ECE 101
Exploring Electrical Engineering
Chapter 3
SI Notation, Units, Unit Conversion
Herbert G. Mayer, PSU
Status 1/11/2016
Taken with permission from PSU Prof. Phillip Wong
Syllabus




Scientific Engineering Notation
Dimensions
Physical Quantities
Units
Scientific & Engineering Notation

Scientific notation is a compact method for
expressing very small or very large numbers.
Format:
exponent
a 10b
mantissa
• The mantissa conveys the
number’s value and accuracy.
• The base and exponent define the
scaling factor.
base
Scientific
Engineering
exponent
multiple of 1
multiple of 3
mantissa
-10 < a < 10
-1000 < a < 1000
2
Example
Number
Scientific
Engineering
0.000001234567
1.23456710-6
1.23456710-6
0.00001234567
1.23456710-5
123.456710-3
0.0001234567
1.23456710-4
12.3456710-3
0.001234567
1.23456710-3
1.23456710-3
0.01234567
1.23456710-2
0.01234567
0.1234567
1.23456710-1
0.1234567
1.234567
1.234567
1.234567
12.34567
1.23456710
12.34567
123.4567
1.234567102
123.4567
1234.567
1.234567103
1.234567103
12345.67
1.234567104
12.34567103
123456.7
1.234567105
123.4567103
1234567
1.234567106
1.234567106
3
Describing Physical Quantities
A physical quantity has three components:
 Dimension (e.g., length, time, etc.)
 Magnitude (quantity)
 Unit (reference amount)
unit
Example: 12.5 m
 length
magnitude
A measurement determines the number of multiples of
a unit that are contained within a physical quantity.
4
Dimensions

Dimensions describe physical quantities

Dimensions are independent of units

Each dimension may have a variety of units

Dimensions are divided into two areas:
 Fundamental (e.g., Length L or Time t)
 Derived (e.g., Velocity = Length / Time)
5
Units

Commonly used unit systems:
 Metric (decimal: meter, kilogram, second)
 Engineering System (US: foot, pound-force, second)

Système International d′Unités (SI) is the adopted
world standard (except United States)
6

SI Base Units
 Length:
meter (m)
 Time: second (s)
 Mass: kilogram (kg)
 Electric current: ampere (A)
 Temperature: kelvin (K)
 Amount of substance: mole (mol)
 Luminous intensity: candela (cd)

SI Supplementary Units
 Plane angle:
radian (rad)
 Solid angle: steradian (sr)
7
SI Unit Prefixes
1024
1021
1018
1015
1012
109
106
103
102
101
yotta
zetta
exa
peta
tera
giga
mega
kilo
hecto
deka
Y
Z
E
P
T
G
M
k
h
da
10-1
10-2
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
deci
centi
milli
micro
nano
pico
femto
atto
zepto
yocto
d
c
m

n
p
f
a
z
y
8
Commonly used Electrical Engineering Units








Resistance (ohm):
Inductance (henry):
Capacitance (farad):
Voltage (volt):
Current (ampere):
Power (watt):
Frequency (hertz):
Wavelength (m):
MΩ kΩ Ω mΩ μΩ nΩ
kH H mH μH nH pH
kF F mF μF nF pF fF aF
MV kV V mV μV nV
MA kA A mA μA nA pA fA
MW kW W mW μW nW pW
THz GHz MHz kHz Hz mHz
km m cm mm μm nm
9
M→106, k→103, 1, m→10-3, →10-6, n→10-9, p→10-12, f→10-15
Multipliers for SI Prefix Conversion
To →
M
k
1
m

n
p
f
M
1
103
106
109
1012
1015
1018
1021
k
10-3
1
103
106
109
1012
1015
1018
1
10-6
10-3
1
103
106
109
1012
1015
m
10-9
10-6
10-3
1
103
106
109
1012

10-12
10-9
10-6
10-3
1
103
106
109
n
10-15
10-12
10-9
10-6
10-3
1
103
106
p
10-18
10-15
10-12
10-9
10-6
10-3
1
103
f
10-21
10-18
10-15
10-12
10-9
10-6
10-3
1
From ↓
Example
0.01 F = ? pF → (0.01 F)(106 pF/F) = 10000 pF
0.009 mV versus 40.5 V. Which one is bigger?
→ (0.009 mV)(103 V/mV) = 9 V.  40.5 V is bigger.
10
Example: Frequency & Wavelength for EM Waves
Electromagnetic waves:
c

f
Speed of light
(n=10-9, M=106, G=109, T=1012, P=1015, E=1018)
Frequency f
Wavelength 
3 Hz – 300 GHz
100 Mm – 1 mm
Microwave
300 MHz – 300 GHz
1 m – 1 mm
Infrared
300 GHz – 405 THz
1 mm – 750 nm
Visible
405 THz – 790 THz
750 nm – 390 nm
Ultraviolet
790 THz – 30 PHz
400 nm – 10 nm
X-Ray
30 PHz – 30 EHz
10 nm – 0.01 nm
more than 30 EHz
Less than 0.01 nm
Name
Radio
Gamma ray
11
12
Unit Conversions

A conversion factor relates the same physical
quantity in two different units.

A conversion factor is always equal to one (1).
1 unit

A
 N unit
B

1 unit A
N unit B
 1 and
1
N unit B
1 unit A
The quantity’s value is multiplied by the conversion
factor to change unit systems.
 N unit B 
  Value N  unit B
Value unit A 
 1 unit A 
13

Exact conversion factors are set by definition.
Example:
12 in
1 ft
1 ft  12 in 

1
1 ft
12 in
2.54 cm
1 in
1 in  2.54 cm 

1
1 in
2.54 cm
1m
100 cm
100 cm  1 m 

1
100 cm
1m


Non-exact conversion factors can be derived from
measured values.
An exact conversion factor becomes non-exact if it is
rounded off: up of down.
14

If a direct conversion factor does not exist, use
several intermediate conversion factors.

If done correctly, the intermediate units will
“cancel” out.
Example:
 12 in   2.54 cm  1 m 
ft to m : 1 ft 


  0.3048 m
 1 ft   1 in  100 cm 
 100 cm  1 in  1 ft  100
m to ft : 1 m 
ft



 1 m  2.54 cm  12 in  30.48
 3.2808 ft
15

Conversions that involve raising values to a power
can be tricky.
Example:
A = πR2 Let R = 1.5 cm.
Find A in m2.
Conversion factor
should be squared
Wrong
exponent
Improper
units.
 1m 
2
Wrong → A   1.5 cm  
  7.110 cm  m
 100 cm 
2
2
Right →
 1m 
4
2
A   1.5 cm  
  7.110 m
 100 cm 
2
16
Example
a) 525 L (liters) = ? ft3
(1000 L = 1 m3)
3
 1 m  1 ft

  18.5 ft 3
525 L  3 
 10 L  0.3048 m 
3
Are there really 24 hours in
a day? Actually, no!
1 day  23 h 56 m 4 s
b) 12 days = ? ms
 24 h  60 m  60 s  103 ms 
  1.0368 109 ms



12 day
 1 day  1 h  1 m  1 s 
c) 65.9 C = ? F
use: °C x 9/5 + 32 = °F
Offset
F 
  32 F  151 F
 5 C 
65.9 C 9
17
Example
For the following dimensional equations, find the base
dimensions of the parameter k:
M-mass, L-length, t-time, T-temperature
1.[M][L][t]–2 = k[M][L]–1[t]–2
2.[L]2[t]–2 = k[M]4[T]2
3. k3[T]6[M]3[L]–5 = [T] –3[t]–6[L]
18
Example
Lead has one of the highest densities of all the pure
metals. The density of lead is 11,340 kg/m3. What is the
density of lead in units of lbm/in3?
Note: 1 kg = 2.20462 lbm
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Example
A solid cylinder of polyethylene plastic ( = 930 kg/m3)
has a diameter of 12.5 mm. If the cylinder is 0.750
yards long, with is the mass and weight of the cylinder
in base SI units?
20