Dimensional analysis


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The metric conversion involves use of conversion factors and then solving problem in stepwise manner.  

How we use the conversion factor to solve the problems of unit conversion

** given unit x Find unit/ given unit = Find unit

** Given unit x related unit/given unit x Find unit/related unit = Find unit

Arrange the conversion factor so that starting ( given ) units cancels, you can do this by arranging the conversion factors so that the starting units is on the bottom of the conversion factor.
You may find one step unit conversion or two step or chain unit conversions.

Systemetic approach :

Sort information from the problem:by identifying the given quantity and unit , the quantity and unit you want & any relationships implied in problem.
Design a strategy to solve the problem: Devise a conceptual plan.
Apply steps in conceptual plan: Check units properly and multiply terms accross the top & divide by each bottom term.

This should be more clear with these examples;

convert 1.76 yd to centimeter:-
sort info ; Given = 1.76 yd ( yards) & Find : length in cm
Strategy : conceptual plan yd ==> m ==> cm, equivalence : 1m = 1.094 yd , 1 cm = 10^-2 m
conversion factors : 1m / 1.094 yd or 1.094 yd/ 1m and 1cm/10^-2m or 10^-2m/1cm
Solution: Given unit x related unit/given unit x Find unit/related unit
so, we use the conversion factor in which we have given & related units at the bottom so that we can cancel the given & related units.

1.76 yd x 1m / 1.094 yd x 1cm/10^-2m = 160.8775 cm = 161 cm