Read Sections 1.10 and Appendix A-1 before viewing this
slide show.
Unit 4
Measurement – Basic Units
•The International System of Units (SI) (1.10)
•Current definitions of the seven base SI units
•Review of exponential notation (Appendix A-1)
•Metric prefixes and their interconversion (1.10)
The SI System (1.10)
• Adopted in 1960 – states standard units to be used in
measurement of seven basic properties as given below.
Physical
Quantity
Name of Unit
Symbol of Unit
Length
meter
m
Mass
kilogram
kg
Time
second
s
Temperature
Kelvin
K
Amount of
substance
mole
mol
Electric current
Ampere
A
Luminous
intensity
candela
cd
Current Definitions of the Seven SI
Units
• Six have very well defined, though somewhat abstract,
descriptions. For example,
– second: The second is the duration of 9 192 631 770 periods of
the radiation corresponding to the transition between the two
hyperfine levels of the ground state of the cesium 133 atom.
– meter: The meter is the length of the path travelled by light in
vacuum during a time interval of 1/299 792 458 of a second.
• Definitions of the other four that have precise definitions
may be found at
http://physics.nist.gov/cuu/Units/current.html
• The kilogram is the only one not precisely defined – see
next slide.
The Kilogram
• The kilogram is called a prototype standard –
there is one chunk of matter that is “the”
kilogram as pictured.
• The official kilogram resides in
France. Several copies are in
existence throughout the
world.
• Concern was raised in 2007 that
the kilogram is losing mass – about 50 millionths
of a gram. This is roughly the mass of a
fingerprint.
Review of Exponential Notation (Appendix A-1)
• Looking at the SI base units gives a strong sense that it
is a metric-based system
• The metric system depends heavily on the ability to
maneuver the decimal point in a number
• Some of the numbers we will see during the semester
are incredibly large or incredibly small and we must have
a system to write and work with these numbers without
difficulty
• Thus there is a need to be conversant in exponential
notation (sometimes called scientific notation)
Review of Exponential Notation (Appendix A-1)
• The concept of exponential notation is based on our base 10
number system:
10  101
100  10 10  102
1000  10 10 10  103
1
 101
10
1
0.01 
 102
10 10
1
0.001 
 103
10 10 10
0.1 
• In the left column, where the numbers are greater than 1, the
power on 10 is the number of decimal places to the right of
the digit “1”
• In the right column, where the numbers are less than 1, the
exponent on 10 is negative and is the number of decimal
places from the decimal place to that just after the digit “1"
Examples of Converting Between Standard
Notation and Exponential Notation
• Consider the following conversions:
63410 m = 6.3410 x 104 m
145.6 s = 1.456 x 102 s
0.00389 kg = 3.80 x 10-3 kg
9.87 x 104 L = 98700 L
5.12 x 10-5 cm = 0.0000512 cm
Metric Prefixes (1.10)
•Part of the beauty of the metric system is that conversion of units is simply a
matter of moving the decimal point. Metric prefixes are used to indicate the
size of the unit. Some of the more common metric prefixes are given in the
table below.
Prefix
Exponential
Expression
Abbreviation
tera-
1012
T
giga-
109
G
mega-
106
M
kilo-
103
k
Base Unit
100
-
deci-
10-1
d
centi-
10-2
c
milli-
10-3
m
micro-
10-6
μ
nano-
10-9
n
Prefix
Exponential
Expression
Abbreviation
tera-
1012
T
giga-
109
G
mega-
106
M
103
k
100
-
10-1
d
centi-
10-2
c
milli-
10-3
m
micro-
10-6
μ
nano-
10-9
n
kiloBase Unit
deci-
Move Left
• Notice in the table:
– The difference in exponents
between two prefixes gives the
number of decimal places to be
moved in a conversion
– If the conversion is from a larger
unit to a smaller unit (down the
table), the decimal point is moved
to the right
– If the conversion is from a smaller
unit to a larger unit (up the table),
the decimal point is moved to the
left
– See examples on the next page
Move Right
Metric Conversions
Examples of Metric Conversion
350 mL = 0.350 L
(mL to L is three decimal places, since going up
the table move three decimal places to the left)
4.52 x 1034 ds = 4.52 x 1035 cs
(ds to cs is one decimal place, since going down
the table move to the right making the exponent
bigger by one)
Prefix
Exponential
Expression
Abbreviation
tera-
1012
T
giga-
109
G
mega-
106
M
103
k
100
-
10-1
d
centi-
10-2
c
milli-
10-3
m
micro-
10-6
μ
nano-
10-9
n
kiloBase Unit
deci-
Move Left
0.459 km = 45900 cm
(km to cm is five decimal places, since going
down the table move five decimal places to the
right)
Move Right
42600 m = 42.6 km
(m to km is three decimal places, since going up
the table move three decimal places to the left)