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all work. If you are not sure how to read the indi-
cated operations, see the section on “Symbols and
Operations” in appendix A.
Step 7: Now ask yourself if the number seems reasonable for
the question that was asked, and ask yourself if the
unit is correct. For example, 250 m/s is way too fast for
a running student, and the unit for speed is not liters.

Step 8: Draw a box around your answer (numbers and units)
to communicate that you have found what you were
looking for. The box is a signal that you have finished
your work on this problem.

For an example problem, use the equation from the pre-
vious section describing the variables of a fuel pump, V = tk,
to predict how long it will take to fill an empty 80-liter tank.
Assume k = 40 L/min.

Step 1
V = 80 L V = tk Step 2
FIGURE 1.13 The ratio of the circumference of any circle to
tk
=
the diameter of that circle is always π, a numerical constant that k = 80 L/min V _ _ Step 3

is usually rounded to 3.14. Pi does not have units because they t = ? k k
cancel in the ratio. V _
t =

k
Step 2: Inspect the list of variables and the unknown, and
(no conversion needed for this problem) Step 4
identify the equation that expresses a relationship be-
tween these variables. A list of equations discussed in _
80 L

each chapter is found at the end of that chapter. Write t = L _ Step 5

the equation on the right side of your paper, opposite 40
min
the list of symbols and quantities. 80 _ L _ _
min

= × Step 6

Step 3: If necessary, solve the equation for the variable in 40 1 L
question. This step must be done before substituting = 2 min Step 7
any numbers or units in the equation. This simplifies
things and keeps down confusion that might otherwise Note that procedure step 4 was not required in this solution.
result. If you need help solving an equation, see the This formatting procedure will be demonstrated through-
section on this topic in appendix A. out this text in example problems and in the solutions to prob-
lems found in appendix E. Note that each of the chapters with
Step 4: If necessary, convert unlike units so they are all the
problems has parallel exercises. The exercises in groups A and
same. For example, if a time is given in seconds and a
B cover the same concepts. If you cannot work a problem in
speed is given in kilo meters per hour, you should con-
group B, look for the parallel problem in group A. You will find
vert the km/h to m/s. Again, this step should be done at
a solution to this problem, in the previously described format,
this point in the procedure to avoid confusion or incor-
in appendix E. Use this parallel problem solution as a model to
rect operations in a later step. If you need help convert-
help you solve the problem in group B. If you follow the sug-
ing units, see the section on this topic in appendix A.
gested formatting procedures and seek help from the appendix
Step 5: Now you are ready to substitute the number value as needed, you will find that problem solving is a simple, fun
and unit for each symbol in the equation (except the activity that helps you to learn to think in a new way. Here are
unknown). Note that it might sometimes be necessary some more considerations that will prove helpful.
to perform a “subroutine” to find a missing value and
1. Read the problem carefully, perhaps several times, to
unit for a needed variable.
understand the problem situation. Make a sketch to help
Step 6: Do the indicated mathematical operations on the you visualize and understand the problem in terms of the
numbers and on the units. This is easier to follow if real world.
you first separate the numbers and units, as shown in 2. Be alert for information that is not stated directly.
the example that follows and in the examples through- For example, if a moving object “comes to a stop,” you
out this text. Then perform the indicated operations know that the final velocity is zero, even though this
on the numbers and units as separate steps, showing was not stated outright. Likewise, questions about
12 CHAPTER 1 What Is Science? 1-12