The Metric System

• The metric system or SI Units is the world wide standard of measurement.
• This system is mostly based on a set of physical constants.
• The US uses a system called the US customary system
• This is based mostly upon a set of traditional standards.
• In the metric system
  • There is only one base unit for each measurement.
  • Conversion between units is done by multiplying and dividing by 10
• The basic measure of length is a meter
• The basic measure of mass is the gram
• The basic measure of volume is the liter
• The prefixes
  • kilo (k) 1000 x base unit
  • hecto (h) 100 x base unit
  • deca (da) 10 x base unit
  • base unit
  • deci (d) 1/10 x base unit
  • centi (c) 1/100 x base unit
  • milli (m) 1/1000 x base unit.
• There are others
  • micro, nano, pico for smaller,
  • Mega, Giga, Tera, Peta for larger.
  • See page 472
• To change units:
  • Ask, Should the number get smaller or larger?
    • meters to kilometers - lots of meters make up a km, so it should get smaller
    • liters to centiliters - a liter is a lot of cl, so it should get larger.
  • Count the number of lines moved on the table.
  • Move the decimal place to the right or left by that much.
• Example: convert 14 g to cg
  • A g is larger than a cg, so the number should get larger.
  • A cg is two lines below a g, so move the decimal to the right by 2.
  • 14g = 1400 cg
• Example convert 450 dal to kl.
  • a da is smaller than a k, so the number should get smaller
  • a da is two lines below a k, so move the decimal to the left by 2.
  • 450 dal = 4.50 l
• An alternative technique.
  • Find a relationship between the units.
  • 1k = 100 da
  • Use dimensional analysis to solve the problem.
• Example convert 14 g to cg.
  • 1 g = 100 cg

  •          100 cg
    14 g x  -------- = 14 x 100 cg = 1400 cg
              1 g
    	

• Example convert 450 dal to kl.

  1 kl = 100 dal
              1 kl
  450 dal x --------  = 450/100 kl = 4.5 kl
            100 dal
      

• What is dimensional analysis?
  • A problem solving method.
  • A way to derive formulas.
  • With each quantity, carry along a unit fraction
  • As above, multiply by the right unit fraction to eliminte undesired units.