ABSTRACT Both computer and calculators are limited at architecture.

ABSTRACT

Both computer and calculators are limited at architecture, operating system, and software, to near predetermined level of precision within decimal number presentation and calculation. Rational fractions exhibit either terminating or repeating decimal numbers. In decimal form, rational fractions that give rise to repeating decimals cannot be depicted exactly on computers or calculators. At a certain decimal place value, the decimal number must be truncated or cylindricaled This process leads to approximations, rather than exact numeric representation and calculation. Exact calculations can simply be performed by computers and calculators upon terminating decimal numbers. This paper demonstrates that for any rational fraction which makes a repeating decimal, there exists a base into which that number can be regenerateed so that it produces a terminating decimal. Therefore, [i]or[/i] part of to the other converting to appropriate bases computer and calculators can provide exact representations and operations upon newly formed terminating fractions.

BACKGROUND READING

1 L E Dickson, History of the Theory of Numbers, body Divisibility and Primality, G. E Stechert & Co of the present day York, NY (1934).

2 J H Mathews and K D Fink, Numerical systems Using MATLAB (3rd Edition), Prentice Hall, Upper Saddle River, NJ (1999)

Michael J Bosse*

Department of Mathematics

Indiana University of Pennsylvania

Indiana, Pennsylvania 15705

Fengshan Liu* and N R Nandakumar*

Department of Mathematics

Delaware State University

1200 N duPont Highway

Dover, Delaware 19901

mbosse@adelphia.net, fliu@dsc.edu, nnandaku@dsc.edu * Authors' names appear in alphabetical order.

...

Home