Section 4
Base Units, Derived Units, and the Metric System
Physical science involves extensive work with “quantitative values”.....numbers that are
measurements or calculation results. All such numbers are communicated with units placed
behind them...such as metres or hours, etc.
There are two types of units :
1. Base Units :
(FUNDAMENTAL, or DEFINED units) Any other calculation result or measurement
may be written as a combination of these basic units.
Length (distance) -
meter (m)
Time-
second (s)
Mass -
kilogram (kg)
Electric Current -
ampere (A)
Temperature -
kelvin (K)
Amount of substance -
mole (mol)
Luminous intensity -
candela (cd)
2. Calculated (derived) values:
Units that we “figure out” by using the base units in some type of calculation.
Examples :
Speed - m/s
Acceleration - m/s2
Area - m2
Force - kg m/s2 (N)
The Metric System ( SI system )
Since the 1960s the International System of Units ("Système
International d'Unités" in French, hence "SI") has been the
internationally recognised standard metric system. Metric units are
widely used around the world for personal, commercial and scientific
purposes. A standard set of prefixes in powers of ten may be used to
derive larger and smaller units from the base units.
The global use of a metric system is intended to provide a common
standard for comparing or communicating science knowledge. Other
system are in use ( like the older “imperial System of Measurement” still
in use in the USA) The newer SI system uses powers of ten, nice and
easy to use when doing conversions, rather than the Imperials odd
conversions like 3 feet per yard, or 5760 feet in a mile. These are less
friendly numbers to work with.
A metric conversion is changing from any one unit to another, but
for the purposes of this 1206 course, you are responsible for conversions
to and from the “BASE UNIT” when you start anywhere between Giga
and nano.
Moving to the SI Unit
Ex.....
Convert 0.28 Megabytes to the SI unit (bytes).
You must recognize that “mega” is the prefix, and
“byte” is the SI unit being referred to.
1.
2.
M is mega, or 106
Replace M with × 10 6
...
meaning we have 0.28 x 106 b
OR... simply move the decimal point 6
places right
3.
Convert this answer to scientific notation OR
normal notation, your choice.
Ex. 2.8 x 105 b
Ex....
OR
280 000 b
thing)
(same
Convert 4.3 µm to the SI unit.
You’re supposed to recognize that µ is micro, meaning 10 -6
AND.... metres is the SI unit referred to.
1.
2.
Replace µ with × 10 -6 , or simply move the
decimal 6 places left
Gives 4.3 × 10 -6 m or 0.000 004 3 m
Moving From the SI Unit to something larger or smaller
Ex.
Convert 567 500 m into kilometres.
1. You should recognize that m is the base (SI) unit
2. You should recognize that “kilo” is × 10 3 , or
simply move your decimal three places left.
3. 567 500 m, when the decimal moves three places,
becomes 567.5 km (note the zeros are dropped because they were
NOT significant digits in the number you started with)
Remember :
When you move from larger units ( the top )
downwards, numbers get bigger while the decimal point
moves right. The opposite is true when moving
upwards.
Table 5. SI prefixes
1. .
Factor
Name
Symbol
1024
1021
1018
1015
1012
109
106
103
102
101
yotta
zetta
exa
peta
tera
giga
mega
kilo
hecto
deca
Y
Z
E
P
T
G
M
k
h
da
ANY SI UNIT that doesn’t have a prefix
Factor
Name
Symbol
10-1
10-2
10-3
10-6
10-9
deci
centi
milli
micro
nano
d
c
m
µ
n
10-12
10-15
10-18
10-21
10-24
pico
femto
atto
zepto
yocto
p
f
a
z
y
When you are converting from a larger prefix to a smaller one, you
multiply the number × 10 ?, and the exponent is always positive. In
other words, move the decimal point “?” places to the right. The
opposite is true when moving from a small prefix to a large one...the
exponent is negative, so move the decimal to the left.
One more conversion you’ll need...
Examples
time conversions
# Days × 24 hrs / day =
hours
# Hours × 60 mins / hr =
minutes
# Minutes × 60 s / min =
seconds
Convert the following....
0.45 kA to A
367 mg to g
4.6 x 10 3 μm to m