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Note that the list of derived units in Figure 3 is only a sampling of different units that can be derived from the base units.
The exponentiation indicator
As is the case throughout these modules, the character "^" that you see used extensively in Figure 3 indicates that the character following the ^ is an exponent. Note also that when the exponent is negative, itis enclosed along with its minus sign in parentheses for clarity.
| Figure 3 . Examples of SI derived units. |
|---|
area square meter m^2
volume cubic meter m^3speed, velocity meter per second m/s
acceleration meter per second squared m/s^2wave number reciprocal meter m^(-1)
mass density kilogram per cubic meter kg/m^3specific volume cubic meter per kilogram m^3/kg
current density ampere per square meter A/m^2 |
As an alternative to explicitly writing powers of ten, SI uses prefixes for units to indicate power of ten factors. Figure 4 shows some of the powers of ten and the SI prefixes used for them.
| Figure 4 . A sampling of SI prefixes. |
|---|
Prefix-(abbreviation) Power of Ten
peta-(P) 10^15tera-(T) 10^12
giga-(G) 10^9mega-(M) 10^6
kilo-(k) 10^3deci-(d) 10^(-1)
centi-(c) 10^(-2)milli-(m) 10^(-3)
micro-(Greek letter mu) 10^(-6)nano-(n) 10^(-9)
pico-(p) 10^(-12)femto-(f) 10^(-15) |
As typically used in physics, the word dimensions means basic types of units such as time, length, and mass (see Figure 2 ).
There are many different units that are used to express length, for example, such as foot, mile, meter, inch, etc.
Because they all have dimensions of length, you can convert from one to another. For example one mile is equal to 5280 feet.
Cannot convert between units of different dimensions
When evaluating mathematical expressions, we can add, subtract, or equate quantities only if they have the same dimensions (although they may not necessarily be given in the same units). For example, it is possible to add3 meters to 2 inches (after converting units), but it is not possible to add 3 meters to 2 kilograms.
To analyze dimensions, you should treat them as algebraic quantities using the same procedures that we will use in the upcoming exercise on manuallyconverting units.
Let's manually work through an exercise to determine the distance from your home to your school in miles given that we know the distance in paces. (I will convertthis to a JavaScript script later in the module.)
As we discussed earlier, you have already determined that the distance from your home to your school is 2112paces. We have also recognized that the length of one of your paces is likely to be different from the length of someone else's paces.
This is a somewhat long and tedious explanation, but unless you already have quite a lot of experience in this area, you should probably bear with me as Iwalk you through it.
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