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Brief answers to these questions were also given at the end of the text. Chapter 1 is a review of basic arithmetic and algebra, which may prove tobe useful to those students who need to have a quick refresher course in basic math. Each section contains sef-tests to help you identify gaps in your knowledge.
The remaining chapters follow the chapter sequence in the text, and are organized in corresponding sections. Only oxid-numbered solutions are provided. For example, figure Figure You should read this chapter during the first few days of your course. It is possible that the instructor will not be covering this basic material in class. Section 1. Each section is in turn composed of three parts: a pretest, a review, and an exit test.
Use the pretest to identify your strengths. If you have difficulties, you should read the review part carefully. If you have no difficulties, you could just refresh your memory by reading the review quickly. The exit test helps you assess what you have learned from studying the review. IF you remain unsure, you should discuss your problems with the instructor. Answers to all self-tests are on page Their sum apes is Find the numbers a 7. Which is the smallest number?
Let us suppose that we wish to measure the interval AB by means of the interval CD being the unit of measurement in figure 1. D PB Figure 1.
Suppose that this occurs 1g times. If, ater doing this, there is a remainder PB, then wwe divide the interval CD into ten parts and measure the remainder with these tenths. Suppose that m; ofthe tenths 40 tothe remainder. If aftr this there is still a remainder, we divide our new measure the tenth of CD into ten parts again ie, we divide CD into a hundred parts and repeat the same operation.
Either the process of measurement comes to an end or it continues. In either case we reach the result that inthe interval AB the whole interval CD is contained rn times, the tenths are contained m; times, the hundredths arecontained ns times, and so on.
Inother words, we derive the ratio AB to CD with increasing accuracy: up to tenths, to hundredths, and so on. A real number may be formally defined as «finite or infinite decimal fraction. Our definition will be complete if we say what we mean by the operations of addition and multiplication for decimal factions.
This is done in such a way that the operations de- fined on decimal fractions correspond to the operations on the magnitudes themselves. In defining the operations on real numbers, the di ficulty is that these numbers are represented in general by infinite decimal fractions, while the well-known rules for these operations refer to finite decimal fractions.
We take the cor- responding decimal fractions up to a given decimal place, say the millionth, and add them up. We are able to define the sur of two numbers with an arbitrary ddogreo of accuracy and in that sense their sum is completely defined up to the chosen degree of accuracy.
Definition 1. The set or collection of all rational numbers is denoted by Q. By a periodic decimal we mean a number that includes a repeating portion in its decimal part. Author : Carl P. Study Aids Posted on Economics, Mathematical Posted on Author : Caroline L. Author : E. Econometrics Posted on Education Posted on Mathematics Posted on Teaching a course with this book is enjoyable and easy. Search Search. Search Advanced Search close Close.
Request Permissions Exam copy. Overview Author s Praise. Summary A new edition of a comprehensive undergraduate mathematics text for economics students. Instructor Resources Downloadable instructor resources available for this title: instructor's manual, slides, and file of figures in the book.
Share Share Share email. Ray Rees. Endorsements Mathematics is the language of economics, and this book is an excellent introduction to that language.
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