First example: You need to modify a given value (e.g. 1'-4 1/4") and don't want to do the math (too many fractions!).
Solution: turn the given value into a formula. Add an equals sign at the beginning and then subtract (in this example) the desired amount as shown in the image below.
Result: Revit evaluates the mathematical statement and returns the result.
Second Example: You are working with a manufacturer's cut sheet and the values are in metric, but you are working in imperial units (or vis versa).
Solution: Simply enter the value, including the units indicator as shown below.
Result: The metric value is translated to imperial (hard, not soft). Revit does not keep track of the original metric input.
Third Example: I know the fraction value, e.g. motor size, and I don't know/recall the decimal equivalent.
Solution: Similar to the first example, just make it a formula; enter the fraction preceded by an equals sign.
Result: The fraction is covered to a decimal based on the result of one divided by three.
One problem I ran into recently using this last trick was the result produced too many decimal places, based on Project Units, and caused a lookup table reference to fail!
Simple stuff, but little things like this can save a lot of time...