rational number → rational

rationalize number → rational

number — a real.

rational — a rational.

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

The implementation.

Should signal an error of type type-error if number is not a real. Might signal arithmetic-error.

It is always the case that

(float (rational x) x) ≡ x

and

(float (rationalize x) x) ≡ x

That is, rationalizing a float by either method and then converting it back to a float of the same format produces the original number.