28
Self-Check
A student learns that 10
4
bacteria, standing in line to register for classes at
Paramecium Community College, would form a queue of this size:
The student concludes that 10
2
bacteria would form a line of this length:
Why is the student incorrect.
0.9Conversions
I suggest you avoid memorizing lots of conversion factors between SI
units and U.S. units. Suppose the United Nations sends its black helicopters
to invade California (after all who wouldn’t rather live here than in New
York City.), and institutes water fluoridation and the SI, making the use of
inches and pounds into a crime punishable by death. I think you could get
by with only two mental conversion factors:
1 inch = 2.54 cm
An object with a weight on Earth of 2.2 lb has a mass of 1 kg.
The first one is the present definition of the inch, so it’s exact. The
second one is not exact, but is good enough for most purposes. The pound
is a unit of gravitational force, while the kg is a unit of mass, which mea-
sures how hard it is to accelerate an object, not how hard gravity pulls on it.
Therefore it would be incorrect to say that 2.2 lb literally equaled 1 kg, even
approximately.
More important than memorizing conversion factors is understanding
the right method for doing conversions. Even within the SI, you may need
to convert, say, from grams to kilograms. Different people have different
ways of thinking about conversions, but the method I’ll describe here is
systematic and easy to understand. The idea is that if 1 kg and 1000 g
represent the same mass, then we can consider a fraction like
10
3
g
1kg
to be a way of expressing the number one. This may bother you. For
instance, if you type 1000/1 into your calculator, you will get 1000, not
one. Again, different people have different ways of thinking about it, but
the justification is that it helps us to do conversions, and it works! Now if
we want to convert 0.7 kg to units of grams, we can multiply 0.7 kg by the
number one:
0.7kg
×
10
3
g
1kg
If you’re willing to treat symbols such as “kg” as if they were variables as
used in algebra (which they’re really not), you can then cancel the kg on top
with the kg on the bottom, resulting in
Chapter 0Introduction and Review
Exponents have to do with multiplication, not addition. The first line should be 100 times longer than the second,
not just twice as long.