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rational, rationalize

rational, rationalize Function

Syntax:

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.

Expanded Reference: rational, rationalize

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