Chemistry Reference
In-Depth Information
The unit
hours
(h) in the time cancels the unit
hour
in the rate, leaving the unit
dollars
in the answer. Each unit is treated as a whole, no matter how many let-
ters it contains. Moreover, for the units to cancel, it does not matter if the unit
is singular (such as hour) or plural (such as hours). If we did not know the equa-
tion to calculate the total wages, we could have put down the time with the unit
hours
and multiplied by the rate of pay, which has the unit
hour
in its denom-
inator. The units tell us that we must multiply!
The previous calculation is an example of the use of the
factor label
method,
also called
dimensional analysis,
in which a quantity is multiplied by
a factor equal or equivalent to 1. The units included in the factor are the labels.
In the previous example, $9 is equivalent to 1 hour (h), and the calculation
changes the number of hours worked to the equivalent number of dollars. To
use the factor label method, first put down the given quantity, then multiply by
a
conversion factor
(a rate or ratio) that will change the units given to the units
desired for the answer. The factor may be a known constant or a value given
in the problem.
To summarize the steps of the factor label method:
1. Put down the
quantity
given (or, occasionally, a ratio to be converted).
2. Multiply the quantity by one or more factors—rates or ratios—which will
change the units
given
to those
required
for the answer. The conversion fac-
tors may be given in the problems, or they may be constants of known
value.
To use the factor label method effectively, we must know the units of all the
quantities involved.
Small diagrams that show the initial units and the final units connected by
the conversion factor are used in many places in this topic to show how to
change a quantity from one of the units to the other. For example, for calculat-
ing the student aide's total wages, we can use the following diagram:
To use the factor label method
effectively, we must know the
units of all the quantities being
dealt with and write them down
as part of the calculation.
Hours
Rate
Dollars
(
)
9 dollars
1 hour
30 hours
= 270 dollars
Diagrams like this will accompany many of the solutions to the in-text exam-
ples. To solve the practice problems and the problems at the end of the chap-
ter, make your own diagrams if necessary.
EXAMPLE 2.1
Change 5445 minutes to hours.
Solution
Put down the quantity given and then multiply it by a factor (which in this
case is known) that changes minutes to hours. The factor should have the unit
