# Dimensional Analysis

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```					Dimensional Analysis

Conversions of Units
UNITS
• The world-wide scientific community uses
the metric system to make measurements.

• SI units: System International d’Unites

• SI units are related by powers of 10
(making it easy to convert between)
Fundamental Units
• Time: seconds (s)
• Length: metres (m)
• Mass: kilograms (kg)

• Other quantities can be described using
these three units. Derived units are
combinations of fundamental units.
• i.e. Speed: m/s
Definitions
• Note: You are NOT responsible for these
definitions! They are just for knowledge
sake!

• Distance (m): “The metre is the length of
the path travelled by light in a vacuum
during a time interval of 1/299 792 458 of
a second.”
Definitions
• Note: You are NOT responsible for these
definitions! They are just for knowledge
sake!

• Mass (kg): “The kilogram is equal to the
mass of the international prototype of the
kilogram.”
Definitions
• Note: You are NOT responsible for these
definitions! They are just for knowledge
sake!

• Time (s): “The second is 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 cesium 133 atom.”
Why do we need to convert units?
• They are EXACT so we can compare
worldwide (even the USA).
• They are used by the scientific community
and have been used since 1960.
Dimensional Analysis

•       Identify the given or known data
(information).
•       Identify the unknown.
•       Plan the solution or calculations by either:
–     setting up a series of conversion factors OR
–     using a formula
•       Check your work by cancelling out units.
Example 1: Conversion within
Fundamental SI units

• A space shuttle orbits the Earth at an
altitude of 300 000 m. What is its altitude
in:
• A) mm
• B) km
Example 2: Conversions between
SI units and non-SI units

• Calculate the number of cm in 20 inches if
you know that 1 inch = 2.54 cm.
Example 3: Multiple step
conversions
• A person on a diet might lose 2.3 kg per
week. Express the mass loss rate in mg
per second.
Questions for you…

•   How many seconds are in 1 year? (note:
1 year is 365.25 days …)

•   Both the 100 yard and the 100m dash
are used in track events. Which is longer
and by how much? (note: 1 yd = 0.9144
m)

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