Chapter 8 Electrical Engineering 143
Math
Scientific Notation
It is very common to encounter extremely large and small numbers when work-
ing with or studying electricity and electronics. Sometimes numbers are too large or
small to be conveniently written. They can be represented using scientific notation.
The base number in scientific notation is a number from 1 to 9 and is multiplied by
a power of ten.
For example, 7 × 103 (seven times ten to the third power) is 7 × 10 × 10 × 10 = 7,000.
The 3 is an exponent. Exponents show how many times to use the number in multi-
plication. Positive exponents are used for numbers larger than the base number, and
negative exponents are used for numbers that are smaller than the base number.
For example, imagine you want to represent 5 Megawatts using scientific nota-
tion. The metric prefix Mega- refers to million. Therefore, you are trying to show
5,000,000 watts. That can be shown as 5 × 10 × 10 × 10 × 10 × 10 × 10. Using scien-
tific notation, it is 5 × 106 watts.
The metric prefix milli- is used to show thousandths of a base number. For
example, 7 milliamperes is 7 thousandths of 1 ampere, or 0.007 amperes. Using
scientific notation, this is shown as 7 × 10–3. The exponent is –3 because the decimal
place moves to the right 3 places from 7 to 0.007.
See Figure  A showing common metric prefixes and the symbols, decimal
value, and value in scientific notation.
Write the following numbers using scientific notation, converting units where
necessary.
1. 8,730,000,000 watts
2. 6,270 nanovolts
3. 0.00047 amperes
4. 4,383,000 ohms
5. 2,000 volts
6. 3.2 kilohms
Prefi x Symbol Value Decimal
Giga- G 109 1,000,000,000
Mega- M 106 1,000,000
Kilo- k 103 1,000
Milli- m 10–3 0.01
Micro- μ 10–6 0.000001
Nano- n 10–9 0.000000001
Pico- p 10–12 0.000000000001
Figure A.
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