In performing calculations with physical quantities, it is good practice to enter each quantity as a number with its associated unit.  Both the number and the unit are then carried through the indicated algebraic operations.  The advantage of this are twofold:  (1) The units for the answer will come out of the calculations automatically.  (2) If you make an error in arranging factors in the calculation , i.e. use the wrong formula, this will become apparent because the final units will be nonsense.

Dimensional Analysis (or Factor-Label) is the method of calculation in which one carries along the units for quantities through all calculations.  Units are multiplied together, divided into each other or canceled.

As an illustration, suppose you want the height of a 6 ft 1.5 in. man in meters.  Use the definitions 1 in. = 2.54 cm and 1 ft = 12in to convert the man's height to meters.  First find the man's height in inches.  Notice how some of the units are canceled.

Next convert inches to centimeters and finally to meters.