The Number System and Common and Decimal Fractions
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
The Number System and Common and Decimal Fractions In our system of numeration we use ten symbols called digitso 1 2 3 4 5 6 7 8 and 9 and combinations of these sym bols Our system of numeration is called the decimal or base ten system There is little doubt that our ten fingers influenced the development of a numeration system based on ten digits Other numeration systems were developed in early cultures and societies Two of the most common were the base five system related to the number of fingers on one hand and the base twenty system related to the number of fingers and toes In some languages the word for five is the same as the word for hand and the word for ten is the same as the word for two hands In our own language the word digit is a syn onym for the word finger that is ten digits ten fingers Still another early system of numera tion was a base sixty system developed by the Mesopotamians and used for centuries These ancient people divided the year into 360 days 6 x 60 To this day we still divide the hour into 60 minutes and the minute into 10 60 seconds Numeration systems of current interest include a binary or base two system 12
NUMERATION SYSTEMS used in computers and a base twelve or duo decimal system It is worthwhile for everyone to become familiar with the principles of the base twelve system of numeration and with those of base two base five or other systems Working with other bases gives deeper insight into the decimal system that most people in the modern world have used since childhood Before considering other sys tems however let us investigate our more familiar decimal system THE DECIMAL SYSTEM The ten digits of our numeration system are used to name the numbers of dots shown in these frames ODO BE E G 0 0 0 0 If we were not familiar with our system of numeration a reasonable method for naming the number of dots in frames showing 10 11 and 12 dots might be somewhat as follows 13
