How Do We Make Measurements?

In our daily lives we are constantly making measurements. We measure
ingredients for recipes, driving distances, gallons of gasoline, weights of
fruits and vegetables, and the timing of TV programs. Doctors and nurses
measure pulse rates, blood pressures, temperatures, and drug dosages.
Chemistry, like other sciences, is based on measurements.
A measurement consists of two parts: a number and a unit. A number
without a unit is usually meaningless. If you were told that a person’s
weight is 57, the information would be of very little use. Is it 57 pounds,
which would indicate that the person is very likely a child or a midget, or 57
kilograms, which is the weight of an average woman or a small man? Or is
it perhaps some other unit? Because so many units exist, a number by itself
is not enough; the unit must also be stated.
In the United States, most measurements are made with the English
system of units: pounds, miles, gallons, and so on. In most other parts of the
world, however, few people could tell you what a pound or an inch is. Most
countries use the metric system, a system that originated in France about
1800 and that has since spread throughout the world. Even in the United
States, metric measurements are slowly being introduced (Figure 1.2). For

example, many soft drinks and most alcoholic beverages now come in metric
sizes. Scientists in the United States have been using metric units all along.
Around 1960, international scientific organizations adopted another
system, called the International System of Units (abbreviated SI). The
SI is based on the metric system and uses some of the metric units. The
main difference is that the SI is more restrictive: It discourages the use of
certain metric units and favors others. Although the SI has advantages over
the older metric system, it also has significant disadvantages. For this reason
U.S. chemists have been very slow to adopt it. At this time, approximately
40 years after its introduction, not many U.S. chemists use the
entire SI, although some of its preferred units are gaining ground.
In this book we will use the metric system (Table 1.1). Occasionally we
will mention the preferred SI unit.
A. Length
The key to the metric system (and the SI) is that there is one base unit for each
kind of measurement and that other units are related to the base unit only by
powers of 10. As an example, let us look at measurements of length. In the English
system we have the inch, the foot, the yard, and the mile (not to mention
such older units as the league, furlong, ell, and rod). If you want to convert one
unit to another unit, you must memorize or look up these conversion factors:
5280 feet 1 mile
1760 yards 1 mile
3 feet 1 yard
12 inches 1 foot
All this is unnecessary in the metric system (and the SI). In both systems
the base unit of length is the meter (m). To convert to larger or smaller
units we do not use arbitrary numbers like 12, 3, and 1760, but only 10, 100,
1/100, 1/10, or other powers of 10. This means that to convert from one
metric or SI unit to another, we only have to move the decimal point. Furthermore,
the other units are named by putting prefixes in front of “meter,”
and these prefixes are the same throughout the metric system and the SI.
Table 1.2 lists the most important of these prefixes. If we put some of these
prefixes in front of “meter,” we have

1 kilometer (km) 1000 meters (m)
1 centimeter (cm) 0.01 meter
1 nanometer (nm) 1029 meter

1 kilometer (km) 1000 meters (m)
1 centimeter (cm) 0.01 meter
1 nanometer (nm) 1029 meter


Table 1.3 Some Conversion Factors Between the English
and Metric Systems
Length Mass Volume
1 in. 2.54 cm 1 oz 28.35 g 1 qt 0.946 L
1 m 39.37 in 1 lb 453.6 g 1 gal 3.785 L
1 mile 1.609 km 1 kg 2.205 lb 1 L 33.81 fl oz
1 g 15.43 grains 1 fl oz 29.57 mL
1 L 1.057 qt

For people who have grown up using English units, it is helpful to have some
idea of the size of metric units. Table 1.3 shows some conversion factors.
Some of these conversions are difficult enough that you will probably
not remember them and must, therefore, look them up when you need them.
Some are easier. For example, a meter is about the same as a yard. A kilogram
is a little over two pounds. There are almost four liters in a gallon.
These conversions may be important to you someday. For example, if you
rent a car in Europe, the price of gas listed on the sign at the gas station will
be in Euros per liter. When you realize that you are spending a dollar per
liter and you know that there are almost four liters to a gallon, you will realize
why so many people take the bus or a train instead.
B. Volume
Volume is space. The volume of a liquid, solid, or gas is the space occupied
by that substance. The base unit of volume in the metric system is the liter
(L). This unit is a little larger than a quart (Table 1.3). The only other common
metric unit for volume is the milliliter (mL), which is equal to 1023 L.
1 mL 0.001 L
1000 mL 1 L
One milliliter is exactly equal to one cubic centimeter (cc or cm3):
1 mL 1 cc
Thus there are 1000 cc in 1 L.
C. Mass
Mass is the quantity of matter in an object. The base unit of mass in the
metric system is the gram (g). As always in the metric system, larger and
smaller units are indicated by prefixes. The ones in common use are
1 kilogram (kg) 1000 g
1 milligram (mg) 0.001 g
The gram is a small unit; there are 453.6 g in one pound (Table 1.3).
We use a device called a balance to measure mass. Figure 1.3 shows two
types of laboratory balances.
There is a fundamental difference between mass and weight. Mass is
independent of location. The mass of a stone, for example, is the same
whether we measure it at sea level, on top of a mountain, or in the depths of
a mine. In contrast, weight is not independent of location. Weight is the