Applied Math: Units of Measurement

Converting from one set of units to another is a critical skill in the WorkKeys Applied Math Assessment. Often it can be necessary to chain together conversions to get the desired units.

Each conversion factor is a ratio that has a value of 1 and can be rearranged from the conversion equation.

That is why we can multiply by a conversion factor and not change the true value, so that the end result is the same value with different units.

For example, if you are given a time of 279457 seconds and want to know how many days that is, you can use a chain of conversion factors to go from seconds to minutes to hours to days.

The factors are arranged so that everything except the units we want will cancel out.

The correct answer choice would then be whichever option is closest to 3.234 days.

Converting Between Related Units
It can be challenging to keep track of all the different ways of communicating the same information about money, time, and other units. Much like how synonyms express the same idea using different words, the same value can be expressed using related units.

Often, the simplest way to see the relationship between similar units is in a table like this one for American currency:

 
From this table it is clear that there are many ways to communicate a value.

For instance, the value $0.50 can be thought of as half of a dollar, two quarters, fifty cents, or several other possibilities.

In this case, there are two relationships to understand: First, there are one hundred cents in a dollar. Second, the different increments of quarters, dimes, nickels, and pennies can be thought of as groups of cents or as fractions of a dollar.

A common example of expressing the same amount of something in different ways is in the measurement of time. There are many different units for time, including seconds, minutes, hours, days, weeks, months, and years. The key is to understand what units are being used and how each relates to the others, a day consists of 24 hours, an hour consists of 60 minutes, and so on.

The table below lists the relationships between the various units, and also explains some commonly used phrases referring to time:

 Example: Suppose you just got a new job that pays ten dollars and 55 cents per hour. You get paid every two weeks. If you are assured that you will work at least 6 hours per shift and have 4 shifts per week, then what is the minimum you should expect (before taxes) in your first paycheck?

To begin, let’s determine the minimum number of hours you will work in the pay period:

Now, multiply the number of hours by the pay rate to find your expected minimum pay:


Working with Mixed Units
Mixed units occur when an amount is communicated in two or more parts with different units on each part. Common examples include measurements in feet and inches as well as times in minutes and seconds or hours and minutes. When solving problems with mixed units, it is very important to check that everything is compatible with the operations required. It is often best to convert the amounts given in the initial problem before beginning any work. Depending on the problem, it may be best to leave the converted units as fractions or as decimals. In some cases, it may even be best to perform the operation on the units separately. Regardless, it is essential to know how units are related to simplify the process of converting.

Example: Suppose you want to find the total height of a two-story house. You determined that each story is 9 ft 9 in tall and the peak of the roof is 6 ft 1 3/4 in above the second story.

To begin, combine all the like units and then simplify:

 
Example: On the other hand, suppose you wanted to find the total square footage (rounded to the nearest square foot) of the same house and the first story is 27 ft 4 in by 64 ft 3 in and the second story is 27 ft 4 in by 57 ft 8 in. In this case, since finding the area requires multiplication, it would be best to convert the measurements to just feet and then multiply: