### 17.7 Rational Approximations

Function File: s = rat (x, tol)
Function File: [n, d] = rat (x, tol)

  Find a rational approximation to x within the tolerance defined by tol using a continued fraction expansion. For example:

      rat (pi) = 3 + 1/(7 + 1/16) = 355/113
      rat (e) = 3 + 1/(-4 + 1/(2 + 1/(5 + 1/(-2 + 1/(-7)))))
              = 1457/536

  Called with two arguments returns the numerator and denominator separately as two matrices.

  See also: rats.

Built-in Function: rats (x, len)

  Convert x into a rational approximation represented as a string. You can convert the string back into a matrix as follows:

      r = rats (hilb (4));
      x = str2num (r)

  The optional second argument defines the maximum length of the string representing the elements of x. By default len is 9.

  See also: format, rat.