By Lloyd Motz

We have designed and written this ebook. no longer as a textual content nor for the pro mathematician. yet for the final reader who's clearly interested in arithmetic as an exceptional intellec­ tual problem. and for the exact reader whose paintings calls for him to have a deeper knowing of arithmetic than he received at school. Readers within the first crew are interested in psychological leisure actions akin to chess. bridge. and numerous sorts of puzzles. yet they typically don't reply enthusiastically to arithmetic due to their unsatisfied studying studies with it in the course of their institution days. The readers within the secondgrouptum to arithmetic as a need. yet with painful resignation and substantial apprehension relating to their talents to grasp the department ofmathematics they wish of their paintings. In both case. the terror of and revulsion to arithmetic felt through those readers frequently stem from their past complex encounters with it. vii viii PREFACE This booklet will express those readers that those fears, frustrations, and basic antipathy are unwarranted, for, as acknowledged, it isn't a textbook choked with lengthy, uninteresting proofs and 1000's of difficulties, really it's an highbrow event, to be learn with excitement. It used to be written to be simply obtainable and with difficulty for the psychological tranquilityofthe reader who willexperience significant success while he/she sees the simplicity of uncomplicated arithmetic. The emphasis all through this booklet is at the transparent rationalization of mathematical con­ cepts.

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1, etc. Consider now the fraction 1/100 which is the product of the two fractions 1/10 x 1/10, also written as 1/102 or 10- 2 , when we use the negative exponent to represent the reciprocal of the fraction 1/100. We may also describe the fraction 1/100 as the quotient of the fraction 1/10 divided by 10. 01 written as a decimal, which leads to the following general rule: Any fraction with 100 as its denominator and an integer as its numerator can be written as a decimal by placing a dot in front of the last two digits of the integer in the numerator.

The number eight would still be 8 or 8 x tOO, but the number fifteen would be 3 x tOO + 101, so that on the base twelve, fifteen would be 13and the number twenty-four would be 2 x 10 1 or 20 and twenty-five would be 2 x 101 + 1, or 21 and so on. The base 2 is of particular importance in computers since only two symbols 0 and 1 are needed to express any number as powers of the base 2, which simplifies computations enormously. , on the base 2 are 1 (t), 10 (2), 11 (3), 100 (4), 101 (5), 110 (6), 111 (7) , tOOO (8), 1001 (9), 1010 (to), where the base 10 expressions for these numbers are written in parentheses after their base 2 representations.

This expression is an example of the decimal representation of fractions with 10 as their denominators. The general rule for expressing fractions with denominators of 10 as decimals is to place a dot in front of the last digit in the numerator. 5, etc. Since a fraction is merely another way of representing the division of one number by another (the numerator by the denominator), we can represent the division of 10 into any integer as a decimal by simply placing a dot in front of the last digit in the integer.

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