1.05 Units and the
Metric System
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1.05 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, pharmacist-
Doctors 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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1.05 Units and the Metric System
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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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1.05 Units and the Metric System
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System of Measurements
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1.05 Units and the Metric System
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Units - These give meaning to the measurement
Rest of the World
uses the metric system.
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1.05 Units and the Metric System
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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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1.05 Units and the Metric System
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There are seven quantities in which all units can be derived; these
are the base units and the SI defines these as:
Quantity
Unit
Symbol
length
meter
m
mass
kilogram
kg
time
seconds
s
temperature
kelvin
K
amount
mole
mol
electric current
ampere
A
luminous intensity
candela
cd
All others units are derived units
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Derived units result from these seven base units.
i.e., vol. (L) derived from m3  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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The SI units employ a series of prefix to indicate
decimal fraction or multiple of units.
Prefix
Symbol
exp factor
factor
Mega
M
10 6
1,000,000
k
10 3
1,000
d
10 -1
1 / 10
c
10 -2
1 / 100
m
10 -3
1 / 1,000
m
n
10- 6
1 /1 ,000,000
10 -9
1 / 1,000,000,000
p
10 -12
1 / 1,000,000,000,000
kilo
deci
centi
milli
micro
nano
pico
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Consider the relationship between each metric prefix.
Prefix
Fraction
Decimal
Exponential
Conversion
Tera
1 000 000 000 000
1 000 000 000 000
1 • e12
1 000 000 000 000 m = 1 Tm
Giga
1 000 000 000
1 000 000 000
1 • e9
1 000 000 000 m = 1 Gm
Mega
1 000 000
1000 000
1 • e6
1 000 000 m = 1 Mm
kilo
1000
1000
1 • e3
1 000 m = 1km
1
1
1
1m = 1m
deci
1/10
0.1
1 • e-1
1m = 10 dm
centi
1 / 100
0.01
1 • e-2
1m = 100 cm
milli
1 / 1000
0.001
1 • e-3
1m = 1000 m
micro
1/1 000 000
.000 00 1
1 • e-6
1m = 1 000 000 m
nano
1/1 000 000 000
.000 000 000 1
1 • e-9
1m = 1 000 000 000 m
pico
1/1 000 000 000 000
.000 000 000 000 1
1 • e-12
1m = 1 000 000 000 000 m
femto 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 (mg) and grams
(g) is either 1g = 1•10-6 mg or 1,000,000 mg = 1g. It is easier to
use the 1,000,000 mg = 1g conversion since this conversion does
not involve negative exponents.
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In the English system, exact conversion factors must be known.
i.e., How many inches in a marathon (26 miles)?
To solve this, must know that there are 63,360 in = 1 mile
Mile

Yard

feet

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
Therefore in a marathon there are :
26 mile ∗
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€
63, 360 in
1 mile
= 1, 647, 360 in
1.05 Units and the Metric System
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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

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 ∗
12
1000 m 100 cm
7
∗
= 1• 10 cm
1 km
1m
1.05 Units and the Metric System
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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, 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
-go figure.
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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
1 lb. = 16 oz
1 Ton = 2000 lb.
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Metric
English - Metric
1 kg = 1000 g
1 g = 1000 mg
1 lb. = 453.6 g
1 kg = 2.205 lb.
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Order of magnitude as expressed via metric measurements
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In class you will be assigned a conversion project. It will be up to you to make the
appropriate conversion. Be prepared to make a presentation on this assignment. You can
create a poster, a PowerPoint slide show or come up with something creative.
Length
English - Metric
miles - km
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Volume
English - Metric
gallons - Liters
Mass
English - Metric
pounds - kg
Distance of one light year
Volume of space
Mass of universe
Distance around the world.
Volume of the sun
Mass of sun, Jupiter, Earth, Moon
Distance San Diego to NY City.
Volume of earth
Mass of water in ocean
Distance SD to LA.
Volume of water in ocean
Mass of Empire State Building.
Distance Pet Co to Qualcomm.
Water of water in great lakes
Mass of Statue of Liberty.
1000 mi km
volume of water in Shamu's pool
Mass of average elephant.
500 mi km
volume of water in Miramar's pool
1 ton g kg
100 mi km
Volume of gasoline in Hummer
300 lb
60 mi km
Volume of water in 21 gallon tank
150 lb
25-mi km
volume of air in lungs
100 lb
10 mi km
volume in 1 gallon
50 lb
1.05 Units and the Metric System
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Prefix
Fraction
Decimal
Exponential
Conversion
Tera
1 000 000 000 000
1 000 000 000 000
1 • e12
1 000 000 000 000 m = 1 Tm
Giga
1 000 000 000
1 000 000 000
1 • e9
1 000 000 000 m = 1 Gm
Mega
1 000 000
1000 000
1 • e6
1 000 000 m = 1 Mm
kilo
1000
1000
1 • e3
1 000 m = 1km
1
1
1
1m = 1m
deci
1/10
0.1
1 • e-1
1m = 10 dm
centi
1 / 100
0.01
1 • e-2
1m = 100 cm
milli
1 / 1000
0.001
1 • e-3
1m = 1000 m
micro
1/1 000 000
.000 00 1
1 • e-6
1m = 1 000 000 m
nano
1/1 000 000 000
.000 000 000 1
1 • e-9
1m = 1 000 000 000 m
pico
1/1 000 000 000 000
.000 000 000 000 1
1 • e-12
1m = 1 000 000 000 000 m
femto 1/1 000 000 000 000 000 .000 000 000 000 000 1
1 • e-15 1m = 1 000 000 000 000 000 m
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1.05 Units and the Metric System
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