CHAPTER 6
FUNDAMENTAL DIMENSIONS AND UNITS
UNITS
 Used to measure physical dimensions
 Appropriate divisions of physical dimensions to keep
numbers manageable
 19 years old instead of 612,000,000
seconds old
Common systems of units
 International System (SI) of Units
 British Gravitational (BG) System of Units
 U.S. Customary Units
Units – SI
 Most common system of units used in the world
 Examples of SI units are: kg, N, m, cm,
 Approved by the General Conference on Weights and
Measures (CGPM)
 Series of prefixes & symbols of decimal multiples
(adapted by CGPM, 1960)
Engineering Fundamentals, By Saeed Moaveni,
Third Edition, Copyrighted 2007
6-3
British Gravitation (BG) System
 Primary units are
 foot (ft) for length (1 ft = 0.3048 m)
 second for time
 pound (lb) for force (1 lb = 4.448 N)
 Fahrenheit (oF) for temperature
9
T  F   T C   32
5
9
T  R   T K 
5
 Slug is unit of mass which is derived from Newton’s
second law
 1 lb = (1 slug)(1 ft/s2)
Engineering Fundamentals, By Saeed Moaveni,
Third Edition, Copyrighted 2007
6-4
U.S. Customary System of Units
 Primary units are
 Foot (ft) for length (1 ft = 0.3048 m)
 second for time
 pound mass (lbm) for mass (1 lbm = 0.453592 kg, 1slug
= 32.2 lbm)
 Pound force (lbf ) is defined as the weight of an
object having a mass of 1 lbm at sea level and at a
latitude of 45o, where acceleration due to gravity is
32.2 ft/s2 (1lbf = 4.448 N)
Engineering Fundamentals, By Saeed Moaveni,
Third Edition, Copyrighted 2007
6-5
Fundamental Unit of Length
meter (m) – length of the path traveled by
light in a vacuum during a time interval of
1/299,792,458 of a second
Engineering Fundamentals, By Saeed Moaveni,
Third Edition, Copyrighted 2007
6-6
Fundamental Unit of Mass
kilogram (kg) – a unit of mass; it is equal to the
mass of the international prototype of the
kilogram
Engineering Fundamentals, By Saeed Moaveni,
Third Edition, Copyrighted 2007
6-7
Fundamental Unit of Time
second (s) – duration of 9,192,631,770 periods of
the radiation corresponding to the transition
between the 2 hyperfine levels of the ground state
of cesium 133 atom
Engineering Fundamentals, By Saeed Moaveni,
Third Edition, Copyrighted 2007
6-8
Fundamental Unit of Electric Current
ampere (A) – constant current which, if
maintained in 2 straight parallel conductors of
infinite length, of negligible circular cross section,
and placed 1 meter apart in a vacuum, would
produce between these conductors a force equal
to 2x10-7N/m length
Engineering Fundamentals, By Saeed Moaveni,
Third Edition, Copyrighted 2007
6-9
Fundamental Unit of Temperature
kelvin (K) – unit of thermodynamic temperature,
is the fraction 1/273.16 of thermodynamic
temperature of the triple point of water
Engineering Fundamentals, By Saeed Moaveni,
Third Edition, Copyrighted 2007
6-10
Fundamental Unit of Amount of
Substance
mole (mol) – the amount of substance of a system
that contains as many elementary entities as there
are atoms in 0.012 kilogram of carbon 12
Engineering Fundamentals, By Saeed Moaveni,
Third Edition, Copyrighted 2007
6-11
Fundamental Unit of Luminous
Intensity
candela (cd) – in a given direction, of a source that
emits monochromatic radiation of frequency
540x1012 hertz and that has a radiant intensity in
that direction of 1/683 watt per steradian
Engineering Fundamentals, By Saeed Moaveni,
Third Edition, Copyrighted 2007
6-12
Unit Conversion
 In engineering analysis and design, there may be a
need to convert from one system of units to another
 When communicate with engineers outside of U.S.
 Important to learn to convert information from one
system of units to another correctly
 Always show the appropriate units that go with your
calculations
 See front & back cover pages for conversion factors
Engineering Fundamentals, By Saeed Moaveni,
Third Edition, Copyrighted 2007
6-13
CASE STUDY:
THE IMPORTANCE OF UNIT
CONVERSIONS
SEPTEMBER 23, 1999
Mars Climate Orbiter Believed To
Be Lost
Mars Climate Orbiter is believed to
be lost due to a suspected navigation
error.
The engine burn began as planned five minutes before the
spacecraft passed behind the planet as seen from Earth.
Flight controllers did not detect a signal when the spacecraft
was expected to come out from behind the planet.
"We had planned to approach the planet at an altitude of
about 150 kilometers (93 miles).
We thought we were doing that, but upon review of the
last six to eight hours of data leading up to arrival, we
saw indications that the actual approach altitude had
been much lower. It appears that the actual altitude
was about 60 kilometers (37 miles). We are still trying
to figure out why that happened," said Richard Cook,
project manager for the Mars Surveyor Operations
Project at NASA's Jet Propulsion Laboratory.
SEPTEMBER 30, 1999
Likely Cause Of Orbiter Loss Found
The peer review preliminary findings
indicate that one team used English
units (e.g., inches, feet and pounds)
while the other used metric units for a
key spacecraft operation.
Significant Digits:
By accuracy of a measurement, we mean the
number of digits, called significant digits, that it
contains.
These are the units we are reasonably certain of
having counted and of being able to rely on in
measurement.
The greater the number of significant digits, of a
measurement, the greater the accuracy of the
measurement, and vice versa.
Significant Digits (Figures)
 Engineers make measurements and carry out
calculations
 Engineers record the results of measurements and
calculations using numbers.
 Significant digits (figures) represent (convey) the extend
to which recorded or computed data is dependable.
Engineering Fundamentals, By Saeed Moaveni, Third Edition,
Copyrighted 2007
6-19
SIGNIFICANT DIGITS
1) All nonzero digits are significant. 1432 has 4 significant
digits.
2) All zeros between significant digits are significant.
40050 m has 4 significant digits.
3) A zero in a whole-number measurement that is specially
tagged, such as by a bar above it, is significant.

40,000 ft has 2 significant digits.
Significant Digits (continued)
3) All zeros to the right of a significant digit and a
decimal point are significant. 6.100 L has 4
significant digits.
4) The number of significant digits for the number 1500
is not clear. 1.5 x 103 has 2 significant digits.
1.50 x 103 has 3 significant digits.
3) Zeros to the left in a decimal measurement that is
less than 1 are not significant. 0.00870 has 3
significant digits.
Significant Digits – How to
Record a Measurement
Least count – one half of
the smallest scale
division
What should we record
for this temperature
measurement?
71 ± 1oF
Engineering Fundamentals, By Saeed Moaveni, Third Edition,
Copyrighted 2007
6-22
Significant Digits – How to
Record a Measurement
What should we record for the length?
3.35 ± 0.05 in.
Engineering Fundamentals, By Saeed Moaveni, Third Edition,
Copyrighted 2007
6-23
Significant Digits – How to
Record a Measurement
What should we record for this pressure?
7.5 ± 0.5 in.
Engineering Fundamentals, By Saeed Moaveni, Third Edition,
Copyrighted 2007
6-24
Significant Digits
 175, 25.5, 1.85, and 0.00125 each has three significant
digits.
 The number of significant digits for the number
1500 is not clear.
 It could be 2, 3, or 4
 If recorded as 1.5 x 103 or 15 x 102, then 2
significant digits
Engineering Fundamentals, By Saeed Moaveni, Third Edition,
Copyrighted 2007
6-25
Significant Digits – Addition
And Subtraction Rules
When adding or subtracting numbers, the result of the
calculation should be recorded with the last significant
digit in the result determined by the position of the last
column of digits common to all of the numbers being
added or subtracted.
For example,
152.47 or
132. 853
+ 3.9
5
156.37
127.853 (your calculator will display)
156.3
127
(however, the results should be
recorded this way)
6-26
Significant Digits – Multiplication
and Division Rules
When multiplying or dividing numbers, the result of
the calculation should be recorded with the least
number of significant digits given by any of the
numbers used in the calculation.
For example,
152.47
or
152.47
×
3.9
÷
3.9
594.633
39.0948717949 (your calculator will
5.9 x 102
display)
39 (however, the result should be
6-27
recorded this
way)
Significant Digits – Examples
276.34
+ 12.782
289.12
2955
x 326
9.63 x 105
Engineering Fundamentals, By Saeed Moaveni, Third Edition,
Copyrighted 2007
6-28
Rounding Numbers
In many engineering calculations, it may be
sufficient to record the results of a calculation to a
fewer number of significant digits than obtained
from the rules we just explained
56.341 to 56.34
12852 to 1.285 x 104
Engineering Fundamentals, By Saeed Moaveni, Third Edition,
Copyrighted 2007
6-29
UNIT CONVERSION:
A person who is 5 feet 9 inches tall and weighs 173 pound
force (lbf ) is driving a car at a speed of 62 miles per hour
over a distance of 25 miles. The outside temperature is 80℉
and the air has a density of .0735 pounds per cubic foot
(lbm/ft3). Convert all of the values given in this example from
U.S. Customary to SI units.
A) Height:
in meters

 1 ft    0.3048 m 
H   5 ft  (9 in) 
   1 ft 

 12 in   

Height:
in centimeters
H  (1.753 m)
 100 cm 


1
m


 1.7526
=175.3cm
m
Weight in
Newtons:
 4.448 N 
W  (173 lb f ) 
 1 lb 
f


 769.50N
mile  5280 ft   0.3048 m 

S

67
Speed of car:


h  mile   1 ft 

 107826 m/h
How do we convert to km/h?
m
Or S  107,826
h
 1 km 

  107.826 km
 1000 m 
h
Distance traveled:
D   25 miles   5280 ft   0.3048 m   1 km 

 


1ft
 1 mile  
1000
m


 40.233 km
Density of air ,  :

1 ft
lbm   0.453 kg 

  0.0735 3  


ft
1
lb
0.3048
m



m

3
 1.176 kg / m
3