Measurement, Length and the Metric System

Discussion

• What does it mean to measure something?
• Assign a number to its size
• When we do this from one side to another, the measure is called length
• Since we are measuring along a line, these are refered to as linear measurements and we use linear units to perform these measurements.
• The English System (or U. S. Customary) is used in the US, Yemen Brunei, and a few small islands.
  • inches, feet, yards, miles
  • but also: rods, leagues, fathoms, cubits, chains, furlongs, ...
  • We are accustom to this system, but it is icreadbly hard to use.
  • There are no natural common standards upon which this is based.
  • These were probably based on body parts, inch = width of thumb, foot = length of a foot. Mile is 1000 paces of a Roman legion.
  • Take a look at the picture on page 461
  • Conversion is tricky
    • 12 inches = 1 foot
    • 3 feet = 1 yard
    • 11760 yards = 1 mile
    • 5280 feet = 1 mile
  • The only way to keep this straight is dimensional analysis.
  • Example

    In Jules Verne's classic, 20,000 leagues under the sea, 
    the narrator states that "I have crossed 20,000 leaguesin 
    that submarine tour of the world," 
    how far did he travel?
    
    We are probably more comfortable expressing this measurement in miles.
    
    1 league = 3.452 miles
                      3.452 miles
    20,000 leagues x ----------- = 20,000 x 3.452 miles = 69,047 miles
                      1 league
    
    	

  • The big problem here is that we have to memorize
    • The names of all of the units.
    • The conversion factors between all units.
    • And this changes for other types of measurement volume, area, weight, ...
• Length in the Metric System
  • The basic unit for measuring length in the metric system is the meter
  • This was originaly defined as 1/100,000,000 of the distance from the north pole to the equator on a line through Paris France.
  • A meter is a little more than a yard.
  • 1 yard = .9 meter (m)
  • The nice part about the metric system is conversion to smaller/larger units is easy.
  • Everything is base 10.
  • A kilometer is equal to 1,000 meters
  • A hectometer is equal to 100 meters
  • A dekameter is equal to 10 meters
  • A meter is equal to one meter.
  • A decimeter is equal to .1 meters (or 10 decimeters = 1 meter)
  • A centimeter is equal to .01 meters (or 100 centimeters = 1 meter)
  • A milimeter is equal to .001 meters (or 1000 milimeters = 1 meter)
  • Memorize the table 9.1 on page 463.
  • To change units,
    • start at the lower unit, and move up.
    • Count the number of steps, this is the number of zeros
    • Use dimensional analysis to convert.
  • Example, convert 2.3 milimeters to hectometers.

    
    hectometers
    dekameter
    meter
    decimeter
    centimeter
    milimeter
    
            you go up five times, so the conversion factor has 5 zeros
    	10000 milimeters = 1 hectometer
    
                               1 hectometer
    	2.3 milimeters x ---------------- = 2.3/100000  hectometers
    	                 100000 milimeters
    
    			 = .00023 hectometers
    	

  • Example convert .35 kilometers to dekameters

    
    kilometers
    hectometers
    dekameter
          You go up two times, so the conversion factor has 2 zeros 
          100 dekameters = 1 kilometer.
    
                            100 dekameters
          .35 kilometers x ----------------  = 100x .35 dekameters
                             1 kilometer
    
    			 = 35 dekameters
        

• Example:

  #30, page 470
  
  convert 26 cm to in
  They give us that 1 in = 2.54 cm
  
            1 in
  26 cm x -------  = 26/2.54 cm = 10.23 cm
          2.54 cm
      

• Example :

  #40  180in to hm
     We know that 1 in = 2.54 cm
  
  hectometers
  dekameter
  meter
  decimeter
  centimeter
  
     10000 cm = 1 hm
  
           2.54 cm     1 hm
  180in x---------- x---------- = 180x2.5/10000 hm = 72/10000 = .0072 hm
           1 in       10000 cm
      

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