At certain points, there will be a need to convert between measurement systems when there are multiple units and types of measurements being used to describe an object or process. Usually, these types of problems involve rates.

For example, in describing the density of steel using customary units, you would say that the density of steel is 490 pounds per cubic foot (490 lb over ft lb ft³ ). However, most manufacturers of steel, as well as the machinery used in the process, rate the density of steel using the metric system. This is because steel is manufactured and shipped all over the world.

Knowing that the density of steel in customary units is 490 lb over ft lb ft³ , what is the density of steel in grams per cubic centimeter (g over cm g cm³ ) ?

• Does this problem require you to convert from metric/SI units to customary units or from customary units to metric/SI units?

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  You will be converting from customary units to metric/SI units.

• Which units will you be converting in this problem?

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  You will be converting pounds to grams and cubic feet to cubic centimeters.

In this situation, you are combining mass/weight and volume measurements, which means that you will need the following two important conversion factors:

Just as you have done before, you will need to write out a plan to follow for the unit conversion. There are two distinct conversions that you will perform; however, let's work on them simultaneously. Be sure to note where your units are in the fraction (numerator or denominator) and cancel them out so that you are left with grams per cubic centimeter.

• What is your plan to perform the unit conversions?

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  Convert the pounds to grams directly. Convert the cubic feet to cubic inches, and then the cubic inches to cubic centimeters.

Click on the image below to access the applet. Use the applet to perform dimensional analysis in order to perform the conversion.

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Use the video below to check your answer.

Pause and Reflect

How does unit conversion for rates compare with unit conversion for quantities?

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With rates, there are two sets of units that must be converted: the units in the original numerator, and the units in the original denominator. With quantities, there is only one set of units in the numerator, and the denominator is 1.

Practice

Source: Concrete Basement, H.Raab, Wikimedia

1. In the construction industry, normal concrete is reported to have a density of 2.3 grams per cubic centimeter
   g over cm ( g cm³ ). However, in the United States, concrete densities are reported in pounds per cubic foot (lb over ft lb ft³ ). What is the density of normal concrete in the United States in customary units
   (lb over ft lb ft³ )?

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   Convert the grams to pounds and the cubic centimeters to cubic feet. Use the conversion factors or the applet from the previous part of the lesson.
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2. The salinity of seawater is approximately 35 grams per liter. The salinity of three Texas bays is shown in the table below.
   
   
   

   If 1 ounce = 28.35 grams, 1 quart = 0.95 liters, 1 in.³ = 16.4 cm³, and 1 liter = 1000 cm³, which bay has a salinity that is greater than seawater?

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   Use unit conversions to convert each bay’s salinity to grams per liter.

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