Example: Unit Conversion Using SIUnitsOf
Use the SIUnitsOf function to return the dimensions of the input argument scaled to the default SI unit system, regardless of your chosen unit system.
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The base dimensions of the default SI unit system are Meter (m), Kilogram (Kg), seconds (s), and Amperes (A).
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1. Show the definition of the permittivity constant in the SI unit system.
2. On the Math tab, in the Units group, click Unit System. Set the unit system to SI.
3. Apply the SIUnitsOf function to constant E.
4. Verify that the result is:
| | The scaling is performed on the units of E and not on its value! Thus the value of 8.854x10-12 is ignored by the SIUnitsOf function. |
5. Click inside the math region containing the SIUnitsOf, then set the unit system to USCS.
6. Verify that the result is:
This result is obtained because:
7. Click inside the math region containing the SIUnitsOf, then set the unit system to CGS.
8. Verify that the result is 1.
This result is obtained because the CGS unit system uses the units Centimeter, Gram, Seconds. Substituting 1m=100cm and 1kg=1000gm we get:
The result of the above multiplication yields no units, and that's why the SIUnitsOf function returns 1.
9. Show that dividing a constant by the SIUnitsOf of that constant returns a unitless constant value:
