GENERAL ELECTRONICS I/ET 131B
COMPONENTS, QUANTITIES, AND UNITS
SCIENTIFIC NOTATION
In electrical and electronic fields, you will find both very small and very large
quantities.
It’s common to have electrical current values of only a few thousandths or even
a few millionths of an ampere.
You will find resistance values ranging up to several thousand or several million
ohms.
Originally developed by ARTHUR G.
EGGERS, BSEE, MBA, Modified by
Joe Miller
1
GENERAL ELECTRONICS I/ET 131B
COMPONENTS, QUANTITIES, AND UNITS
SCIENTIFIC NOTATION
Scientific notation provides a convenient method to express large and small
numbers and to perform calculations involving such numbers.
In scientific notation, a quantity is expressed as a product of a number between
1 and 10 and a power of ten.
For example:
150, 000  1.5  105
0.00022  2.2  10 4
Originally developed by ARTHUR G.
EGGERS, BSEE, MBA, Modified by
Joe Miller
2
GENERAL ELECTRONICS I/ET 131B
COMPONENTS, QUANTITIES, AND UNITS
SCIENTIFIC NOTATION
Exponential Notation
Convenient method to express large and small numbers.
The exponent indicates the number of places that the decimal point is moved to
the right or left to produce the decimal number.
106 =
105 =
104 =
103 =
102 =
101 =
100 =
Originally developed by ARTHUR G.
EGGERS, BSEE, MBA, Modified by
Joe Miller
1,000,000
100,000
10,000
1,000
100
10
1
10-6 = 0.000001
10-5 = 0.00001
10-4 = 0.0001
10-3 = 0.001
10-2 = 0.01
10-1 = 0.1
3
GENERAL ELECTRONICS I/ET 131B
COMPONENTS, QUANTITIES, AND UNITS
SCIENTIFIC NOTATION
Exponential Notation
If the exponent is positive
10 4  1  10 4  10000.  10, 000
If the exponent is negative
10 4  1  10 4  0.0001
Originally developed by ARTHUR G.
EGGERS, BSEE, MBA, Modified by
Joe Miller
4
GENERAL ELECTRONICS I/ET 131B
COMPONENTS, QUANTITIES, AND UNITS
SCIENTIFIC NOTATION
Example 1-1
Express each number in scientific notation
( a ) 200
200  2  10 2
(b ) 5000
5000  5  103
(c ) 85, 000
85, 000  8.5  10 4
( d ) 3, 000, 000
3, 000, 000  3  10 6
Originally developed by ARTHUR G.
EGGERS, BSEE, MBA, Modified by
Joe Miller
5
GENERAL ELECTRONICS I/ET 131B
COMPONENTS, QUANTITIES, AND UNITS
SCIENTIFIC NOTATION
Example 1-2
Express each number in scientific notation
( a ) 0.2
0.2  2  10 1
(b ) 0.005
0.005  5  10 3
(c ) 0.00063
0.00063  6.3  10 4
( d ) 0.000015
0.000015  1.5  10 5
Originally developed by ARTHUR G.
EGGERS, BSEE, MBA, Modified by
Joe Miller
6
GENERAL ELECTRONICS I/ET 131B
COMPONENTS, QUANTITIES, AND UNITS
SCIENTIFIC NOTATION
Example 1-3
Express each of the following as a regular decimal number:
( a ) 1  10 5
1  105  100, 000
(b ) 2  103
2  103  2000
(c ) 3.2  10 2
3.2  10 2  0.032
( d ) 250  10 6
250  10 6  0.000250
(e ) 2.5  10 6
2.5  10 6  0.0000025
Originally developed by ARTHUR G.
EGGERS, BSEE, MBA, Modified by
Joe Miller
7
GENERAL ELECTRONICS I/ET 131B
COMPONENTS, QUANTITIES, AND UNITS
SCIENTIFIC NOTATION
Calculations Using Powers of Ten
Addition:
1. Express the numbers to be added in the same power of ten.
2. Add the numbers without their powers of ten to get the sum.
3. Bring down the common power of ten, which is the power of ten of the sum.
Example 1-4
Add 2  10 6 and 5  10 7 and express the result in scientific notation.
1. Express the numbers to be added in the same power of ten.
 2  10    50  10 
6
6
2. Add 2 + 50 =52.
3. Bring down the common power of ten (106), and the sum 52  106.
52  10 6  5.2  107
Originally developed by ARTHUR G.
EGGERS, BSEE, MBA, Modified by
Joe Miller
8
GENERAL ELECTRONICS I/ET 131B
COMPONENTS, QUANTITIES, AND UNITS
SCIENTIFIC NOTATION
Calculations Using Powers of Ten
Subtraction:
1. Express the numbers to be subtracted in the same power of ten.
2. Subtract the numbers without their powers of ten to get the difference.
3. Bring down the common power of ten, which is the power of ten of the difference.
Example 1-5
Subtract 2.510-12 from 7.510-11 and express the result in scientific notation.
1. Express the numbers to be subtracted in the same power of ten.
(7.510-11) - (0.2510-11)
2. Subtract 7.5 - 0.25 =7.25.
3. Bring down the common power of ten (10-11), and the difference is 7.25  10-11.
Originally developed by ARTHUR G.
EGGERS, BSEE, MBA, Modified by
Joe Miller
9
GENERAL ELECTRONICS I/ET 131B
COMPONENTS, QUANTITIES, AND UNITS
1.4 ENGINEERING NOTATION
Power
10-18
10-15
10-12
10-9
10-6
10-3
10-2
10-1
101
103
106
109
1012
1015
1018
Originally developed by ARTHUR G.
EGGERS, BSEE, MBA, Modified by
Joe Miller
d
Metric Prefixes for Powers of Ten
Prefix
Abbreviation
attoa
femtof
picop
nanon
microµ
millim
centic
decidekakilomegagigaterapetaexa-
da
k
M
G
T
P
E
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