By Lloyd Motz

We have designed and written this booklet. no longer as a textual content nor for the pro mathematician. yet for the overall reader who's certainly drawn to arithmetic as an outstanding intellec tual problem. and for the specified reader whose paintings calls for him to have a deeper figuring out of arithmetic than he bought at school. Readers within the first crew are attracted to psychological leisure actions resembling chess. bridge. and numerous forms of puzzles. yet they typically don't reply enthusiastically to arithmetic due to their unsatisfied studying reviews with it in the course of their tuition days. The readers within the secondgrouptum to arithmetic as a need. yet with painful resignation and significant apprehension concerning their talents to grasp the department ofmathematics they want of their paintings. In both case. the terror of and revulsion to arithmetic felt through those readers frequently stem from their prior problematic encounters with it. vii viii PREFACE This booklet will exhibit those readers that those fears, frustrations, and common antipathy are unwarranted, for, as acknowledged, it isn't a textbook jam-packed with lengthy, dull proofs and hundreds of thousands of difficulties, quite it truly is an highbrow event, to be learn with excitement. It was once written to be simply available and with trouble for the psychological tranquilityofthe reader who willexperience enormous success whilst he/she sees the simplicity of uncomplicated arithmetic. The emphasis all through this booklet is at the transparent clarification of mathematical con cepts.

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When any fraction is changed to a decimal the digits in the decimal either end after a definite number or they repeat themselves in identical groups (cycles). 3333 . . 16666 . 142857142857 . . 1111 . . 0000 as often as we please, but there is no need to continue after the digits in the decimal repeat themselves singly or in groups as in the decimal for 1/7. We have already discussed the multiplication of fractions but it is worth repeating the rule that the product of any number of fractions is a fraction whose numerator is the product of all the individual numerators and whose denominator is the product of all the individual THE NUMBER SYSTEM 4S denominators.

Having received elaborate and precise instructions as to the problem at hand, the computer proceeds to grinding out figures at a prodigious rate . In the course of this operation it in many ways apes the process of a human calculation. The machine can organize its problem into separate steps; it can use the results obtained in one step to execute the next; sometimes partial results are laid aside, that is, 'remembered,' while an intermediate step is carried through; trial and error methods are frequently used.

This may at first appear puzzling, if not meaningless, when the integer in the numerator consists of a single digit such as 7 giving the fraction 7/100. What does placing a dot in front of the last two digits mean if we have only one digit? , since a zero in front of an integer does not change its value. 07, or 7/100 (seven hundredths) . In the same way we obtain the decimal equivalent of thousandths by placing a dot in front of the last three digits, and so on. 126 means one hundred and twenty-six thousandths (126/1000 or 63/500).