Rationalize[x] takes Real numbers in x that are close to rationals, and converts them to exact Rational numbers.
Rationalize[x, dx] performs the conversion whenever the error made is smaller in magnitude than dx.
Example: Rationalize[3.78].
Rationalize[x, dx] yields the rational number with the smallest denominator that lies within dx of x.
Rationalize[N[Pi]] does not give a rational number, since there is none "sufficiently close" to N[Pi]. A rational number is considered "sufficiently close" to a Real if , where is chosen to be .
Rationalize[x, 0] converts any x to rational form. See The Mathematica Book on the web: Section 3.1.3. See also: Chop, Round, ContinuedFraction.
Rationalize[x] takes Real numbers in x that are close to rationals, and converts them to exact Rational numbers. 
. 
does not give a rational number, since there is none "sufficiently close" to N[Pi]. 
is considered "sufficiently close" to a Real 
if 
, where 
is chosen to be 
. 