The Foundations of Chemistry

EXAMPLE 1-3 Unit Factors

Express 1.47 mi in inches.

Plan

First we write down the units of what we wish to know, preceded by a question mark. Then
we set it equal to whatever we are given:

__? inches
1.47 miles

Then we choose unit factors to convert the given units (miles) to the desired units (inches):

miles 88n feet 88n inches

Solution

__? in.
1.47 mi
9.31 104 in. (calculator gives 93139.2)

Note that both miles and feet cancel, leaving only inches, the desired unit. Thus, there is no
ambiguity as to how the unit factors should be written. The answer contains three significant
figures because there are three significant figures in 1.47 miles.

12 in.



1 ft

5280 ft



1 mi

We relate (a) miles to feet and then

(b) feet to inches.

In the interest of clarity, cancellation

of units will be omitted in the

remainder of this book. You may find

it useful to continue the cancellation

of units.

1-9 The Unit Factor Method (Dimensional Analysis) 27

Within the SI and metric systems, many measurements are related to one another by
powers of ten.

EXAMPLE 1-4 Unit Conversions

The Ångstrom (Å) is a unit of length, 1 10 ^10 m, that provides a convenient scale on which
to express the radii of atoms. Radii of atoms are often expressed in nanometers. The radius of
a phosphorus atom is 1.10 Å. What is the distance expressed in centimeters and nanometers?

Problem-Solving Tip:Significant Figures

“How do defined quantities affect significant figures?”Any quantity that comes from a

definitionis exact, that is, it is known to an unlimited number of significant figures. In

Example 1-3, the quantities 5280 ft, 1 mile, 12 in., and 1 ft all come from definitions,

so they do not limit the significant figures in the answer.

Problem-Solving Tip:Think About Your Answer!

It is often helpful to ask yourself, “Does the answer make sense?” In Example 1-3, the

distance involved is more than a mile. We expect this distance to be many inches, so a

large answer is not surprising. Suppose we had mistakenly multiplied by the unit factor

(and not noticed that the units did not cancel properly); we would have

gotten the answer 3.34 10 ^3 in. (0.00334 in.), which we should have immediately rec-

ognized as nonsense!

1 mile



5280 feet