Units of Measure
Treating Units Like Numbers
Units of Measure must be used to correctly
solve Algebra 1 word problems. It is easy to find the conversions for
one unit to another. You can use your favorite search engine to easily
find conversion factor tables.
So finding the conversion factors is not the problem. The problem is - How
do you use these factors to solve problems without making a mistake in converting Units of Measure?
When you convert say inches to feet it is pretty easy to see that you
divide the inches by 12. However, when you do more complex conversions
with units you are less familiar with it becomes more difficult to know
if you should multiply or divide by the conversion factor.
This website is dedicated to sharing with your our Homework-Help-Secrets
that make it easier for you to get good grades with less effort. The
secret you are about to learn we call the Unit Equation Approach to
converting from one Unit of Measure to another.
The Unit Equation Approach is simply treating Units of Measure like numbers as
illustrated for single conversions of Units of Measure in the picture below.
Unit Equation Approach - Single Conversions
We start our explanation of the Unit Equation Approach with the
simple single conversion of inches to feet. In this approach we not only
perform the arithmetic operations of multiplication and division on the
numbers but also on the units.
We see that 60 inches is multiplied by the conversion factor for inches
to feet of 1 ft/12 inches. We have to put the inches on the bottom
(denominator) and the feet on the top (numerator) in order for the units
of inches to cancel out as shown by the strike mark in the picture.
So we see that 60 inches is equal to 5 feet.
In the second example we convert 500 grams to kilograms. Here we must
multiply by the conversion factor 1 kg/1,000 g. In this case we have to
put the grams in the denominator so it will cancel the gram unit in the
500 g as shown in the picture. So we see that 500 gram is equal to 0.5
kilogram.
In the third single conversion example we convert miles to feet. In
this case we must multiply by the conversion factor of 5,280 ft/1 mi
putting miles in the denominator so it will cancel out the mi units of
1.5 mi. So we see that 1.5 miles is equal to 7,920 ft.
We give two examples of more complex multiple conversions of Units of
Measure in the picture below.
Unit Equation Approach - Multiple Conversions
For the first multiple conversion example we convert Miles/Hour
(mph) to Feet/Second (fps). We see that first we must multiply by the
conversion factor for ft-mi in the form of 5,280 ft/1 mi so that the
miles will be in the denominator and so cancel out the mi units of 60
mi/hr as shown by the black strike through.
Second, we must convert hours to minutes by multiplying by 1 hr/60 min
so that hr is in the numerator and so will cancel out the hr in the
denominator of 60 mi/hr as shown by the red reverse strike through.
Third and last, we convert minutes to seconds by multiplying by the
conversion factor for min to sec in the form of 1 min/60 sec so that min
is in the numerator and will cancel out the min in the denominator of
1hr/60min as shown by the blue X.
So, we see that the only units left not canceled out are ft/sec and
thus, 60 mi/hr equals 88 ft/sec.
In the second multiple conversion example we convert Gram/Milliliter to
Pounds/Gallon. We see first that we must multiply by the conversion
factor for lbs-g in the form of 1 lbs/453.6 g so that the g is in the
denominator and will cancel the g in 1 g/1 ml as shown by the black
strike through.
Second, we must convert milliliters to liters by multiplying by the
conversion factor in the form of 1,000 ml/1 L such that the ml is in the
numerator and will cancel out the ml in the denominator of 1 g/1 ml as
shown by the red reverse strike through.
Third and last, we convert liters to gallons by multiplying the
conversion factor for L-gal in the form of 3.7852 L/1 gal so that the L
is in the numerator and will cancel the L in the denominator of 1,000
ml/1 L as shown by the blue X.
So, we see that the only units left not canceled out are lbs/gal and
thus, 1 g/1 ml (which is the density of water) is equal to 8.345
lbs/gal.
The Unit Equation Approach can be used to convert any Unit of Measure
without having to worry if you should multiply or divide by the
conversion factor you find in the tables. You simply put the conversion
factor in the form that allows you to cancel out the units that you
don't want and proceed to the next unit conversion.
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