Dimensional analysis, also known as factor-label method or unit-factor method, is a method to convert one different type of unit to another. This way, we can convert to a different unit, but their values are the same. To convert from one unit to another, we make use of a conversion factor, which is a numerical quantity that we can multiply or divide to the number or quantity that we want to convert.
As an example, if we want to know how many minutes are in 3 hours, what do we do? We generally think as follows:
1 hour = 60 minutes
3 hour = 3 × 60 minutes = 180 minutes
(here the conversion factor 60 minutes)
We use conversion factors accordingly so that the answer comes in the desired unit and biased results are avoided.
Example:
To find out how many feet are in 140 centimeters (cm). In this, we have to convert centimeters into feet. Since we can’t convert centimeters directly into feet, so we will convert it into inches, and then convert inches to feet. This involves calculation of two conversion factors.
So 1 inch = 2.54 cm
1 cm = 1/2.54 inches
12 inches = 1 feet
12 × 2.54 cm = 1 feet
30.48 cm = 1 feet
1 cm = 1/30.48 feet
Then , 140 cm = 140 × 1/30.48 feet
= 4.59 feet
