MAT082::Lecture Note::Week 10

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Overview

Take a peek at this histogram (bar graph) and this one.
Take a peek at this graph.
What did the zero say to the eight? Answer.
YouTube.com:: Mr. Math does percentages
Some exercises.
Go over... Assessment: Percents #0
Begin units of measurement.

Assignment(s):

Assessment: Week 9 Review

Quote of the Week {Furman.edu:: Mathematical Quotations Server}
The future is something which everyone reaches at the rate
of sixty minutes an hour, whatever he does, whoever he is.
-- C.S. Lewis (01898-01963) {Irish author; more...} [future] [log]
BARS of the Week {NASA.gov:: Astronomy Picture of the Day}
Pueblo CO | Aurora CO | Brush CO [log]

Some Exercises

a) A pecan pie is cut into 5 pieces. Four-fifths of the pie is consumed. Herb eats one-ninth of the remaining pie. How much pie is left after Herb treats himself? b) Write the whole number 4 as a fraction. c) Solve: 4 + (7/8) d) Solve: 4 * (7/8) e) Solve: 4 - (7/8) f) Solve: 4 ÷ (7/8) g) Every unit fraction has ____ for its numerator.

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Let's Peek at MathIsFun.com

MathIsFun.com::Decimals, Fractions and Percentages

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Introduction to Measurements

Merriam-Webster Online [http://w-m.com] defines measurement as follows.
   1 : the act or process of measuring
   2 : a figure, extent, or amount obtained by measuring : DIMENSION
Measurements 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 is 100 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 mile
Exercise: Convert 36 inches to feet. We are given that one foot equals twelve 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. 36 ~~in.~~ * ------ = ------- * ~~36 in.~~ 12 ~~in.~~ ~~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 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~~ ---------- * ---------- * -------- 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

Money
   5 pennies per 1 nickel
   2 nickels per 1 dime
   5 nickels per 1 quarter
   4 quarters per 1 dollar
A penny is one hundreth of a dollar (i.e. $0.01) and a dime is one 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 fahrenheit

Formula: Fahrenheit to Kelvin
K = (°F + 459.67) / 1.8

The 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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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.

GDT::BAB:: Domain Names by the Euro

GDT::BAB:: Scottsdale-based Canadian Company--Isotechnika

GDT::BAB:: U.K. Allocates Funds For Hector [04 April 2006]

~~That's my .02 cents on the subject.~~

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Unit of Measurement: Temperature

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 fahrenheit
Formula: Fahrenheit to Kelvin
   K = (°F + 459.67) / 1.8
The 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 is 136 °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."

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