ECE 101Exploring Electrical Engineering
Chapter 3SI Notation, Units, Unit Conversion
Herbert G. Mayer, PSUStatus 11/30/2015
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:
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ba 10
mantissa base
exponent• The mantissa conveys the
number’s value and accuracy.
• The base and exponent define the scaling factor.
Scientific Engineering
exponent multiple of 1 multiple of 3
mantissa -10 < a < 10 -1000 < a < 1000
Example
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Number Scientific Engineering0.000001234567 1.23456710-6 1.23456710-6
0.00001234567 1.23456710-5 123.456710-3
0.0001234567 1.23456710-4 12.3456710-3
0.001234567 1.23456710-3 1.23456710-3
0.01234567 1.23456710-2 0.012345670.1234567 1.23456710-1 0.12345671.234567 1.234567 1.23456712.34567 1.23456710 12.34567123.4567 1.234567102 123.45671234.567 1.234567103 1.234567103
12345.67 1.234567104 12.34567103
123456.7 1.234567105 123.4567103
1234567 1.234567106 1.234567106
Describing Physical Quantities
A physical quantity has three components: Dimension (e.g., length, time, etc.) Magnitude (quantity) Unit (reference amount)
Example: 12.5 m
A measurement determines the number of multiples of a unit that are contained within a physical quantity.
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length
magnitude
unit
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)
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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)
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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)
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SI Unit Prefixes
1024 yotta Y 10-1 deci d1021 zetta Z 10-2 centi c1018 exa E 10-3 milli m1015 peta P 10-6 micro 1012 tera T 10-9 nano n109 giga G 10-12 pico p106 mega M 10-15 femto f103 kilo k 10-18 atto a102 hecto h 10-21 zepto z101 deka da 10-24 yocto y
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Commonly used Electrical Engineering Units
Resistance (ohm): MΩ kΩ Ω mΩ μΩ nΩ Inductance (henry): kH H mH μH nH pH Capacitance (farad): kF F mF μF nF pF fF aF Voltage (volt): MV kV V mV μV nV Current (ampere): MA kA A mA μA nA pA
fA Power (watt): MW kW W mW μW nW
pW Frequency (hertz): THz GHz MHz kHz Hz
mHz Wavelength (m): km m cm mm μm nm
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M→106, k→103, 1, m→10-3, →10-6, n→10-9, p→10-12, f→10-15
Example0.01 F = ? 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.
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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 ↓To →
Multipliers for SI Prefix Conversion
→ (0.01 F)(106 pF/F) = 10000 pF
Example: Frequency & Wavelength for EM Waves
Electromagnetic waves:
(n=10-9, M=106, G=109, T=1012, P=1015, E=1018)
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Name Frequency f Wavelength Radio 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
Gamma ray more than 30 EHz Less than 0.01 nm
f
c
Speed of light
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Unit Conversions
A conversion factor relates the same physical quantity in two different units.
A conversion factor is always equal to one (1).
The quantity’s value is multiplied by the conversion factor to change unit systems.
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BA
BA unit
unit1
unitunit NValue
NValue
1unit1
unitand1
unit
unit1unitunit1
A
B
B
ABA
N
NN
Exact conversion factors are set by definition.
Example:
Non-exact conversion factors can be derived from measured values.
An exact conversion factor becomes non-exact if it is rounded off.
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1in 12
ft 1
ft 1
in 12 in 12 ft 1
1cm 2.54
in 1
in 1
cm 2.54 cm 2.54 in 1
1m 1
cm 100
cm 100
m 1 m 1 cm 100
If a direct conversion factor does not exist, use several intermediate conversion factors.
If done correctly, the intermediate units will “cancel” out.
Example:
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ft 3.2808
ft 48.30
100
in 12
ft 1
cm 2.54
in 1
m 1
cm 100m 1:ft tom
ft 1:m ft to
ft 1
in 12
cm 100
m 1m 0.3048
in 1
cm 2.54
Conversions that involve raising values to a power can be tricky.
Example:A = πR2 Let R = 1.5 cm. Find A in m2.
Wrong →
Right →
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cm 100
m1cm5.1 2A
Conversion factor should be squared
Improper units.
Wrong exponent
242
2 m 101.7cm 100
m1cm5.1
A
mcm 101.7 2
Conversion factors should always include units
Including units allows the conversion to be checked quickly for consistency
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2
2
fth
Btu428
1
12
1
54.2
100
1
1
3600
06.1055
1
1
11350
Example:
Just outside the earth’s atmosphere, the solar heat flux is approximately 1350 W/m2. Express the heat flux in units of Btu/hft2. Note: W = J/s and 1 Btu 1055.06 J
Avoid this!
2
2
2 fth
Btu428
ft1
in12
in1
cm54.2
cm100
m1
hr1
s3600
J06.1055
Btu1
W1
sJ1
m
W1350
Example
a) 525 L (liters) = ? ft3 (1000 L = 1 m3)
b) 12 days = ? ms
c) 65.9 C = ? F
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3
3
3
3
ft5.18m3048.0
ft1
L10
m1L525
ms100368.1s1
ms10
m1
s60
h1
m60
day1
h24day12 9
3
F151F32C
F
5
9C9.65
Offset
Are there really 24 hours in a day? Actually, no!1 day 23 h 56 m 4 s
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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]
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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?