Metric System
Basic Skills
Systéme International
• The metric system is an international decimalized system
of measurement created in France in 1791 during the
French Revolution.
• Since the 1960s the International System of Units
("Système International d'Unités" in French) has been the
internationally recognized standard metric system.
• This system is commonly called the “SI” system. The “SI”
or metric system is widely used around the world for
personal, commercial, and scientific purposes.
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Systéme International
Name
Symbol
Quantity
meter
m
length
kilogram
kg
mass
second
s
time
Ampere
A
electric current
Kelvin
K
thermodynamic temperature
candela
cd
luminous intensity
mole
mol
amount of substance
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Length, Mass, Time
• Length (m): defined as the distance traveled by light in a
vacuum during a tiny fraction of time.
• Mass (kg): defined by an “International Prototype Kilogram”
made of a platinum-iridium alloy and stored in a vault in
Sèvres, France.
• Time (s): 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 cesium 133 atom.”
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Standard Prefixes for SI Units
Prefix
Symbol
Factor
Factor as Exponent
peta
tera
giga
mega
kilo
hecto
deca
P
T
G
M
k
h
da
1 000 000 000 000 000
1 000 000 000 000
1 000 000 000
1 000 000
1 000
100
10
= 10 15
= 10 12
= 10 9
= 10 6
= 10 3
= 10 2
= 10 1
deci
centi
milli
micro
nano
pico
femto
d
c
m
µ
n
p
f
0.1
0.01
0.001
0.000 001
0.000 000 001
0.000 000 000 001
0.000 000 000 000 001
= 10 -1
= 10 -2
= 10 -3
= 10 -6
= 10 -9
= 10 -12
= 10 -15
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Prefix: kilo
• “kilo” represents a factor of 1000. So a kilometer is 1000 meters, a
kilogram is 1000 grams, &etc.
• Use kilometers to measure longer distances. 1 kilometer is 0.621
miles. Have you every run a 10K race? How far is a 5K run?
• When we do problems, we will generally want to convert
distances/lengths into meters.
• To convert kilometers to meters – multiply by 1000 (or move the
decimal 3 places to the right).
• To convert meters to kilometers – divide by 1000 (or move the
decimal 3 places to the left).
• Think: in any given distance, there are more meters than there are
kilometers (just like there would be more inches than feet!)
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Prefix: kilo (practice)
• Convert into meters:
o 4 kilometers
o 3.5 km
o 0.45 km
4,000 meters
= ______________
3,500 meters
= ______________
= ______________
450 meters
• Convert into kilometers:
o 1200 meters
o 11,000 m
o 750 m
1.2 kilometers
= ______________
11 kilometers
= ______________
0.75 kilometers
= ______________
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Prefix: milli
• “milli” represents a factor of 1/1000th. So a millimeter is 1/1000th
of a meter, a millisecond is 1/1000th of a second, &etc.
• Use millimeters to measure small lengths. 1 millimeter is about the
thickness of your finger nail
• When we do problems, we will generally want to convert
distances/lengths into meters.
• To convert millimeters to meters – divide by 1000 (or move the
decimal 3 places to the left).
• To convert meters to millimeters – multiply by 1000 (or move the
decimal 3 places to the right).
• Think: in any given length, there are more millimeters than there
are meters (just like there would be more inches than feet!)
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Prefix: milli (practice)
• Convert into meters:
o 5 millimeters
o 340 mm
o 16.5 mm
0.005 meters
= ______________
0.340 meters
= ______________
= ______________
0.0165 meters
• Convert into millimeters:
o 1.0 meters
o 0.88 m
o 0.003 m
1000 millimeters
= ______________
880 millimeters
= ______________
3 millimeters
= ______________
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Prefix: centi
• “centi” represents a factor of 1/100th. So a centimeter is 1/100th of
a meter, a centigram is 1/100th of a gram, &etc.
• Use centimeters to measure small lengths. 1 centimeter is about
the width of your finger nail. 1 inch = 2.54 centimeters.
• When we do problems, we will generally want to convert
distances/lengths into meters.
• To convert centimeters to meters – divide by 100 (or move the
decimal 2 places to the left).
• To convert meters to centimeters – multiply by 100 (or move the
decimal 2 places to the right).
• Think: how many cents are there is a dollar? How many
centimeters is a meter? How do you write 25 cents as a dollar
amount? Isn’t it $0.25? It’s the same for centimeters!
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Prefix: centi (practice)
• Convert into meters:
0.25 meters
o 25 centimeters = ______________
1.65 meters
o 165 cm
= ______________
o 1.5 cm
= ______________
0.015 meters
• Convert into centimeters:
o 1.0 meters
o 0.78 m
o 0.06 m
100 centimeters
= ______________
78 centimeters
= ______________
6 centimeters
= ______________
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Converting Centimeters & Millimeters
• 10 millimeters = 1 centimeter
• A meter stick has 100 centimeter marks, and 1000
little tick marks for millimeters.
• Think: since a millimeter is smaller than a centimeter,
there will be more millimeters in any given length
than there are centimeters!
• How long is the paper clip?
About 2.1 centimeters, but
21 millimeters!
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Centimeter and Inch Rulers
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Area & Volume
• Area is a two dimensional
concept (length x length).
In the metric system, area is
measured in m2 (square
meters)
What is the length of the longest
side, surface area of the top, and the
volume?
• Volume is a three
dimensional concept (length
x length x length). In the
metric system, volume is
measured in m3 (cubic
meters).
• We also use liters in the
metric system. 1 m3 = 1000
liters!
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