(11C) Arithmetic with Fractions

[Thomas Klemm]

(09-16-2018 10:06 PM)Dieter Wrote:  A better algorithm would first determine the LCM of the denominators.

But even then the nominator numerator would be 100 instead of 31 due to rounding to 10 significant digits:

\(\begin{align*}
\frac{123,456,799}{123,456}-\frac{988,297,396}{988,291} &= \frac{123,456,799\times1,537}{123,456\times1,537}-\frac{988,297,396\times192}{988,291\times192} \\
&= \frac{189,753,100,063}{189,751,872}-\frac{189,753,100,032}{189,751,872} \\
&= \frac{189,753,100,063-189,753,100,032}{189,751,872} \\
&= \frac{31}{189751872}
\end{align*}
\)

W. Kahan explains in the linked paper how to avoid this.

Kind regards
Thomas