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Unit Conversion Learning Goals

- The student will be able to use and convert

between different numeric representations of

quantitative data. (A1.12)

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.

Unit Conversionand Fermi Questions

- SPH3U

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.

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.

The SI System

- Physics uses SI (Système international) units, in

which the base units are

The SI System

- Physics uses SI (Système international) units, in

which the base units are - mass

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.

The SI System

- Physics uses SI (Système international) units, in

which the base units are - mass kilogram (kg)
- length

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.

The SI System

- Physics uses SI (Système international) units, in

which the base units are - mass kilogram (kg)
- length metre (m)
- time

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.

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.

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

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)

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

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)

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.

Derived Units

- Other units may be derived from these base units.

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

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)

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).

Prefixes

- A metric prefix may be used to indicate a unit

that is some power of ten larger or smaller than

the SI unit.

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

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

Common Prefixes

- 109

Common Prefixes

- 109 Giga (G)

Common Prefixes

- 109 Giga (G)
- 106

Common Prefixes

- 109 Giga (G)
- 106 Mega (M)

Common Prefixes

- 109 Giga (G)
- 106 Mega (M)
- 103

Common Prefixes

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

Common Prefixes

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

Common Prefixes

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

Common Prefixes

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

Common Prefixes

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

Common Prefixes

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

Common Prefixes

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

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

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)

All the Prefixes

Common Prefixes

- For example,
- 2 ms

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).

Common Prefixes

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

Common Prefixes

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

Common Prefixes

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

Common Prefixes

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

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

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.

Write the following in SI base units

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

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

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

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

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

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

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 ???

Unit Conversions

- Formally, to express a measurement in different

units of the same physical quantity, we multiply

the measurement by 1

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.

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.

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.

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.

Conversion Practice

- Convert 7.2 hours to seconds.

Conversion Practice

- Convert 7.2 hours to seconds.

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.

Multiple Conversion Factors

- Converting some units may require multiplying by

more than one conversion factor.

Multiple Conversion Factors

- Converting some units may require multiplying by

more than one conversion factor. For example,

Multiple Conversion Factors

- Converting some units may require multiplying by

more than one conversion factor. For example,

Multiple Conversion Factors

- Converting some units may require multiplying by

more than one conversion factor. For example,

Multiple Conversion Factors

- Converting some units may require multiplying by

more than one conversion factor. For example,

Multiple Conversion Factors

- Converting some units may require multiplying by

more than one conversion factor. For example,

Non-standard Conversions

- Note that this method of unit conversion works

for non-metric and even non-standard units.

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?

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?

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).

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?

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.

Fermi Questions

- These assumptions may be rewritten as conversion

factors and multiplied to convert units of

people to units of piano tuners

Fermi Questions

- These assumptions may be rewritten as conversion

factors and multiplied to convert units of

people to units of piano tuners

Fermi Questions

- These assumptions may be rewritten as conversion

factors and multiplied to convert units of

people to units of piano tuners

Fermi Questions

- These assumptions may be rewritten as conversion

factors and multiplied to convert units of

people to units of piano tuners

Fermi Questions

- These assumptions may be rewritten as conversion

factors and multiplied to convert units of

people to units of piano tuners

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.

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.

More Practice

- From Homework Set 1
- Unit Conversion and Fermi Questions