#### 12.2.54 rational, rationalize [Function] ¶

`rational` number ⇒ rational

`rationalize` number ⇒ rational

#### Arguments and Values:: ¶

number—a real.

rational—a rational.

#### Description:: ¶

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.

#### Examples:: ¶

     (rational 0) ⇒  0
     (rationalize -11/100) ⇒  -11/100
     (rational .1) ⇒  13421773/134217728 ;implementation-dependent
     (rationalize .1) ⇒  1/10

#### Affected By:: ¶

The implementation.

#### Exceptional Situations:: ¶

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

#### Notes:: ¶

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.