Rationalize

Usage

• 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.

Notes

• 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

, where

is chosen to be

• Rationalize[x, 0] converts any x to rational form.

• See Section 3.2.2.

• See also: Chop, Round, ContinuedFraction, LatticeReduce.

• Related package: NumberTheory`Rationalize`.

• New in Version 1.

Further Examples