52 Understanding the Rule for Powers of Ten
Raising 10 to a power means multiplying 10 by itself a certain number of times. The number of times you multiply 10 is equal to the exponent. So, for example, 10 to the power of 3 means multiplying 10 by itself 3 times, resulting in the number 1000.
This looks like 103 = 10 × 10 × 10 = 1000
Electrical Units
Electricians use quantities in very large numbers or very small numbers.
- Large Unit Example: Transmission lines transmit at voltages of 500,000 volts.
- Small Unit Example: Computers deal in currents of 0.000 000 001 amperes.
It is very easy to miss a zero when writing the numbers out!
The solution is to express all of the numbers in terms of POWER OF 10.
Engineering notation uses only those powers of 10 with an exponent that is a multiple of three.
Example: 10-9 , 10-6 , 10-3 , 103 , 106
Each one of these engineering metric notational values is associated with a prefix. Instead of writing a number with a large power of 10, a metric prefix which represents the multiplier is placed ahead of the UNIT.
Example:
25 000 Volts = 25 × 103 Volts = 25 Kilovolts = 25 kV (the kilo represents 103)
It is important to learn the prefixes in order to convert from one to another. The following can help!
| Prefix | Name | Exponent |
|---|---|---|
| P | pico | [latex]10^{-12}[/latex] |
| N | nano | [latex]10^{-9}[/latex] |
| µ | micro | [latex]10^{-6}[/latex] |
| m | milli | [latex]10^{-3}[/latex] |
| no prefix | no prefix | [latex]10^{0}=1[/latex] |
| k | kilo | [latex]10^{3}[/latex] |
| M | mega | [latex]10^{6}[/latex] |
| G | giga | [latex]10^{9}[/latex] |
Example
EXPRESS 2 500 Volts in Kilovolts:
2 500 V = _______ kV
Replace the Prefixes with the appropriate powers of 10.
2 500 X (100 V) = _______ X (103) V
The power of 10 on the right-hand side is bigger than the power of ten on the left.
To keep the equation balanced the coefficient must be reduced by the same factor. That is, divided by 103.
To divide by 103 , move the decimal point of the coefficient three places to the left
2 500 X 100 V =2.5 X 103 V
2 500 = 2.5 kV