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.