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MAT082 :: Lecture Note :: Week 12
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Overview
Assignment(s):

Quote of the Week {Furman.edu:: Mathematical Quotations Server}
Although he may not always recognize his bondage,
modern man lives under a tyranny of numbers.
-- Nicholas Eberstadt (?????-) { political scientist/economist; more... } [numbers] [log]
BARS of the Week {NASA.gov:: Astronomy Picture of the Day}
Kingman AZ | US Hwy-2 VT | US Hwy-136 IL [log]

Introduction to the Metric System

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  [non-SI]
Metric Prefixes
   101  deka-  da
   102  hecto- h
   103  kilo-  k
   106  mega-  M
   109  giga-  G
   1012 tera-  T
   1015 peta-  P
   1018 exa-   E
   1021 zeta-  Z
   1024 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- y

   1 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 meter

The 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

[nano--very, very, very small]

Update::2008.11.13

From nano-tech... 

   "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 high-tech... 

   "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 edge-router solutions, with 
    up to 6.4 terabits per second of total capacity and up to four 
    times the line-card speed available on the market, with 
    400 gigabits per slot."

NewsFactor.com::Cisco Unveils 'Zettabyte-Era' 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-?

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Some Measurement Hyperlinks

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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Unit of Measurement: Length Example (miles to kilometers)

Tempe and Show Low are 163 miles apart. Calculate this distance in kilometers. 

   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 kilometers
      163 miles x -------------- =  --------------- x 163 miles
                     163 miles         1 mile

      1.61 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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Unit of Measurement: Length Example (miles to inches)

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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Unit of Measurement: Time Example (seconds to day)

Given. 

   60 seconds per 1 minute
   60 minutes per 1 hour
   24 hours per 1 day

Let'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     60 minutes     24 hours
      ----------  x  ----------  x  --------
       1 minute        1 hour        1 day


      60 * 60 * 24  =  86,400 

   Answer.

      86,400 seconds
      --------------
          1 day

A 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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Unit of Measurement: Money

The first definition for money given by Merriam-Webster 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 (01918-02002) { 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 is one 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.

That's my .02 cents on the subject.

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