0. ECE 221 Electric Circuit Analysis I Chapter 3
SI Notation, Units, Unit Conversion
Herbert G. Mayer, PSU & CCUT
Status 10/2/2015
Taken with permission from Prof. Phillip PSU ECE

1. Syllabus Scientific Engineering Notation Dimensions
Physical Quantities
Units

2. Scientific & Engineering Notation
Scientific notation is a compact method for expressing very small or very large numbers.
Format:
The mantissa conveys the number’s value and accuracy
The base and exponent define the scaling factor
exponent
mantissa
base
Scientific
Engineering
exponent
multiple of 1
multiple of 3
mantissa
-10 < a < 10
-1000 < a < 1000 2

3. Example: Number Scientific Engineering 0.000001234567 1.23456710-6
10-5
10-3
10-4
10-3
10-3
10-2
10-1
10
102
103
104
103
105
103
106 3

4. Describing Physical Quantities
A physical quantity has three components:
Dimension (e.g., length, time, etc.)
Magnitude (quantity)
Unit (reference amount)
Example: m
A measurement determines the number of multiples of a unit that are contained within a physical quantity
unit
 length
magnitude

5. 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)

6. 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

7. SI Supplementary Units
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)

8. SI Unit Prefixes 1024 yotta Y 10-1 deci d 1021 zetta Z 10-2 centi c
1018 exa E milli m
1015 peta P micro 
1012 tera T nano n
109 giga G pico p
106 mega M femto f
103 kilo k atto a
102 hecto h zepto z
101 deka da yocto y

9. 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 9

10. Multipliers for SI Prefix Conversion
M→106, k→103, 1, m→10-3, →10-6, n→10-9, p→10-12, f→10-15
Example:
0.01 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.
From ↓
To →
Multipliers for SI Prefix Conversion M k 1 m  n p f
103
106
109
1012
1015
1018
1021
10-3
10-6
10-9
10-12
10-15
10-18
10-21
→ (0.01 F)(106 pF/F) = pF 10

11. Example: Frequency & Wavelength for EM Waves Electromagnetic waves:
(n=10-9, M=106, G=109, T=1012, P=1015, E=1018)
Speed of light
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 11

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