This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# FractionalPart

 FractionalPart[x]gives the fractional part of x.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• FractionalPart[x] in effect takes all digits to the right of the decimal point and drops the others.
• FractionalPart[x] yields a result when x is any numeric quantity, whether or not it is an explicit number.
• For exact numeric quantities, FractionalPart internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable \$MaxExtraPrecision.
• FractionalPart applies separately to real and imaginary parts of complex numbers.
Find the fractional part of a real number:
Find the fractional part of a real number:
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 Scope   (5)
Use exact numeric quantities:
Manipulate FractionalPart symbolically:
Evaluate an integral:
Negative numbers:
Complex numbers:
Infinite arguments give symbolic results:
Series expansion:
 Applications   (6)
Plot fractional parts of powers:
Plot fractional parts of powers of a Pisot number:
Iterate the shift map with a rational initial condition:
Irrational initial condition:
See the degradation in precision for approximate real numbers:
Make a Bernoulli polynomial periodic and plot it:
De-nest FractionalPart functions:
Guard digits influence the result of FractionalPart:
Numerical decision procedures with default settings cannot simplify this expression:
Using a larger setting for \$MaxExtraPrecision gives the expected result:
Convergence of the Fourier series of FractionalPart:
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