending point. A ray has a starting point, but no ending point.
Let
A
andB
be two points on the same line.<> <AB> line: AB __ AB segment: AB > AB> ray: AB < <AB ray: ABLines are often used in pairs and there are four types of pairs: intersecting, parallel, perpendicular, and skewed. Intersecting lines cross each other; parallel lines never touch and are always equal distance apart; perpendicular lines form right angles; and skewed lines never intersect nor are they parallel (they are not in the same plane). [Railroad tracks provide an example of parallel lines.]
A   CiD  B The line segments AB and CD intersect and are perpendicular. The vertex (i.e. point) where they intersect is labeled 'i'.Angles
An angle is formed when two lines intersect.
There are four types of angles: straight, right angle, acute, and obtuse. Angles are measured using degrees (a fraction of a circle [360°]).
straight angle ... 180° right angle ...... 90° acute angle ...... less than 90° obtuse angle ..... greater than 90° but less than 180°Jason Kidd, professional basketball player, when traded to a new team, was quoted he was going to help turn the team around
360°
.
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A polygon is a closed plane figure bounded by straight lines (i.e. sides). Common polygons are squares, rectangles, and triangles.
Every polygon contains at two or more angles.
A quadrilateral is a polygon having four sides.
A parallelogram is a quadrilateral where opposite sides are both parallel and equal length.
A rectangle is a parallelogram consisting of four right angles. A square is a rectangle where all four sides are equal length.
rhombus  parallelogram having 4 sides of equal length trapezoid  exactly one pair of opposite sides parallelA triangle is a threesided polygon.
The following is list of some other polygons.
type #sides #angles  Triangle........ 3 3 Quadrilateral... 4 4 Pentagon........ 5 5 Hexagon......... 6 6 Heptagon........ 7 7 Octagon......... 8 8 Nonagon........ 9 9 Decagon........ 10 10Two polygons are congruent if they are the same size and shape (i.e. corresponding angles and sides are equal). Two polygons are similar if they have the same shape, but different sizes.
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A circle is a plane figure consisting of points that are equal distance from a center point.
radius: distance from circle center to a circle point diameter: distance across a circle through the centerThe diameter of a circle is equal to two times its radius.
d = 2 * r where d is the diameter and r is the radiusThe circumference of a circle is its perimeter (i.e. distance around the circle).
C = 2 * pi * r where C is circumference; pi is the value 3.14; and r is radius C = pi * d where d is the diameterThe value of
pi
approximates the fraction22/7
.The area of a circle is the number of "square units" needed to cover the circle.
A = pi * r^{2} where A is area; pi is the value 3.14; and r is radius ["Why do they say 'pie are square' when pies are round?"]* * * * * r * *+ * + is the center of the circle * * * * * *GDT::BAB:: Washington Tree May Be Dying
Demon.co.ukPi
http://gwydir.demon.co.uk/jo/numbers/interest/pi.htm
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A perimeter is a measure of the distance around a region. [Hint: perimeter]
rectangle P = 2 * length + 2 * width square P = 4 * side triangle P = side a + side b + side cAn area is a measure of the surface of a region.
rectangle A = length * width square A = side^{2} triangle A = 0.5 * base * heightSquare Yard Example
[Saturday, 24 April 2004, Arizona Republic]
The U.S. Department of Agriculture reported that most of western Nebraska has at least 15 grasshoppers per square yard. Some areas had as many as 370 grasshoppers in a square yard. [Anything over 40 is considered severe.]
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Plane Figures
Recall, a plane is a flat surface that spans to infinity. A plane figure is a geometric form that lies on a plane.
Triangles
A triangle has three sides that form three angles. The sum of the three angles total 180°.
The following are special types of triangles.
equilateral  all sides have equal length and all angles are equal isoceles  two sides are same length; angles opposite the equals size are equal scalene  no sides have the same length and no angles are equal right  has a right angle; the side opposite the right angle is the hypotenuse and the other two sides are legsIf you know the length of two sides of a right triangle, then the length of the third side can be calculated using the Pythagorean Theorem.
a^{2} + b^{2} = c^{2} where 'a' and 'b' are the legs and 'c' is the hypotenuseGDT::BAB:: Find X
The perimeter of a triangle is the sum of the length of its sides.
The area of a triangle is onehalf the product of its base length and height.
1 A =  * b * h 2 + / /  /  h /  /  ++ bGDT::BAB:: Triangles In Space May Be Signals
Quadrilaterals
parallelogram  opposite sides are parallel and have equal length rectangle  parallelogram with 4 right angles square  rectangle with equal length sides rhombus  parallelogram having 4 sides of equal length trapezoid  exactly one pair of opposite sides parallel
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Volume is measured in "cubic" units. The volume of a figure is the number of cubes required to completely fill it.
Volumes are used for cubes, rectangular prisms, irregular prisms, cylinders, pyramids, cones, spheres, and ellipsoids.
Math.com::Geometry:: Cylinders, cones and spheres
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Scientific notation is another method for writing large and small numbers.
Numbers written in scientific notation take on the following format.
d.d... * 10^exponent 'd' are digits, where the digit to the left of the decimal point is not zero 123 = 1.23 * 10^2 123,000 = 1.23 * 10^5 5,100,000,000 = 5.1 * 10^9 123,001,000,000 = 1.23001 * 10^11 0.1 = 1.0 * 10^1 0.025 = 2.5 * 10^2 0.005703 = 5.703 * 10^3 0.0000000009 = 9.0 * 10^10PurpleMath.com:: Scientific Notation
KhanAcademy.org::Introduction to scientific notation
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