Exact computer calculations with infinitely repeating decimals

TL;DR: For any rational fraction which produces a repeating decimal, there exists a base into which that number can be converted so that it produces a terminating decimal, and through converting to appropriate bases computers and calculators can provide exact representations and operations on newly formed terminating fractions.

Abstract: Both computers and calculators are limited by architecture, operating system, and software, to some predetermined level of precision within decimal number presentation and calculation. Rational fractions produce either terminating or repeating decimal numbers. In decimal form, rational fractions that produce repeating decimals cannot be represented exactly on computers or calculators. At some decimal place value, the decimal number must be truncated or rounded. This process leads to approximations, rather than exact numeric representation and calculation. Exact calculations can only be performed by computers and calculators on terminating decimal numbers. This paper demonstrates that for any rational fraction which produces a repeating decimal, there exists a base into which that number can be converted so that it produces a terminating decimal. Therefore, through converting to appropriate bases computers and calculators can provide exact representations and operations on newly formed terminating fractions.