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Measurement&Conversions

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  • 1. We need a reliable system of measurement to obtain useful data.
  • 2. Before standardized units:
    • Measurement used to be subjective
      • One “foot” really was the length of a human foot. Obviously, foot size varies.
    • In order to have consistency, there is a need for a standardized system of units.
      • One foot should be the same length for every person.
  • 3. International System (S.I.) of Units:
    • Developed in the late 1700s
    • You may recognize as the “Metric” system.
    • Our “English” system was eventually standardized also, but the S.I. system is used by most countries and the international scientific community.
      • We will use the S.I. system in class.
      • Based on 10– What is English system based on?
  • 4. S.I. Base Units:
    • Base units can be measured directly. Units for other measurements are calculated from base units.
    • * One meter is equal to approximately 3 feet, 3 inches.
    s second time K, °C Kelvin, deg. Celsius temperature g gram mass m meter length S.I. Abbrev. S.I. Unit Measurement
  • 5. Prefixes
    • kilo- (k), 1000 times
    • centi- (c), 1/100 th (There are 100 cents in one dollar.)
    • milli- (m), 1/1000 th
    • Example:
    • 1 km = 1000 meters
    • 1 cm = 0.01 meter (100 cm = 1 m)
    • 1 mm = 0.001 meter (1000 mm = 1 m)
  • 6. What does this mean?
    • 1 kilometer (km) is approximately 0.6 miles
    • 1 meter (m) is approximately the length from your fingertips to your opposite shoulder
    • 1 centimeter (cm) is approximately the width of the tip of your pinky
      • 2.54 cm = 1 inch
    • 1 millimeter (mm) is approximately the width of a paperclip wire
  • 7.
    • Is this a ridiculous speed limit sign?
    • What does it mean?
    • 120 km/h = 75 mi/h
  • 8. How do they fit together?
    • 10 mm = 1 cm
    • 100 cm = 1 m
    • 1000 m = 1 km
  • 9. Converting units:
    • Convert 1 km to centimeters.
      • Known: 1 km = 1000 m, 1 m = 100 cm
      • Therefore, 1000 m = 1 and 100 cm = 1
      • 1 km 1 m
      • 1 km x 1000 m x 100 cm = 100,000 cm
      • 1 km 1 m
      • 1 km 1000 m 100 cm = 100,000 cm
      • 1 km 1 m
  • 10.
    • Mass is a measure of the amount of matter (stuff) that something is made of.
    Would you expect an elephant or a mouse to have a greater mass? An elephant is made of a greater amount of stuff and, therefore, has a greater mass. In this class we will measure mass in grams or kilograms . The mass of a penny is about 2 ½ to 3 grams. The mass of your teacher is about 50,000 grams (50 kg). The mass of an elephant is about 5,000,000 grams (5,000 kg).
  • 11. Are mass and weight the same? We will compare mass and weight later. However, we measure mass with the same equipment we use to measure weight– a scale or “beam balance”. VB-302-3000 Electronic Precision Balance Scale [Online]. Flex Weigh Direct 2006-07. http://www.flexweighdirect.com/vb3023000/ The mass of this object is 2000 grams.
  • 12. S.I. Derived Units
    • Derived units are combinations of base units.
    • Measurements of size:
      • Length is a 1-dimensional
      • size measured in
      • meters (m)  base unit.
      • Area is a 2-dimensional size
      • measured in
      • square meters (m 2 ).
      • Volume is a 3-dimensional
      • size measured in
      • cubic meters (m 3 ).
      • Area and volume are
      • given in derived units.
    3 m 3 m 3 m 3 m 3 m 3 m The length of this line = 3 m. The area of this square = 3 m x 3 m = 9 m 2 . The volume of this cube = 3 m x 3 m x 3m = 27 m 3 .
  • 13.
    • What is the area of a sheet of computer paper?
    •  Area is a 2-dimensional measurement.
    •  Area = length x width
    •  Area = 0.22 m x 0.28 m
    •  Area = 0.062 m 2
    • Square meters are a
    • combination of meters
    • (meters x meters) 
    • derived unit.
    0.22 m 0.28 m
  • 14.
    • Volume is a measure of the amount of space something occupies or contains.
    • Imagine a pool ball and a tennis ball.
    • Compare the mass and volume of the two objects.
    • The two objects occupy approximately the same amount of space and so have approximately equal volumes.
    • The pool ball has a much greater mass than the tennis ball, as you can tell when you pick up the two objects.
    • Compare the mass and volume of a basketball and a bowling ball.
  • 15. We use volume measurements everyday. Example: The gas tank in my car contains 15 gallons of gasoline (when it is full). Example: A bread recipe calls for 2 cups of water and 3 tablespoons of oil. In science class, the unit we will use to measure the volumes of liquids is the liter (L) . Think of the amount of space occupied by a 1-liter or 2-liter bottle of soda.
  • 16. The equipment we will use to measure liquid volume in class will be the beaker and the graduated cylinder . Beakers are generally used to measure larger volumes. They do not have many markings. 250 ml Bomex Glass Beaker [Online]. Research Laboratory Supply, Inc. 2008. Researchsupply.net Graduated Cylinder, Glass, 50 ml [Online]. Science Stuff, Inc. 2008. Sciencestuff.com. Graduated cylinders get their name from many small markings (similar to a ruler) that are used to take a wide variety of large and small measurements.
  • 17.
    • What volume of water does an Olympic-sized swimming pool contain?
    •  Volume is a 3-dimensional measurement.
    •  Volume = length x width x height (depth).
    •  Since area = length x width,
    • then volume = area x height.
    width = 25 m length = 50 m depth = 2 m Volume = l x w x d Volume = 50 m x 25 m x 2 m Volume = 2500 m 3
  • 18. 25 m 2 m 50 m Volume = 2 m x 25 m x 50 m Volume = 2500 m 3 This volume is equivalent to 2500 cubes of 1 m 3 (1 m x 1 m x 1 m)
  • 19.
    • So is volume measured in cubic meters (m 3 ) or in liters (L)?
      • Solids measured in m 3 only.
      • Liquids and gases measured in m 3 or L.
    • What is the connection?
      • 1 cm 3 = 1 mL for liquids and gases
      •  This is the conversion factor , which allows us to convert a measurement from one type of units to another.