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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:
Click for copyable input
Click for copyable input
Use exact numeric quantities:
FractionalPart threads element-wise over lists:
Manipulate FractionalPart symbolically:
Evaluate an integral:
TraditionalForm formatting:
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:
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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