Working through this chapter of the study guide will enable you to:

1. See how our senses act as the basic inputs for information about the world around us.
2. Learn to distinguish between fundamental quantities, standard units, and derived units.
3. Understand why the units in which measurements are made are just as important as the actual numbers that are recorded when you take the measurement.
4. Discuss some of the various systems of units that are currently in use.
5. Express quantities involving numbers of all sizes using powers-of-10 notation.
6. Convert measurements from one system of units into another system, or from one unit to another within a given system.

Discussion

We are glad that you have decided to let us help you learn about physical science by using our student study guide. By this time you have probably had at least one lecture covering measurement, and you should have read the first several sections of Chapter 1 in the textbook. If this is not the case, you are not quite ready to utilize the full potential of this study guide. Please do not try to use this study guide as your sole source for learning physical science. This study guide is designed to supplement the information you get in class and that you read in the textbook. It is not a stand-alone reference source.

One of the first things that must be done in any course of study is to establish a language that can be used by instructors and students alike when dealing with that subject. In science, an extremely important part of this language is the measurement of various quantities, but this is just not possible unless a good system of units has been established and is understood by everyone. As you proceed in this course, you will soon learn the definitions of many new terms that have specific meanings when applied to physical science. For now, we are going to concentrate on the basic definitions necessary to take and understand measurements. We will also review some of the relationships among these measurements, and explore how we can use them in our everyday lives.


Section  1.1The Senses

Interactions with our environment are very important to our safety and to our ability to cope with the changing conditions around us. These interactions depend on the uses we make of our senses: sight, hearing, smell, touch, and taste. Not only must we use our senses, but we often must also quantify information about the things around us before we can communicate this information to others. Making accurate and precise measurements helps us to improve our understanding of the world and enables us to predict how future events will turn out under similar circumstances. The basics of measurement must, therefore, be learned before we can proceed further with our study of the interesting physical principles that relate to our everyday lives. We must, however, be careful about the information derived from our senses because casual interpretation of this information can sometimes be deceiving, as in the case where warm water feels quite hot if we place our cold hand in it after coming in from playing in the snow, but the same warm water could feel cool to our hand if we had been soaking in a very hot bath before placing our hand in it.


Section  1.2Introduction to the Scientific Method

When we study physical science, we should identify the fundamental quantities that relate to the common phenomena that we are studying. Using a well-established method of investigation called the scientific method enables us to develop working definitions (often expressed in equation form) and finally theories that explain the interaction of these concepts with actual physical processes. Without such definitions, meaningful communication about the processes occurring in the world around us would be impossible. It is, therefore, extremely important that a thorough understanding of the interrelationship between measurement and theory be understood early in our study of the physical sciences.

Equations are often cited by students as the biggest "problem" that they have in a science course. This is unfortunate because equations are not put into books to confuse you; they are designed simply as a shorthand notation to aid you in writing and remembering the specific relationships between important quantities. If you don't understand an equation, it is usually not because the equation itself is confusing, but simply because you don't yet understand the underlying concepts, and the relationships between those concepts, that the equation is designed to help you remember.


Section  1.3Standard Units and Systems of Units

The identification of the fundamental quantities in which all measurements are taken (length, mass, and time) allows us to better comprehend our physical environment and discuss it intelligently. Once we have identified these fundamental quantities, it is necessary to establish exact meanings for these quantities in the form of standardized definitions and then to assign standard units to them. Without standardized measurements it would not be possible to record exact information about the various concepts of interest in science or in any other technical area of study in today's fast-paced society.

It is very important that we differentiate between standard units and fundamental quantities. Standard units are internationally accepted references used to define the size of the units used when discussing fundamental quantities. The units in almost all current systems of measurement are based on standards that have been adopted in the International System of Units (the SI) as shown in the following table. Appendix I lists the exact definitions of these seven standard units as established in the International System of Units. Make sure you look these over carefully and study not only the unit names but also their exact definitions.

FUNDAMENTAL QUANTITIES			SI UNITS
1.	length		meter (m)
2.	mass		kilogram (kg)
3.	time		second (s)
4.	electric current		ampere (A)
5.	temperature		kelvin (K)
6.	amount of substance		mole (mol)
7.	luminous intensity		candela (cd)

Section 1.4More on the Metric System

The standard units for length, mass, and time in both the metric system and SI can be best remembered by using the acronym mks system. The three letters, mks, stand for meter, kilogram, and second. Another acronym, cgs, can be used to describe a set of smaller units. Here cgs stands for centimeter, gram, and second. This system is currently treated as a derived system where the standard units kilogram, meter, and second are used to define the cgs equivalents. One of the greatest advantage of the metric system is that it is a decimal (base-10) system. Therefore, the metric system allows for easy conversion to larger and smaller units.


Section  1.5Derived Quantities and Conversion Factors

The above table lists the basic units found in the International System of Units, but it is equally important that you know how other units that are used every day are related to these seven standard definitions. Most units, such as the foot when used as a unit of length, are defined as some fractional part of the SI unit the meter. Even combinations of units (derived units) rely on the basic definitions laid down in the SI. Remember that derived units may be expressed as combinations of the fundamental SI units, such as the derived units used for velocity (m/s, mi/h, ft/s, etc.), or can be given entirely new names such as the watt, which is a power unit that combines mass, length, and time units. All derived units are based directly on the seven standard units shown above.

The application of conversion factors to change between units within a single system or between two different systems of units is explained fully in this section of the textbook, and several good examples of their use are presented in the Solved Problems section of this Study Guide. Please take time now to learn how to perform conversions, because this process will be needed quite often throughout this course. The inside back fly-leaf of the textbook provides a handy reference that can be consulted when measurements must be converted from one set of units into another.

Units can be combined by multiplication or cancelled by division, and sometimes may even be grouped together and given an entirely new name. An example of the latter is the unit "newton," which is used for force in the International System of Units. One newton is the same as the combination of units, "kilogram meter/second squared." Tracking units through a calculation to see how they combine or cancel is a good way to check the "setup" of a problem and make sure that the equation you are using is in the right format. Appendixes I - VII in the textbook can give you additional help with units and problem solving techniques. Although you may not need all the skills they offer this early in the course, we strongly recommend that you read them over now so that you will be familiar with their content and can thus find the relevant material in them when you need it later.


Section 1.6Significant Figures

When you make a measurement, it is simply a comparison of an unknown physical quantity with a standard unit. No measurement or answer to a problem is complete until both the number and the units have been specified. Get into the habit right now of giving complete answers to problems and numerical questions in such a way that both the number and the units are clearly stated. Don't forget that any measurement of a real physical quantity should also be accompanied by some estimation of the error involved in the measurement.

Errors are always present to some degree in any measurement, and the actual accuracy of a measurement must be expressed by the formatting of the number itself. The number of significant figures used in the number portion of any measurement indicates how precise the data is. To keep from implying unwarranted precision in a number than has actually been measured or calculated, it is often necessary to drop digits from the end of a calculated quantity. To this end, make sure that you know, and can use, the rules for rounding a number to the specific number of digits that are required in any given situation, as illustrated in the textbook and discussed in Appendix VII.


Section 1.7Powers-of-10 Notation

Another important mathematical tool is the use of powers-of-10 notation when very large or very small measurements are recorded. Many areas of physical science have come to rely heavily on this form of notation, and you will regularly see it in scientific writing. The exponent on the 10 is used simply to place the decimal point; large positive exponents represent very large numbers and large negative exponents indicate very small numbers (less than one). Powers-of-10 notation is also needed to specify the proper number of significant figures in a number when there are leading or trailing zeros needed to properly locate the decimal point. In such cases, powers-of-10 notation assures that no ambiguity in notation is present when the number is properly written.

This section of the textbook also explains the use of prefixes on units to adjust the size of these units so that they are more appropriate in certain measurements. As an example, the prefix kilo can be applied to a unit such as meter to construct a unit for length measurement (kilometer) that is 1000 times larger than the basic unit (meter) and which is more appropriate for discussing the distances between cities or the speed of an automobile than the base unit, meter, would be. Table 1.1 in Appendix I lists the prefixes representing powers of ten. Additional information on the mathematical manipulation of numbers expressed in powers-of-10 notation may be found in Appendix VI in the textbook.


Section  1.8Approach to Problem Solving

Problems may sometimes be solved by inspired guesses, but it is almost always better to proceed in a careful, systematic manner when working on them. The best procedure is to follow the three-step approach that is outlined in the textbook. (Also see Appendix II.) Reading the problem, identifying the known and unknown quantities, and then applying the proper physical relationship (often expressed as an equation) to the problem is quite likely to reward you with enough insight to solve the problem correctly.

Now it's time to get to the real heart of this web-based student study guide. The preceding review should be helpful, but many students have trouble with the questions and, in particular, the problems found on exams and quizzes. Our goal in this study guide is to cover most of the types of questions and problems that you may encounter on tests. The more practice you have in answering sample questions and working example problems, the better your understanding will be. You should also do better on examinations, no matter who makes up the test questions, but you have to play fair. If all you do is look over the answers and read over the problem solutions in this study guide, you will not be getting full benefit from this material.

Please try to answer the questions and work the problems by yourself before you look at the answers.

We don't expect you to get them all correct by yourself. If you could, you wouldn't need the help we are providing. On the other hand, if you let us do all the work, you will not learn to reason things out for yourself, and you will have missed a great deal of what this course is designed to teach you. Working with us, you will not only solve problems and answer questions yourself, but you can then check them to see how well you have learned the material. You can also correct any errors you may have made before your instructor discovers them for you on a test or quiz.

We hope you will enjoy this course, not only for the content of the subject matter but also for the personal satisfaction of doing well in a course that many students are afraid may be too difficult for them. We don't believe this is true, and we hope that after a few weeks of study you will agree with us. Remember that there are also questions and problems at the end of each chapter in the textbook. These, too, can aid you in perfecting your skills and testing your knowledge of this material.


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