The Metric System
Units, Definitions and History
History
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The disparate measurement system was one of the
most frequent causes of disputes amongst
merchants and between citizens and tax collectors
across Europe.
Leaders of the French revolutionary governments
decided a new system was need.
1791: first official adoption of a universal measuring
system.
1799: final proclamation of metric system placed in
the Archives of the Republic.
Today, 95% of the world’s population live in
metricated countiries.
SI Units
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Seven base units in SI
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Time (second)
Length (meter)
Mass (kilogram)
Temperature (Kelvin)
Amount of a substance (mol)
Electric current (ampere)
Luminous intensity (candela)
SI Units Cont.
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Derived units in SI
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Volume: derived unit is the cubic
meter (m3); cubic centimeter is more
commonly used (cm3). For liquids, the
liter is used; 1 L = 1 dm3.
Density: ratio that compares the mass
of an object to its volume. The units
for density are often expressed as
g/cm3
Prefixes Used with SI Units
Prefix
Symbol
Factor
S.N.
Example
giga
G
1 000 000 000
109
Gigameter (Gm)
mega
M
1 000 000
106
Megagram (Mg)
kilo
k
1 000
103
Kilometer (km)
deci
d
1/10
10-1
Deciliter (dL)
centi
c
1/100
10-2
Centimeter (cm)
milli
m
1/1000
10-3
Milligram (mg)
micro
µ
1/1 000 000
10-6
Microgram (µg)
nano
n
1/1 000 000 000
10-9
Nanometer (nm)
pico
p
1/1 000 000 000 000
10-12
Picometer (pm)
Dimensional Analysis
A technique for converting from
one unit to another
Conversions WITHIN the Metric
System
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You can simply move the decimal
point...
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But you have to know how to move it!!
Metric Unit Conversions
Metric Unit Conversions
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Use this to remember the metric
prefixes:
“King Henry Died By Drinking
Chocolate Milk

The first letters represent the prefixes
(kilo, hecto, deca, base, deci, centi,
milli)
Example
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It is common for runners to do a
“10K” run. This means they are
running 10 kilometers. How many
millimeters is that?
A lot!!!
Answer
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Look at the staircase graphic...
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Start on the prefix “kilo”
Move down the staircase 6 steps (don't
count the step you start on) to get to
the prefix “milli”
This means you move the decimal point
6 places to the RIGHT
10 km is converted to 10,000,000 mm
Beyond the Metric System
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If you need to convert to or from
units that are NOT metric units, we
use a unit conversion technique
called... “dimensional analysis”
D.A.
Conversion Factors
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In dimensional analysis, we make
conversion factors into fractions that
we will multiply by.
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For example, one conversion factor is:
1 inch = 2.54 cm
We can make two fractions out of this...
1 inch
2.54 cm
OR
2.54 cm
1 inch
Example
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A pencil is 17.8 cm long, what is its
length in inches?
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Start with the “given”:
17.8 cm
Multiply by the “conversion factor”
17.8 cm
x 1 inch
2.54 cm
=
Example
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A pencil is 17.8 cm long, what is its
length in inches?
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Cross cancel “like” units:
17.8 cm
x 1 inch
2.54 cm
=
Example
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A pencil is 17.8 cm long, what is its
length in inches?
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Do the math using the correct number of
significant figures (based on given
information)
17.8 cm x
1 inch
2.54 cm
=
7.01 in.
Which number goes on top and
bottom in the conversion factor?
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Usually...
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The unit you WANT goes on TOP
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The unit you want to CANCEL goes on
BOTTOM
Example
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A pencil is 8.1 inches, how many cm
is it?
8.1 inches x 2.54 cm = 21 cm
1 inch
The unit we WANT is cm so we put 2.54
cm on TOP of the conversion factor.
Multi-Step Example
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Sometimes, we must “string”
several conversion factors together
to get from one unit to another.
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Ex. Mrs. DeLong's class is 47 minutes
long. How many days long is this???
Multi-Step Example
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Need to go from minutes to hours to
days
47 min
x 1 hr
x 1 day
60 min
24 hrs
Notice how “like” units can be
cross-canceled.
=
Multi-Step Example
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Need to go from minutes to hours to days
47 min
x 1 hr
x 1 day = 0.033 days
60 min 24 hrs
Notice how “like” units can be
cross-canceled.