1.04 Units and the
Metric System
Dr. Fred Omega Garces
Chemistry 100
Miramar College
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1.04 Units and the Metric System
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Measurements
In our daily lives we deal with making
measurement routinely.
i.e., How much gasoline is required to fill your gas tank?
What time did you wake up this morning? How fast did
you drive to school today ?
Doctors, nurses, pharmacistDoctors and nurses make measurement constantly.
Measurements like pulse rate, blood pressure,
temperature, drug dosage.
Math - The language of Science
Scientist make countless measurement during their
experiment to prove or disprove theory.
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1.04 Units and the Metric System
January 10
Numbers without meaning
What is your response if I told you that
I weigh 64.4
You would either think I was
mad or anorexic.
In any measurement Magnitude
(the number) as well as Unit
(meaning) must be stated.
Otherwise it is Meaningless
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1.04 Units and the Metric System
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System of Measurements
What units are used?
America
English System
1 ft = 12 in
1 yd= 3 ft
1 mi. = 1,760 Yd
1 mi = 5280 ft
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The Rest of the
World
Metric System
1 km = 1000 m
1 m = 100 cm
1 m = 1•109 nm
1.04 Units and the Metric System
Scientific
Community
Le System
International d’Unites
time g sec
length g m
mass g kg
temperature g Kelvin
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Units – gives meaning to the measurement
What are Units ?
Standards used for quantitative comparison.
i.e., Ft, mi, in, cm, mi/hr, km/min, gal, J, cal
The U.S. prefers the English Unit system.
Rest of the World
uses the metric system.
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1.04 Units and the Metric System
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Metric system and the
Le Systeme International d'Unites (SI)
The Metric system is convenient because it uses only
one fundamental unit for each type of measurement,
and all of its conversion factors are multiples of 10.
The scientific community uses an updated metric plan
called the SI units.
SI (Le Systeme International d'Unites)
There are seven (7) quantities in which all units can be
derived, this is the basis of the SI units; all other
units are derived from these seven
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1.04 Units and the Metric System
January 10
SI units
There are seven quantities (fundamental) in which all units can be
derived; these are the base units and the SI defines these as:
All others units are derived units
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1.04 Units and the Metric System
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Relationship of
SI to SI Derived
Units
Relationships of the
SI units to SI
derived units with
special names
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1.04 Units and the Metric System
January 10
What are Derived Units ?
Derived units result from these seven base units.
i.e., vol. (L) derived from m3 g meters.
energy (J) derived from N•m or (kg•m / s2) • m
pressure (psi) derived from lb. /in2 or (kg /m2)
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1.04 Units and the Metric System
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Ease of conversion of the SI units
The SI units employ a series of prefix to indicate
decimal fraction or multiple of units.
10
Prefix
Symbol
exp factor
factor
Mega
M
10 6
1,000,000
kilo
k
10 3
1,000
deci
d
10 -1
1 / 10
centi
c
10 -2
1 / 100
milli
m
10 -3
1 / 1,000
micro
10- 6
1 /1 ,000,000
nano
m
n
10 -9
1 / 1,000,000,000
pico
p
10 -12
1 / 1,000,000,000,000
1.04 Units and the Metric System
January 10
Metric Prefix Relationship
Consider the relationship between each metric prefix.
Prefix
Tera
Giga
Mega
kilo
deci
centi
milli
micro
nano
pico
femto
Fraction
Decimal
Exponential
Conversion
1 000 000 000 000
1 000 000 000 000
1 • e12
1 000 000 000 000 m = 1 Tm
1 000 000 000
1 000 000 000
1 • e9
1 000 000 000 m = 1 Gm
1 000 000
1000 000
1 • e6
1 000 000 m = 1 Mm
1000
1000
1 • e3
1 000 m = 1km
1
1
1
1m = 1m
1/10
0.1
1 • e-1
1m = 10 dm
1 / 100
0.01
1 • e-2
1m = 100 cm
1 / 1000
0.001
1 • e-3
1m = 1000 m
1/1 000 000
.000 00 1
1 • e-6
1m = 1 000 000 m
1/1 000 000 000
.000 000 000 1
1 • e-9
1m = 1 000 000 000 m
1/1 000 000 000 000
.000 000 000 000 1
1 • e-12
1m = 1 000 000 000 000 m
1/1 000 000 000 000 000 .000 000 000 000 000 1
1 • e-15 1m = 1 000 000 000 000 000 m
In using the metric system conversion factor in dimensional analysis
remember to use the conversion ratio that makes sense. For example
the conversion between micrograms (µg) and grams (g) is either 1g =
1•10-6 µg or 1,000,000 µg = 1g. It is easier to use the 1,000,000 µg = 1g
conversion since this conversion does not involve negative exponents.
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1.04 Units and the Metric System
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Conversion within English System
In the English system, exact conversion factors must be known.
i.e., How many inches in a marathon (26 miles 385 yards)?
To solve this, must know that there are 63,360 in = 1 mile
Mile
n
Yard
n
feet
n
inches
To solve this problem the relationship between miles and in must
be known. In fact to convert between miles, yards, feet and
inches each relationship (conversion factor) must be known.
Length
1 Mi. = 1,760 yd = 5,280 ft = 63,360 in
1 yards = 3 ft = 36 in
Therefore in 26 miles, there are :
26 mile ∗
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63,360 in
1 mile
1.04 Units and the Metric System
= 1,647,360 = 1.6 million inches
January 10
Conversion within Metric System.
Advantage of the metric system is that converting from one unit to
the other is just a matter of multiplying or dividing by 10's.
i.e., How many centimeters in a 100 km ?
To solve this, simply need to know that kilo means 1000, therefore
there are 1000m = 1 km (conversion factor) and that there are 100
cm = 1 m
Kilometers
meters
n
n
centimeters
This is very useful in science, especially when you have to work
numerical problems.
Length
1 km = 1000 m, 1 m = 100 cm
Therefore 100 km is equal to:
100 km ∗
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1.04 Units and the Metric System
1000 m
1 km
∗
100 cm
1m
= 1 • 10 7 cm
January 10
English and Metric System.
In science, measurement is based on the metric system (SI). Life in America is a bit more complicated because we live in a
global world that uses the metric system but at home we use
the English system.
The metric system (or SI) is very useful in science, especially
when you have to work numerical problems. When dealing with
the metric system the conversion is easy.
When dealing with English and metric, the conversion factor
between two units must be known: i.e., 1 inch = 2.54 cm
In the automotive industry, the U.S. still uses
predominately the English system. If you want a wrench for
example that is the next size smaller than a 7/16 -inch, it
would be logical to use 6/16-inch. The correct next lower
size is actually labeled 6/16-inch. It becomes really
complicated if you are looking for the next smaller size for
3/4-inch because it is not 2/4 (or 1/2-inch) it is actually
11/16-inch
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-go figure.
1.04 Units and the Metric System
January 10
Other Metric relationship.
Length - distance
English
1 ft = 12 in
1 yd= 3 ft
1 mi. = 1,760 yd.
Metric
English - Metric
Metric
English - Metric
1 km = 1000 m
1 m = 100 cm
1 m = 1•109 nm
1 in = 2.54 cm
1 mi. = 1.609 km
Volume - space
English
1 gal = 4 qt
1 qt = 2 pt
1pt = 16 fl oz.
1 L = 1000 ml
1 ml = 1 cm3 = 1 cc
1 gal = 3.785 L
1 fl oz = 29.57 ml
Mass - quantity of matter
English
Metric
1 lb. = 16 oz
1 Ton = 2000 lb.
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1 kg = 1000 g
1 g = 1000 mg
1.04 Units and the Metric System
English - Metric
1 lb. = 453.6 g
1 kg = 2.205 lb.
January 10
Some interesting measurements
Order of magnitude as expressed via metric measurements
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1.04 Units and the Metric System
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Summary
Measurement - Measurement Consist of a Magnitude (a number) and a Unit (the meaning)
Unit system - Le Systeme International d'Unites ( SI ) There are three unit
systems. The English, Metric and SI (Le Systeme International d'Unites). The SI is derived from the metric and is more specific.
The Metric system is based on prefixes which relates the magnitude of a number
to another by factors of 10. Prefix
Tera
Giga
Mega
kilo
deci
centi
milli
micro
nano
pico
femto
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Fraction
Decimal
Exponential
Conversion
1 000 000 000 000
1 000 000 000 000
1 • e12
1 000 000 000 000 m = 1 Tm
1 000 000 000
1 000 000 000
1 • e9
1 000 000 000 m = 1 Gm
1 000 000
1000 000
1 • e6
1 000 000 m = 1 Mm
1000
1000
1 • e3
1 000 m = 1km
1
1
1
1m = 1m
1/10
0.1
1 • e-1
1m = 10 dm
1 / 100
0.01
1 • e-2
1m = 100 cm
1 / 1000
0.001
1 • e-3
1m = 1000 m
1/1 000 000
.000 00 1
1 • e-6
1m = 1 000 000 m
1/1 000 000 000
.000 000 000 1
1 • e-9
1m = 1 000 000 000 m
1/1 000 000 000 000
.000 000 000 000 1
1 • e-12
1m = 1 000 000 000 000 m
1/1 000 000 000 000 000 .000 000 000 000 000 1
1 • e-15 1m = 1 000 000 000 000 000 m
1.04 Units and the Metric System
January 10