rational number => rational
rationalize number => rational
Arguments and Values:
rational and rationalize convert reals to rationals.
If number is already rational, it is returned.
If number is a float, rational returns a rational that is mathematically equal in value to the float. rationalize returns a rational that approximates the float to the accuracy of the underlying floating-point representation.
rational assumes that the float is completely accurate.
rationalize assumes that the float is accurate only to the precision of the floating-point representation.
(rational 0) => 0 (rationalize -11/100) => -11/100 (rational .1) => 13421773/134217728 ;implementation-dependent (rationalize .1) => 1/10
Side Effects: None.
Should signal an error of type type-error if number is not a real. Might signal arithmetic-error.
See Also: None.
It is always the case that
(float (rational x) x) == xand
(float (rationalize x) x) == xThat is, rationalizing a float by either method and then converting it back to a float of the same format produces the original number.