What if you went to the grocery store and bought 3 gallons of milk? Could you determine how many pints of milk you purchased? Or how about if you bought 16 pints of milk? How many gallons would this be? In this Concept, you'll learn to make conversions like these so that you can solve real-world problems.
Real-world information is given in dimensions, or the units in which the value is measured. For example, the following are all examples of dimensions.
Analyzing dimensions can help you solve problems in travel, astronomy, physics, engineering, forensics, and quality. Solving problems by converting dimensions or canceling dimensions is the focus of this Concept.
Consider the distance formuladistance=rate⋅time. This formula can be rewritten for rate. rate=distancetime. If distance is measured in kilometers, and time is measured in hours, the rate would have the dimensions kilometershours.
You can treat dimensions as variables. Identical units can divide out, or cancel. For example, kilometershour⋅hour→kilometershour⋅hour→kilometers.
Sometimes the units will not divide out. In this case, a conversion factor is needed.
Since kilometers≠meters, you need to convert kilometers to meters to get the answer. You know there are 1,000 meters in a kilometer. Therefore, you will need to multiply the original dimension by this factor.
A long list of conversion factors can be found at this website.
You are traveling in Europe and want to know how fast to drive to maximize fuel efficiency. The optimal driving speed for fuel efficiency is 55 miles per hour. How fast would that be in kilometers per hour?