Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[RepeatingDecimal] instead.

pdexpand returns the periodic decimal expansion of the given rational number n.

Every rational number has a periodic (or terminating) decimal expansion. The converse is also true; a periodic expansion always represents a rational number.

The result is returned as in the form $'\mathrm{PDEXPAND}'\left(s\,q\,\mathrm{np}\,p\right)$ where s is the sign of n, q the positive integer part, np the non-periodic part, and p the periodic part of n.

Use convert/rational to find the rational number of a periodic decimal expansion.

The command with(numtheory,pdexpand) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{numtheory}\right)\:$

$\mathrm{pdexpand}\left(\frac{1}{7}\right)$

$\mathrm{PDEXPAND}\left(1\,0\,\left[\right]\,\left[1\,4\,2\,8\,5\,7\right]\right)$

$\mathrm{convert}\left(\,\mathrm{rational}\right)$

$\frac{1}{7}$

$\mathrm{pdexpand}\left(-\frac{83}{74}\right)$

$\mathrm{PDEXPAND}\left(\mathrm{-1}\,1\,\left[1\right]\,\left[2\,1\,6\right]\right)$

$\mathrm{convert}\left(\,\mathrm{rational}\right)$

$-\frac{83}{74}$