BUILT-IN MATHEMATICA SYMBOL

FractionalPart

FractionalPart[x]
gives the fractional part of x.

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:

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Use exact numeric quantities:

FractionalPart threads element-wise over lists:

Manipulate FractionalPart symbolically:

Evaluate an integral:

Negative numbers:

Complex numbers:

Infinite arguments give symbolic results:

Series expansion:

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: