The Number System and Common and Decimal Fractions
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
NUMERATION SYSTEMS ore than 5 000 years ago an Egyptian ruler recorded perhaps with a bit of exaggeration the capture of 120 000 prisoners 400 000 oxen and 1 422 000 goats This event was inscribed on a ceremonial mace or club that is now in a museum in Oxford England The ancient Egyptians developed the art of counting to a high degree but their system of numeration was very crude For example the number 1 000 was symbolized by a picture of a lotus flower and the number 2 000 was symbol ized by a picture of two lotus flowers growing out of a bush Although these symbols called hieroglyphics permitted the Egyptians to write large numbers the numeration system was clumsy and awkward to work with The number 999 for instance required 27 individual marks 10
King Narmer of ancient Egypt pictured above recorded great military feats and the capture of prisoners on maces and palettes He exaggerated these figures using hieroglyphics that represented very large numbers Hirmer Fotoarchiv Munich 11
