# SI Units, Metric Conversions, Dimensional Analysis

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```					              Drill – 9/23
1. How many seconds are in 9.7 hours?

2. How did you figure out that answer?
SI Units, Metric Conversions,
& Dimensional Analysis
• A major theme of science
is communication and
collaboration. We need a
single measurement
system for everyone.
• Le Systeme International
d’Unites - SI
SI UNITS
Quantity         Unit Name   Abbreviation
Length            Meter          m
Mass             Kilogram       kg
Time            Second          s
Temperature           Kelvin         K
Amount of           Mole          mol
substance
Electric current      Ampere         A

Luminous intensity    Candela         cd
• We use SI prefixes to represent quantities
that are larger or smaller than the base
units.
Prefix   Abbreviation   Conversion
giga     G              1 Gm = 109 m
mega     M              1 Mm = 106 m
kilo     k              1 km = 1000 m
hecto    h              1 hm = 100 m
deca     da             1 dam = 10 m
1 meter (1 m)
deci     d              1 m = 10 dm
centi    c              1 m = 100 cm
milli    m              1 m = 1000 mm
micro    μ              1 m = 106 μm
nano     n              1 m = 109 nm
Dimensional Analysis
• Dimensional Analysis is a method used to
make conversions. This method helps us
organize information without becoming
confused about what units are being
cancelled or multiplied/divided.
Rules
1. You must use Dimensional Analysis to
solve conversion problems
2. Always show all your work
3. Include units
4. Make sure your units cancel out
5. Everything on the top is multiplied
Everything on bottom is divided from the top
Conversion Factors
• A ratio (or fraction) derived from the
equality between two different units that
can be used to convert from one unit to
the other.
• Conversion factors always equal one
because the two values are equal to each
other.
Conversion Factors
4 quarters         1 dollar
=1                =1
1 dollar           4 quarters

60 minutes         1 hour
=1                =1
1 hour             60 minutes

1m                 100 cm
=1                =1
100 cm             1m
Convert 62.0 inches to centimeters

• First we need to map out what we are
doing.
62.0 in  ___ cm
Convert 62.0 inches to centimeters
• Second we need to determine our
conversion factor

How many centimeters are in one inch?
2.54 cm = 1 in

1 in              2.54 cm            Note: We could have also
=1                =1       used that 1cm = .394 inch
2.54 cm           1 in               but as a general rule, the
larger unit gets the 1!
Convert 62.0 inches to centimeters

• Third, we multiply our given by the
conversion factor…making sure to arrange
the conversion factor so that the units
CANCEL!

62.0 in X 2.54 cm
= 157.48 cm
1 in

Note: Units that are both on the top and the
bottom cancel
Convert 62.0 inches to centimeters

• Lastly, we make sure that we reached our
“destination” and that we have the correct
number of significant figures.

157.48 cm  157 cm

Note: Conversions factors do not follow
significant figure rules, they are not
measured and do not show accuracy.
Multiple Conversions
• When conversions require several steps,
Dimensional Analysis is extremely useful.
It helps organize information so we can
think through problems step-by-step.
How many feet are in 965 cm?
• 1. Map it out: 965 cm  ___ ft
• 2. Find conversion factors:
How many feet are in 965 cm?

965 cm        1 in         1 ft
X             X           = 31.66  31.7 ft
2.54 cm       12 in
You are cooking for a large group of
people. You must change the recipe to
accommodate all the guests. How many
gallons will 384 teaspoons of vanilla
extract occupy?
– 1 Tablespoon (T) = 3 teaspoons (t)
– 1 cup (c) = 16 Tablespoons
– 1 pint (pt) = 2 cups
– 1 quart (qt) = 2 pints
– 1 gallon (gal) = 4 quarts

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