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### 4.11.2 Conversion to rational numbers

Each of the classes `cl_R`, `cl_RA`, `cl_F` defines the following operation:

`cl_RA rational (const type& x)`

Returns the value of `x` as an exact number. If `x` is already an exact number, this is `x`. If `x` is a floating-point number, the value is a rational number whose denominator is a power of 2.

In order to convert back, say, `(cl_F)(cl_R)"1/3"` to `1/3`, there is the function

`cl_RA rationalize (const cl_R& x)`

If `x` is a floating-point number, it actually represents an interval of real numbers, and this function returns the rational number with smallest denominator (and smallest numerator, in magnitude) which lies in this interval. If `x` is already an exact number, this function returns `x`.

If `x` is any float, one has

• `cl_float(rational(x),x) = x`
• `cl_float(rationalize(x),x) = x`

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