Reviewing Scientific Notation

Many of the numbers you will deal with will either be very large (e.g., Avogadro s number — 6.02 x 10 ) or very small (e.g., Planck s constant— 6.63 X 10 J s). Rather than write these numbers with all of the zeros, it is much easier to use scientific (or exponential) notation 

Determine M by moving the decimal point so that you leave only one nonzero digit to the left of the decimal. 

Determine n by counting the number of places that you moved the decimal point. If you move it to the left, the value of n is positive. If you move the decimal to the right, the value of n is negative. 

Sample Write the following numbers in scientific notation  

There are a variety of problem-solving strategies that you will use as you prepare for and take the AP exam. Dimensional analysis, sometimes known as the factor label method, is one of the most important of the techniques for you to master. 

To change a number into scientific notation you must do two things  

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The Great Lakes contain 22 700 km3 of water. Is there exactly that amount of water in the Great Lakes No, 22 700 km3 is an approximate value. The actual volume could be anywhere from 22 651 km3 to 22 749 km3. You can use scientific notation to rewrite 22 700 km3 as 2.27 x 104 km. This shows that only three digits are significant. (See Appendix E at the back of the book, if you would like to review scientific notation.)... 

Student Annotation Appendix 1 reviews scientific notation. 

Chemistry is full of calculations. Our basic goal is to help you develop the knowledge and strategies you need to solve these problems. In this chapter, you will review the Metric system and basic problem solving techniques, such as the Unit Conversion Method. Your textbook or instructor may call this problem solving method by a different name, such as the Factor-Label Method and Dimensional Analysis. Check with your instructor or textbook as to for which SI (Metric) prefixes and SI-English relationships will you be responsible. Finally, be familiar with the operation of your calculator. (A scientific calculator will be the best for chemistry purposes.) Be sure that you can correctly enter a number in scientific notation. It would also help if you set your calculator to display in scientific notation. Refer to your calculator s manual for information about your specific brand and model. Chemistry is not a spectator sport, so you will need to Practice, Practice, Practice. 

Another way to determine the number of significant figures in a number is to express it in scientific (exponential) notation. The number of digits shown is the number of significant figures. For example 2.305 x 10 5 would contain 4 significant figures. You may need to review exponential notation. 

Notice how numbers that are either very large or very small are indicated in Table 1.4 using an exponential format called scientific notation. For example, the number 55,000 is written in scientific notation as 5.5 X 104, and the number 0.003 20 as 3.20 X 10 3. Review Appendix A if you are uncomfortable with scientific notation or if you need to brush up on how to do mathematical manipulations on numbers with exponents. 

A good portion of the AP Chemistry Test deals with calculations, either with or without the aid of a calculator. For all of these problems, there are two different components—the chemistry component and the math component. Most of this book is devoted to a review of the chemistry component of the problems, but this chapter is designed to review a few important mathematical skills that you will need to know as you work through the problems. Three skills that are critical to success on the AP Chemistry Test use significant figures, scientific notation, and dimensional analysis. 

Appendices A, B, and C are important pedagogically. Appendix A discusses experimental error and scientific notation. Appendix B introduces the SI system of units used throughout the book and describes the methods used for converting units. Appendix B also provides a brief review of some fundamental principles in physics,... 

The Math Handbook helps you review and sharpen your math skills so you get the most out of understanding how to solve math problems involving chemistry. Reviewing the rules for mathematical operations such as scientific notation, fractions, and logarithms can also help you boost your test scores. 

The prefixes in Table 2.4 are represented by the powers of 10 used in scientific, or exponential, notation for writing large and small numbers. For example, 10 = 10 X 10 X 10 = 1000. Appendix B reviews this notation. 

If you are familiar with scientific nofa-fion, you will see fhaf fhe following statemenfs are frue. To convert from % to ppm or ppb, simply multiply by 10" or 10, respectively. To convert from ppb fo ppm or %, simply divide by lO" or 10. respectively. To review the use of scientific notation, see Appendix B. 

Scientific notation, in which large and small numbers are represented by a number between 1 and multiplied by 10 with an exponent, is reviewed in Appendix B. 

NEW BASIC MATH SKILLS APPENDIX To aid the flow of introductory chemistry material in Chapter I, a review of topics in basic mathematics skills, including scientific notation and use of significant figures, with numerous examples, now appears in Appendix A. Related exercises remain in the Measurements and Calculations section at the end of Chapter 1. 

The SI system is based on seven fundamental units, or base units, each identified with a physical quantity (Table 1.1). All other units are derived units, combinations of the seven base units. For example, the derived unit for speed, meters per second (m/s), is the base unit for length (m) divided by the base unit for time (s). (Derived units that are a ratio of base units can be used as conversion factors.) For quantities much smaller or larger than the base unit, we use decimal prefixes and exponential (scientific) notation (Table 1.2). (If you need a review of exponential notation, see Appendix A.) Because the prefixes are based on powers of 10, SI units are easier to use in calculations than English units. 

Only a few basic mathematical skills are required for the study of general chemistry. But to concentrate your attention on the concepts of chemistry, you will find it necessary to have a firm grasp of these basic mathematical skills. In this appendix, we will review scientific (or exponential) notation, logarithms, simple algebraic operations, the solution of quadratic equations, and the plotting of straight-line graphs. 

Chapter 4 provides an opportunity for you to apply the chemical calculation skills you learned as a result of studying Chapter 3. Scientific notation, dimensional analysis, metric units, significant figures, temperature, proportionality, and density are needed to understand the concepts and work the problems in this introduction to gases. You may find that you occasionally need to review Chapter 3 as you study this chapter. If so, don t be concerned. All successful science students review and refine their understanding of prior material-even content from prior coursework—as they learn new ideas. In fact, we selected the topics of Chapter 4, in part to give you a chance to apply your calculating skills immediately after you learned them. 

Review math concepts used In chemistry place values, positive and negative numbers, percentages, solving equations, interpreting graphs, and writing numbers in scientific notation. 

Chapter 1, Chemistry in Our Lives, introduces the concepts of chemicals and chemistry, discusses the scientific method in everyday terms, guides students in developing a study plan for learning chanistry, and now has a new section of Key Math Skills, which reviews basic math needed for learning chemistry. The section on Writing Numbers in Scientific Notation was moved from Chapter 2 and is now part of the section of Key Math Skills in this chapter. 

The review articles on the interpretation of band spectra and the agreement on notation for diatomic molecules in which MulUken was actively involved marked the end of the period of MuUiken s scientific life in which he successfully worked out a systematization of the data on the spectra of diatomic molecules and a concomitant understanding of their structure. He then shifted to the study of polyatomic molecules and to valence-related problems. The transition was accompanied by an increasing awareness of the necessity to propagandize among chemists his work on band spectra, his preliminary ideas on the chemical bond, and his criticism of Heitler and London s suggestions. 

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