Metric Conversions,
Dimensional Analysis,
and Scientific Notation
International System of Units (SI)
• Built on a set of seven
metric units, called
base units (base units
contain no
prefix…examples are
grams, meter, and
liter)
 Prefixes are added to
the names of SI base
units to represent
quantities that are
larger or smaller than
the base units
(examples are
kilogram, centimeter,
and milliliter)
Official SI Units of Measurement
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Length – meter (m)
Mass – kilogram (kg)
Time – second (s)
Temperature – Kelvin (K)
Amount of substance – mole (mol)
Electric current – ampere (A)
Luminous intensity – candela (cd)
Metric Prefixes and Symbols
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Giga —G 1,000,000,000
Mega —M 1,000,000
Kilo –k 1,000
Hecto –h 100
Deca –da 10
BASE
Deci – d 0.1
Centi – c 0.01
Milli – m 0.001
Micro--µ 0.000001
Nano—n 0.000000001
Bigger than base
King Henry Died
By Drinking
Chocolate Milk
Smaller than base
How would you write…
--Millisecond
--Decagram
--Deciliter
--Gram
--Kilometer
--Centigram
Which is larger?
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1 centimeter or 1 meter?
1 decagram or 1 gram?
1 millimeter or 1 centimeter?
1 kiloliter or 1 liter?
1 decimeter or 1 hectometer?
1 gram or 1 milligram?
1 milliliter or 1 kiloliter?
Hardest part about converting
between units…what are the
equivalences??
• This can be easy though! Use your chart to help you!
100 cm?
• 1 meter = _________
• Start by thinking…which is larger? 1 meter or 1
centimeter?
• Since a meter is larger, we are going to need many
centimeters to equal 1 meter.
• So how many centimeters do we need? Use the prefix
“centi” to help you! “Centi-” means “hundreth” so a
centimeter is a hundreth (1/100) of a meter.
• Therefore it takes 100 centimeters to equal 1 meter.
What are the equivalences??
1000 meters?
• 1 kilometer = _________
• Which is larger? 1 kilometer or 1 meter? 1 kilometer
• Since a kilometer is larger, we are going to need many
meters to equal 1 kilometer.
• So how many meters do we need? Use the prefix
“kilo” to help you! “Kilo-” means “thousand” so a
kilometer is a thousand meters.
• Therefore it takes 1000 meters to equal 1 kilometer.
What are the equivalences??
0.001 gram?
• 1 milligram = _________
• Which is larger? 1 milligram or 1 gram? 1 gram
• Since 1 gram is larger, a milligram will only be a
fraction of the gram.
• What fraction? Use the prefix “milli” to help you!
“Milli-” means “thousandth” so a milligram is a
thousandth (1/1000) of a gram.
• 1/1000 of a gram = 0.001 gram
• Therefore, 1 milligram = 0.001 grams
Practice on your own! Example:
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1000 liters
1 kiloliter = ______
100
1 gram = _______
centigrams
1000 millimeters
1 meter = ______
10
1 decagram = _________
grams
10
1 liter = ________
deciliters
0.001 liters
1 milliliter = _______
0.01 grams
1 centigram = ______
Derived SI units
***Made by combining multiple
single SI units!
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Area – square meter (m2)
Volume – cubic meter (m3)
Density – kg per cubic meter (kg/m3)
Molar mass – kg per mole (kg/mol)
Concentration – moles per liter (M)
Molar volume – cubic meters per mol
(m3/mol)
Scary problem?
• (80) x
(50) x (1) x (40) x (30) x (2)
(40)(30) (20)
(80)
(50)
(1)
= ?
No! Mark out commonalities on the top and
the bottom when all numbers are multiplied!
(80) x
(50) x (1) x (40) x (30) x (2) = 2 = 1
(40)(30) (20)
(80)
(50)
(1) 20 10
Dimensional Analysis
• The technique of converting between units
Uses:
1. Unit equalities – an equation that shows how
different units are related (ex. 1 cm = 0.01 m)
2. Conversion factors – equation that always equals
one (ex. 1cm/0.01m)
*Multiply the conversion factor so that units you
do not want cancel, and the unit that you do
want ends up on top.
Example Problems
• A baker uses 1.5 tsp of vanilla extract in each
cake. How much vanilla is consumed to make
800 cakes? (1 tsp = 5 mL)
Conversion factor: 1.5 tsp or 1 cake
1 cake
1.5 tsp
Use it!
800 cakes x 1.5 tsp = 1200 tsp
1 cake
Answer  1200 tsp
What did we just do? Went from
one unit to another…
• Start with writing down the current unit
• Use as many conversion factors as
necessary to go from the current units
to the desired units
• Make sure the undesired units “cancel
out” (by being located on the top and
bottom) leaving only the desired unit
on the top at the end
Example Problems
• A person drinks eight glasses of water a day.
Each glass contains 300 mL. How many mL
will a person drink in 1 yr?
• Conversion factors: 8 glasses of water or 1 day
Also: 1 glass of water
300 mL
1 day
or
300 mL
1 glass of water
1 year x 365 days x 8 gl. of water
1 year
1 day
Answer  876,000 mL
8 gl. of water
x 300 mL
=
1 gl. of water
Practice on your own!
Example:
• A roll of copper wire contains 15 m of
wire. What is the length of the wire in
centimeters?
– Start by writing down the current units
15 meters
– Use conversion factors to go from current
unit (meters) to desired unit (centimeters)
15 meters x 100 centimeters = 1500 cm
1 meter
Dimensional Analysis
• Convert 18 inches to feet
18 inches x
1 foot = 1.5 foot
12 inches
• Convert 6489 feet to miles
– (Note: 1 mile = 5280 feet)
6489 feet x
1 mile = 1.23 miles
5280 feet
Double it Up!
• Convert 32 miles/hour to feet/second.
32 miles x 1 hour x 1 min x 5280 ft = 46.9 ft/sec
1 hour
60 mins 60 sec
1 mile
Scientific Notation
Steps for converting:
• Insert a decimal into the original number to create a
new number that is between the value of 1 and 10.
Ex. 123,000,000,000  1.23000000000
• To find the exponent, count the number of places
from the decimal to the end of the number.
Ex. In 123,000,000,000 there are 11 places therefore
we write it as 1.23 x 1011
• Numbers less than 1 (decimal numbers) will have
negative exponents
Ex. 0.000001 will be written as 1 x 10-6
Scientific Notation Practice!
Convert the following:
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12,000
456
7,000,000
0.0043
0.09833
30
0.30
8