Abstract

This chapter discusses computation with real numbers. The rational number methods of computation can be adapted to the solution of all computational problems with irrational numbers in a manner that is satisfactory for practical purposes. For any irrational number, there can be found a rational number that differs from it by less than an amount as small as that wished to be specified; such a rational number is, therefore, said to be approximately equal to the irrational number. Computations with irrational numbers can then be replaced by the same computations with approximately equal rational numbers to obtain sums, products, powers, differences, and quotients, which are approximately equal to the corresponding results for the given irrational numbers. The chapter discusses the practical methods of addition of real numbers by the method of decimal approximation, the decimal multiplication of real numbers, columnar algorithm for subtraction of natural numbers for the subtraction of decimal real numbers, and representation of the quotient of any two terminating decimals as the quotient of two integers for division

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