Metric System
Metric Prefixes -Dimensional Analysis
In 1960 the International Bureau of Weights and
Measures (Sevres, France) adopted the "International System of Units",
also known as "SI" units.
7 base units are used. All other SI units
are derived from combinations of these base units:
length: meter (m)
mass: kilogram (kg)
time: second (s)
electric current: ampere (A)
temperature: kelvin (K)
amount of substance: mole (mol)
luminous intensity: candela (cd)
General Punctuation Rules:
a) use space instead of comma to separate numbers into groups of three
ex: 63 000 000
m
0.000 000 003 m
b) use decimals instead of fractions to express
partial units
c) space between the numeric value and unit
symbol
d) do not use periods after symbols
e) all abbreviations are singular
f) follow capitalization rules as given in
problems
The following pages reproduce a portion of the software program
available to students. They demonstrate how to use metric prefixes, complete
dimensional analysis problems, and reviews SI metrics. Please read each screen carefully. You might want to make
notes. Additional problems are available from Mr. Jones.
Metric Prefixes are
combined with a unit to indicate that the unit has been multiplied by a certain
power of 10. Prefixes are to be used to keep numerical values in tables,
results, and specifications between 0.1 and 1000.
example: 144 000 N = 144 kN
Six basic prefixes are used commonly. They
will be used to demonstrate the basic principles. Less common prefixes are
given in the metric appendix.
The first example: kilo (abbreviated
with lowercase 'k'
This prefix represents 3 decimal places, usually associated with 1000.
examples: 1 km = 1000 meters (1000
m) 2.3 kJ = 2 300
Joules (2 300 J)
Another example: centi
(abbreviated with lowercase 'c'
This prefix represents 2 decimal places, usually associated with 0.01
examples: 100 cm = 1 meter (1
m) 2.3 E 2 cm = 2.3 meters
(2.3 m)
Another commonly used metric prefix is milli
('m')
examples: 1000 mL = 1 liter (1
L) 2.3 E 3 mL = 2.3
liters (2.3 L)
Less common but used occasionally are the
following:
mega ('M') 1 000 000 (1 E 6)
micro ('µ') 0.000 001 (1 E - 6)
nano ('n') 0.000 000 001 (1 E - 9)
The remaining prefixes and their multiplication
factors can be seen in the metric appendix.
back to top of page
Dimensional
Analysis Examples
Dimensional analysis is also called the
factor-label method of problem solving. It is a way of setting up a
problem in a constant fashion that breaks the problem down into simple
steps. Each step is a ratio that must equal 1, thus canceling out some
preceding unit.
example problem: 4.4 km
= ? m
solution: 4.4 km x 1000 m
= 4 400 m
1
km
(note that the 'km' cancel and you multiply 4.4 times 1000 to get
your answer)
problem: 4.4 km = ?
cm
solution: 4.4 km x 1000 m
x 100 cm = 4.4 E 5 cm
1 km 1 m
solution using scientific
notation: 4.4 km x 1 E 3 m
x 1 E 2 cm = 4.4 E 5 cm
1 km 1m
problem without metric
prefixes: 4.4 weeks = ? seconds
solution: 4.4 wk x 7 day x 24
hour x 60 minute x 60
seconds = 2.7 E 7 s
1 wk 1
day 1
hour 1
minute
some points of interest:
