The Number System and Common and Decimal Fractions
Introduction I magine being a Roman citizen confronted with a math problem 2 000 years ago In the days of ancient Rome if a merchant or tax collector needed to calculate thirteen plus sixty nine he would use pebbles or metal disks as counters Romans moved these pebbles on marked boards to work out problems Later the counters were strung on wires mounted in a frame People used this device called an abacus instead of working out their problems in writing because they could not carry ten conveniently with their cumbersome system of writing numbers The Roman numeral sys tem in which letters represent numbers was dominant in Europe for nearly 2 000 years However even simple addition of Roman numerals in our example XIII LXIX was difficult The math world made a great advancement when the Hindu Arabic numeral system sim plified matters several hundred years later by replacing a cumbersome XXIV with the sleek expression 24 In math efficiency is key With a simplified decimal system of numeration mathematicians could now concentrate on 10 depth and meaningful discovery in the field
Ancient Roman merchants and tax collectors calculated math problems using a device called an abacus such as the one shown here Science Society Picture Library Getty Images of mathematics and mathematicians would of course find the new HindurArabic numerals easier to read and write In this text the reader will be pulled into the world of how we conceive of count and write numbers explaining both the importance and practical applications of each number system
The Number System and Common and Decimal Fractions Today's student might remark But calculators and computers yield exact com putations for us This is true But the computer must first be programmed or told how to perform The number system that calculators and computers use is what is called a binary system which might be a new concept for the reader As explained in this book an understanding of the underlying basis of modern mathematical tools including the binary system will enhance the reader s skills in using both the tools and the math Does this suggest that for instance the decimal system that the math student is familiar with must now be tossed out The answer of course is no The reader will also find new ways to explore those systems with which he or she is already quite familiar Lucid and captivating explanations will enhance understanding of the number systems under lying all mathematics such as techniques for converting from one base system to another applications of various base systems con version of common fractions into decimal fractions and conversion of decimals back into common fractions 10
INTRODUCTION Included are hints and practice problems that make the mastery of these techniques eas ier to accomplish Each example is shown with a simple illustration without which the reader might easily fall into little errors and traps that could make the calculation frustrating When asked to add mixed fractions even the best of math students might be initially stumped for lack of just a single hint that would get the whole process started This book of number systems decimals and fractions and the many techniques it explains is therefore a handy tool for any middle or high school student or his or her parent to have on the shelf for both problem solving and historical
