When we analyze the relationships between different quantities, identify their units of measurement, and convert these quantities for equal comparison, we are using dimensional analysis. Dimensional analysis uses a or conversion factor, to change units of measurement while maintaining the value of the measurement. In a conversion factor, the numerator and equal the same amount, just in different For example, to convert 3 miles into feet, you would 3 miles by a conversion factor created from the units of miles and feet. Because 1 mile equals 5,280 feet, two conversion factors can be created:1 mile or 5,280 feet/1 mileMultiplying any number, such as 3 miles, by either of these does not change the number's over value. To determine which conversion factor we use, we place the unit we do want in the bottom, while we put the unit we want to get rid of on th

The question is incomplete, however, from the portion given, we can see that the text is based on using dimensional analysis to convert units of measurement.

We relate our given unit to the desired or expected unit :

From the text:

To convert 3 miles into feets :

The given unit = 3 miles

The expected or desired unit = feets

The relationship between Given and desired unit :

1 mile = 5280 feets

(5280 feets / 1 mile )

With the unit we want or desire placed at the bottom

To convert a given number of miles to feets ;

Multiply the given value by the relation defined :

Hence,

3 miles to feets :

3 miles × (5280 feets / 1 mile)

Miles cancels out

3 × 5280 feets = 15,840 feets

Another example :

Convert ; 10 minutes into seconds :

1 minute = 60 seconds

given unit = minute ; desired unit = seconds

Relationship = (60 seconds / 1 unit)

10 minutes × (60 seconds / 1 minute)

Minute cancels out :

10 × 60 seconds = 600 seconds

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