The Foundations of Chemistry

Suppose we start with the equality

1 in.
2.54 cm

We can perform the same operation on

both sides of the equation. Let’s cube

both sides:

(1 in.)^3 
(2.54 cm)^3 
16.4 cm^3

so the quantity

 1

is a unit factor.

(1 in.)^3



(2.54 cm)^3

1-9 The Unit Factor Method (Dimensional Analysis) 29

involves shifting the decimal point to the leftby three places. How do we know to move

it to the left? We know that the gram is a larger unit of mass than the milligram, so the

number of grams in a given mass must be a smallernumber than the number of

milligrams. After you carry out many such conversions using unit factors, you will

probably begin to take such shortcuts. Always think about the answer, to see whether it

should be larger or smaller than the quantity was before conversion.

Unity raised to anypower is 1. Anyunit factor raised to a power is still a unit factor,
as the next example shows.

EXAMPLE 1-7 Volume Conversion

One liter is exactly 1000 cm^3. How many cubic inches are there in 1000 cm^3?

Plan

We would multiply by the unit factor 
2.

1

54

in

c

.

m

to convert cm to in. Here we require the cube
of this unit factor.

Solution

__? in.^3
1000 cm^3 

3


1000 cm^3 
61.0 in.^3

Example 1-7 shows that a unit factor cubedis still a unit factor.

EXAMPLE 1-8 Energy Conversion

A common unit of energy is the erg. Convert 3.74 10 ^2 erg to the SI units of energy, joules,
and kilojoules. One erg is exactly 1 10 ^7 joule (J).

Plan

The definition that relates ergs and joules is used to generate the needed unit factor. The sec-
ond conversion uses a unit factor that is based on the definition of the prefix kilo-.

Solution

__?J
3.74 10 ^2 erg
3.74 10 ^9 J

__?kJ
3.74 10 ^9 J
3.74 10 ^12 kJ

Conversions between the English and SI (metric) systems are conveniently made by
the unit factor method. Several conversion factors are listed in Table 1-7. It may be help-
ful to remember one each for

length 1 in.
2.54 cm (exact)

mass and weight 1 lb
454 g (near sea level)

volume 1 qt
0.946 L or 1 L
1.06 qt

1 kJ



1000 J

1  10 ^7 J



1 erg

1 in.



16.4 cm^3

1 in.



2.54 cm