Introductory Chemistry: A Foundation - Zumdahl S.S., DeCoste D.J. 2019

Measurements and Calculations


· To learn the English, metric, and SI systems of measurement.

The part of a measurement called a unit tells us what scale or standard is being used to represent the results of the measurement. From the earliest days of civilization, trade has required common units. For example, if a farmer from one region wanted to trade some of his grain for the gold of a miner who lived in another region, the two people had to have common standards (units) for measuring the amount of the grain and the weight of the gold.

The need for common units also applies to scientists, who measure quantities such as mass, length, time, and temperature. If every scientist had her or his own personal set of units, complete chaos would result. Unfortunately, although standard systems of units did arise, different systems were adopted in different parts of the world. The two most widely used systems are the English system used in the United States and the metric system used in most of the rest of the industrialized world.

Critical Thinking

· What if you were not allowed to use units for one day? How would this affect your life for that day?

The metric system has long been preferred for most scientific work. In 1960 an international agreement set up a comprehensive system of units called the International System (le Système Internationale in French), or SI . The SI units are based on the metric system and units derived from the metric system. The most important fundamental SI units are listed in Table 2.1. Later in this chapter we will discuss how to manipulate some of these units.

Table 2.1. Some Fundamental SI Units

Physical Quantity

Name of Unit














Chemistry in Focus Critical Units!

How important are conversions from one unit to another? If you ask the National Aeronautics and Space Administration (NASA), very important! In 1999 NASA lost a million Mars Climate Orbiter because of a failure to convert from English to metric units.

The problem arose because two teams working on the Mars mission were using different sets of units. NASA’s scientists at the Jet Propulsion Laboratory in Pasadena, California, assumed that the thrust data for the rockets on the Orbiter they received from Lockheed Martin Astronautics in Denver, which built the spacecraft, were in metric units. In reality, the units were English. As a result the Orbiter dipped kilometers lower into the Mars atmosphere than planned, and the friction from the atmosphere caused the craft to burn up.

NASA’s mistake refueled the controversy over whether Congress should require the United States to switch to the metric system. About of the world now uses the metric system, and the United States is slowly switching from English to metric. For example, the automobile industry has adopted metric fasteners, and we buy our soda in -liter bottles.

Units can be very important. In fact, they can mean the difference between life and death on some occasions. In 1983, for example, a Canadian jetliner almost ran out of fuel when someone pumped pounds of fuel into the aircraft instead of kilograms. Remember to watch your units!

See Problem 2.156

Because the fundamental units are not always a convenient size, the SI system uses prefixes to change the size of the unit. The most commonly used prefixes are listed in Table 2.2. Although the fundamental unit for length is the meter (m), we can also use the decimeter (dm), which represents one-tenth of a meter; the centimeter (cm), which represents one one-hundredth of a meter; the millimeter (mm), which represents one one-thousandth of a meter; and so on. For example, it’s much more convenient to specify the diameter of a certain contact lens as cm than as m.

Table 2.2. The Commonly Used Prefixes in the Metric System




Power of for Scientific Notation














Measurements consist of both a number and a unit, and both are crucial. Just as you would not report a measurement without a numerical value, you would not report a measurement without a unit. You already use units in your daily life, whether you tell somebody, “Let’s meet in one hour” (hour is the unit) or you and your friends order two pizzas for dinner (pizza is the unit).