### 7.2.1 Transform a floating point number into a rational

Rational numbers can be approximated by floating point numbers, but since floating point numbers are not exact, they cannot typically be converted back to the original rational number. However, the float2rational or exact command will try convert a floating point to a nearby rational number.

- float2rational takes d, a floating point number.
- float2rational(d) returns a rational number q close to d; namely such that |d−q|<epsilon, where epsilon is defined in the CAS configuration (Cfg menu, see Section 2.5.7, item 2.5.7) or with the cas_setup command (see Section 2.5.10).

#### Examples

float2rational(0.3670520231)

Output for epsilon=1e-10:

127
346

evalf(363/28)

12.9642857143 |  |  |  |  |  |  |  |  |  |

float2rational(12.9642857143)

363
28

If two representations are mixed, for example:

1/2+0.7

the rational is converted to a float.

1.2 |  |  |  |  |  |  |  |  |  |

1/2+float2rational(0.7)

6
5