Unit Conversion of Measurements

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Unit Conversion of Measurements
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Derived Unit

• A derived unit is a combination of the base
  units such as area (_m2_), volume, pressure,
  weight, force, and speed.

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Dimensional Analysis

• Sometimes the unit in which a quantity was
  measured must be converted to a different unit so
  it can be used in mathematical operations.
• Suppose you have half a pizza and you want to
  know how many slices you have. Pizza and slices
  cannot be compared because they are different
  units. To compare them, you need a conversion
  factor. If a pizza has 8 slices, then 1 pizza 8
  slices. This can be rewritten in the following
  ways.

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Dimensional Analysis

• If a pizza has 8 slices, then 1 pizza 8 slices.
  This can be rewritten in the following ways.

• These are conversion factors. Notice that both
  fractions are equal to 1. This means that if you
  multiply them by another value, the value will
  not change.

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Dimensional Analysis

• You can use a conversion factor to convert the
  amount of pizza into the number of slices. There
  are four slices in half a pizza.

• Notice that the conversion factor was chosen so
  that the new unit, slices, appears in the answer
  and the original unit, pizza, cancels.

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Simple Conversions

• How many meters are in 54 cm?

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Determine the possible conversion factors

• The two units in this problem are m and cm. We
  know that 1 m 100 cm. So,

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Decide which conversion factor will give the
desired unit for the answer

• The answer needs to be in m. To get m we need to
  use the conversion factor that has m in the
  numerator and divides by cm (to cancel cm in the
  original value).

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Multiply the original value by the conversion
factor.
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A roll of copper wire contains 15 m of wire.
What is the length of the wire incentimeters?

• possible conversion factors
• 1 m/ 100 cm or 100cm/ 1m
• 2. conversion factor used
• 100 cm / 1m
• 3. multiply original value
• 15 m x 100cm/ 1m 1 500 cm

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Practice Lets convert the following

1. 1. 550 mm ____.550______m
2. 3.5 s ___3500_________ ms
3. 1.6 kg _____1600_______g
4. 2500 mg __.002500_______kg

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Density and Specific Gravity
Would the density of a person by the same on the
surface of the earth and on the surface of the
moon?

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• Density the amount of matter in an object per
  unit volume
• As the temperature of a material increases, the
  density tends to decrease.
• In the lab, the density of an irregularly shaped
  object is found by water displacement

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Density

• D m/v
• m mass (in grams)
• V volume (in cm3, ml or if a gas L)
• D density (g/cm3 , solid,
• g/ml liquid,
• g/L, gas)

• A student finds a shiny piece of metal she thinks
  is aluminum. In the lab, she determines that the
  metal has a volume of 245 cm3 and a mass of 612
  g. Is the metal aluminum?

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Solving the Problem by Density
d 612g/245 cm3 d 2.5 g/cm3

• D m/v

Density of Al 2.70 g/cm3 Density of the metal
2.50g/cm3
m
d
v
NO the metal is not Aluminum
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PROBLEM

• A plastic ball with a volume of 19.7 cm3 has a
  mass of 15.8 g. Would the ball float or sink in
  a container of gasoline? (density of gas
  0.66-0.69g/cm3)
• A piece of iron has a mass of 2.25 g. What is its
  volume?

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Specific Gravity

• Specific gravity a ratio of the density of a
  substance to the density of another substance
  (usually water) at the same temperature
• Density of water at 4ºC 1.0g/cm3
• Gravity density of substance (Specific
  g/cm3)
• density of water
  (g/cm3)

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Specific Gravity

• Specific gravity has no units b/c they cancel
  out
• At 4ºC what can you say about the density of an
  object and its specific gravity?
• Specific gravity is measured using a hydrometer

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Three Temperature Scales

• Fahrenheit
• Celsius
• Kelvin

• Based on the freezing boiling point of alcohol
• Based on the freezing boiling point of water
• Based on absolute zero (temperature at which
  there is no molecular motion

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Temperature Conversions

• K C 273

• C K - 273

Example A gas has a temp. of 90 C. What is
the Kelvin temperature?
Temperature scale Boiling point of water Freezing point of water Absolute zero
Fahrenheit 212 32 - 459
Celsius 100 0 - 273
Kelvin 373 273 0