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#### 6.6.2.5 Exact and Inexact Numbers

R5RS requires that, with few exceptions, a calculation involving inexact
numbers always produces an inexact result. To meet this requirement,
Guile distinguishes between an exact integer value such as ‘`5`’ and
the corresponding inexact integer value which, to the limited precision
available, has no fractional part, and is printed as ‘`5.0`’. Guile
will only convert the latter value to the former when forced to do so by
an invocation of the `inexact->exact`

procedure.

The only exception to the above requirement is when the values of the
inexact numbers do not affect the result. For example `(expt n 0)`

is ‘`1`’ for any value of `n`

, therefore `(expt 5.0 0)`

is
permitted to return an exact ‘`1`’.

- Scheme Procedure:
**exact?***z* - C Function:
**scm_exact_p***(z)* Return

`#t`

if the number`z`is exact,`#f`

otherwise.(exact? 2) ⇒ #t (exact? 0.5) ⇒ #f (exact? (/ 2)) ⇒ #t

- C Function:
*int***scm_is_exact***(SCM z)* Return a

`1`

if the number`z`is exact, and`0`

otherwise. This is equivalent to`scm_is_true (scm_exact_p (z))`

.An alternate approch to testing the exactness of a number is to use

`scm_is_signed_integer`

or`scm_is_unsigned_integer`

.

- Scheme Procedure:
**inexact?***z* - C Function:
**scm_inexact_p***(z)* Return

`#t`

if the number`z`is inexact,`#f`

else.

- C Function:
*int***scm_is_inexact***(SCM z)* Return a

`1`

if the number`z`is inexact, and`0`

otherwise. This is equivalent to`scm_is_true (scm_inexact_p (z))`

.

- Scheme Procedure:
**inexact->exact***z* - C Function:
**scm_inexact_to_exact***(z)* Return an exact number that is numerically closest to

`z`, when there is one. For inexact rationals, Guile returns the exact rational that is numerically equal to the inexact rational. Inexact complex numbers with a non-zero imaginary part can not be made exact.(inexact->exact 0.5) ⇒ 1/2

The following happens because 12/10 is not exactly representable as a

`double`

(on most platforms). However, when reading a decimal number that has been marked exact with the “#e” prefix, Guile is able to represent it correctly.(inexact->exact 1.2) ⇒ 5404319552844595/4503599627370496 #e1.2 ⇒ 6/5

- Scheme Procedure:
**exact->inexact***z* - C Function:
**scm_exact_to_inexact***(z)* Convert the number

`z`to its inexact representation.

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