Unit Conversion: Learning Goals

1
Unit Conversion Learning Goals

• The student will be able to use and convert
  between different numeric representations of
  quantitative data. (A1.12)

2
Unit Conversion Learning Goals

• The student will be able to use and convert
  between different numeric representations of
  quantitative data. (A1.12)
• The student will also be able to use methods of
  unit conversion to make Fermi approximations of
  physical quantities.

3
Unit Conversionand Fermi Questions

• SPH3U

4
Why all the fuss about units?

• Measurements of physical quantities must be
  expressed in terms of units that are defined by
  convention and related to some standard.

5
Why all the fuss about units?

• Measurements of physical quantities must be
  expressed in terms of units that are defined by
  convention and related to some standard.
• For example, the measurement or calculation of a
  length may never be expressed as just 2.5
• units must be given to indicate if the length is
• 2.5 km, 2.5 m, or 2.5 cm.

6
The SI System

• Physics uses SI (Système international) units, in
  which the base units are

7
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass

8
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass kilogram (kg)
• Historically the mass of 1 litre of water,
• now defined as the mass of the
• International Prototype Kilogram,
• a chunk of platinum-iridium alloy
• stored in a vault in Paris.

9
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass kilogram (kg)
• length

10
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass kilogram (kg)
• length metre (m)
• Historically 1/10,000,000 of the distance from
  the Earths equator to the North Pole, now
  defined as the length of the path travelled by
  light in vacuum during a time interval of 1/299
  792 458 of a second.

11
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass kilogram (kg)
• length metre (m)
• time

12
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass kilogram (kg)
• length metre (m)
• time second (s)
• Historically 1/(24  60  60) of the day, now
  defined as the duration of 9 192 631 770 periods
  of the radiation corresponding to the transition
  between the two hyperfine levels of the ground
  state of the caesium 133 atom.

13
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass kilogram (kg)
• length metre (m)
• time second (s)
• Minutes and hours are also acceptable units use
  whichever time interval is appropriate to the
  situation being studied.

14
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass kilogram (kg)
• length metre (m)
• time second (s)
• electric current

15
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass kilogram (kg)
• length metre (m)
• time second (s)
• electric current ampere (A)

16
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass kilogram (kg)
• length metre (m)
• time second (s)
• electric current ampere (A)
• temperature

17
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass kilogram (kg)
• length metre (m)
• time second (s)
• electric current ampere (A)
• temperature kelvin (K)

18
The SI System

• Physics uses SI (Système international) units, in
  which the base units are
• mass kilogram (kg)
• length metre (m)
• time second (s)
• electric current ampere (A)
• temperature kelvin (K)
• However, since 1 degree K 1 degree C (the
  scales just have different zero points), we will
  also be using Celsius.

19
Derived Units

• Other units may be derived from these base units.

20
Derived Units

• Other units may be derived from these base units.
• For example,
• acceleration may be expressed in units of m/s/s
  (metres per second per second) or m/s2

21
Derived Units

• Other units may be derived from these base units.
• For example,
• acceleration may be expressed in units of m/s/s
  (metres per second per second) or m/s2
• force may be expressed in units of kg m/s2, also
  known as Newtons (N)

22
Derived Units

• Other units may be derived from these base units.
• For example,
• acceleration may be expressed in units of m/s/s
  (metres per second per second) or m/s2
• force may be expressed in units of kg m/s2, also
  known as Newtons (N) and
• energy may be expressed in units of kg m2/s2,
  also known as Joules (J).

23
Prefixes

• A metric prefix may be used to indicate a unit
  that is some power of ten larger or smaller than
  the SI unit.

24
Prefixes

• A metric prefix may be used to indicate a unit
  that is some power of ten larger or smaller than
  the SI unit.
• For example,
• 1 km

25
Prefixes

• A metric prefix may be used to indicate a unit
  that is some power of ten larger or smaller than
  the SI unit.
• For example,
• 1 km 1000 m or 1 103 m

26
Common Prefixes

• 109

27
Common Prefixes

• 109 Giga (G)

28
Common Prefixes

• 109 Giga (G)
• 106

29
Common Prefixes

• 109 Giga (G)
• 106 Mega (M)

30
Common Prefixes

• 109 Giga (G)
• 106 Mega (M)
• 103

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Common Prefixes

• 109 Giga (G)
• 106 Mega (M)
• 103 kilo (k)

32
Common Prefixes

• 109 Giga (G)
• 106 Mega (M)
• 103 kilo (k)
• 10-2

33
Common Prefixes

• 109 Giga (G)
• 106 Mega (M)
• 103 kilo (k)
• 10-2 centi (c)

34
Common Prefixes

• 109 Giga (G)
• 106 Mega (M)
• 103 kilo (k)
• 10-2 centi (c)
• 10-3

35
Common Prefixes

• 109 Giga (G)
• 106 Mega (M)
• 103 kilo (k)
• 10-2 centi (c)
• 10-3 milli (m)

36
Common Prefixes

• 109 Giga (G)
• 106 Mega (M)
• 103 kilo (k)
• 10-2 centi (c)
• 10-3 milli (m)
• 10-6

37
Common Prefixes

• 109 Giga (G)
• 106 Mega (M)
• 103 kilo (k)
• 10-2 centi (c)
• 10-3 milli (m)
• 10-6 micro (m)

38
Common Prefixes

• 109 Giga (G)
• 106 Mega (M)
• 103 kilo (k)
• 10-2 centi (c)
• 10-3 milli (m)
• 10-6 micro (m)
• 10-9

39
Common Prefixes

• 109 Giga (G)
• 106 Mega (M)
• 103 kilo (k)
• 10-2 centi (c)
• 10-3 milli (m)
• 10-6 micro (m)
• 10-9 nano (n)

40
All the Prefixes
41
Common Prefixes

• For example,
• 2 ms

42
Common Prefixes

• For example,
• 2 ms 2 10-6 s
• Know how to enter this number in your calculator
• (usually as either 2 EXP -6
• or 2 EE -6
• or 2 10x -6).

43
Common Prefixes

• For example,
• 2 ms 2 10-6 s
• 2 ns

44
Common Prefixes

• For example,
• 2 ms 2 10-6 s
• 2 ns 2 10-9 s

45
Common Prefixes

• For example,
• 2 ms 2 10-6 s
• 2 ns 2 10-9 s
• 20 ns

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Common Prefixes

• For example,
• 2 ms 2 10-6 s
• 2 ns 2 10-9 s
• 20 ns 20 10-9 s

47
Common Prefixes

• For example,
• 2 ms 2 10-6 s
• 2 ns 2 10-9 s
• 20 ns 20 10-9 s or 2 10-8 s

48
Common Prefixes

• For example,
• 2 ms 2 10-6 s
• 2 ns 2 10-9 s
• 20 ns 20 10-9 s or 2 10-8 s
• Calculators will accept either 20 x 10-9 s or 2 x
  10-8 s.

49
Write the following in SI base units

• 4.3 Mm
• 35 cm
• 7 mA
• 0.5 mA
• 300 ns
• 450 g

50
Write the following in SI base units

• 4.3 Mm 4.3 106 m
• 35 cm
• 7 mA
• 0.5 mA
• 300 ns
• 450 g

51
Write the following in SI base units

• 4.3 Mm 4.3 106 m
• 35 cm 35 10-2 m or 3.5 10-1 m or 0.35 m
• 7 mA
• 0.5 mA
• 300 ns
• 450 g

52
Write the following in SI base units

• 4.3 Mm 4.3 106 m
• 35 cm 35 10-2 m or 3.5 10-1 m or 0.35 m
• 7 mA 7 10-6 A
• 0.5 mA
• 300 ns
• 450 g

53
Write the following in SI base units

• 4.3 Mm 4.3 106 m
• 35 cm 35 10-2 m or 3.5 10-1 m or 0.35 m
• 7 mA 7 10-6 A
• 0.5 mA 0.5 10-3 A or 5 10-4 A
• 300 ns
• 450 g

54
Write the following in SI base units

• 4.3 Mm 4.3 106 m
• 35 cm 35 10-2 m or 3.5 10-1 m or 0.35 m
• 7 mA 7 10-6 A
• 0.5 mA 0.5 10-3 A or 5 10-4 A
• 300 ns 300 10-9 s or 3 10-7 s
• 450 g

55
Write the following in SI base units

• 4.3 Mm 4.3 106 m
• 35 cm 35 10-2 m or 3.5 10-1 m or 0.35 m
• 7 mA 7 10-6 A
• 0.5 mA 0.5 10-3 A or 5 10-4 A
• 300 ns 300 10-9 s or 3 10-7 s
• 450 g ???

56
Unit Conversions

• Formally, to express a measurement in different
  units of the same physical quantity, we multiply
  the measurement by 1

57
Unit Conversions

• Formally, to express a measurement in different
  units of the same physical quantity, we multiply
  the measurement by 1 or rather, a conversion
  factor that is equal to 1.

58
Unit Conversions

• Formally, to express a measurement in different
  units of the same physical quantity, we multiply
  the measurement by 1 or rather, a conversion
  factor that is equal to 1.
• If the unit we want to cancel out is in the
  numerator of the measurement, it goes in the
  denominator of the factor. The unit we want to
  get goes in the numerator.

59
Unit Conversions

• If the unit we want to cancel out is in the
  numerator of the measurement, it goes in the
  denominator of the factor. The unit we want to
  get goes in the numerator.

60
Unit Conversions

• If the unit we want to cancel out is in the
  numerator of the measurement, it goes in the
  denominator of the factor. The unit we want to
  get goes in the numerator.

61
Conversion Practice

• Convert 7.2 hours to seconds.

62
Conversion Practice

• Convert 7.2 hours to seconds.

63
Conversion Practice

• Convert 7.2 hours to seconds.
• Dont round this 25920 s to significant digits if
  youre going to use it in a calculation.

64
Multiple Conversion Factors

• Converting some units may require multiplying by
  more than one conversion factor.

65
Multiple Conversion Factors

• Converting some units may require multiplying by
  more than one conversion factor. For example,

66
Multiple Conversion Factors

• Converting some units may require multiplying by
  more than one conversion factor. For example,

67
Multiple Conversion Factors

• Converting some units may require multiplying by
  more than one conversion factor. For example,

68
Multiple Conversion Factors

• Converting some units may require multiplying by
  more than one conversion factor. For example,

69
Multiple Conversion Factors

• Converting some units may require multiplying by
  more than one conversion factor. For example,

70
Non-standard Conversions

• Note that this method of unit conversion works
  for non-metric and even non-standard units.

71
Non-standard Conversions

• Note that this method of unit conversion works
  for non-metric and even non-standard units.
• Example Ms. Rosebery is 167 cm tall. A marathon
  is 42 195 m. How many Ms. Roseberys are there in
  a marathon?

72
Non-standard Conversions

• Example Ms. Rosebery is 167 cm tall. A marathon
  is 42 195 m. How many Ms. Roseberys are there in
  a marathon?

73
Fermi Questions

• Fermi questions are estimation problems, named
  after the physicist Enrico Fermi, who was famous
  for making very good approximate calculations
  given very little data (including an estimate of
  the strength of the atomic bomb detonated in the
  Trinity test based on the distance travelled by
  pieces of paper dropped from his hand during the
  blast).

74
Fermi Questions

• The questions are designed to teach dimensional
  analysis (i.e., unit conversion) and the
  importance of clearly identifying one's
  assumptions.
• One famous question, attributed to Enrico Fermi
  himself, is How many piano tuners are there
  working in Chicago?

75
Fermi Questions

• A typical solution to this problem might include
  the following assumptions
• There are approximately 5,000,000 people living
  in Chicago.
• On average, there are two persons in each
  household in Chicago.
• Roughly one household in twenty has a piano that
  is tuned regularly.
• Pianos that are tuned regularly are tuned on
  average about once per year.
• It takes a piano tuner about two hours to tune a
  piano, including travel time.
• Each piano tuner works eight hours in a day, five
  days in a week, and 50 weeks in a year.

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Fermi Questions

• These assumptions may be rewritten as conversion
  factors and multiplied to convert units of
  people to units of piano tuners

77
Fermi Questions

• These assumptions may be rewritten as conversion
  factors and multiplied to convert units of
  people to units of piano tuners

78
Fermi Questions

• These assumptions may be rewritten as conversion
  factors and multiplied to convert units of
  people to units of piano tuners

79
Fermi Questions

• These assumptions may be rewritten as conversion
  factors and multiplied to convert units of
  people to units of piano tuners

80
Fermi Questions

• These assumptions may be rewritten as conversion
  factors and multiplied to convert units of
  people to units of piano tuners

81
Fermi Questions

• These assumptions may be rewritten as conversion
  factors and multiplied to convert units of
  people to units of piano tuners
• or, to 1 significant digit, 100 piano tuners.

82
Fermi Questions

• Scientists and engineers often calculate Fermi
  estimates of the answer to a problem before
  turning to more sophisticated methods to
  calculate a precise answer. This provides a
  useful check on the results where the complexity
  of a precise calculation might obscure a large
  error, the simplicity of Fermi calculations makes
  them far less susceptible to such mistakes.

83
More Practice

• From Homework Set 1
• Unit Conversion and Fermi Questions