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MachineNumberQ[expr]

returns True if expr is a machine‐precision real or complex number, and returns False otherwise.

Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Possible Issues  
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Tech Notes
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MachineNumberQ

MachineNumberQ[expr]

returns True if expr is a machine‐precision real or complex number, and returns False otherwise.

Examples

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Basic Examples  (1)

Check whether numbers are machine numbers or not:

Wolfram Language code: MachineNumberQ[Sin[1000.]]
Wolfram Language code: MachineNumberQ[Exp[1000.]]

Scope  (1)

Complex numbers:

Wolfram Language code: MachineNumberQ[1. + 0.I]
Wolfram Language code: MachineNumberQ[1. + 10 ^ 1000I]

Complex numbers are only considered machine numbers if both real and imaginary parts are machine numbers:

Wolfram Language code: {r, i} = {Re[#], Im[#]}&[1. + 10 ^ 1000I]
Wolfram Language code: Map[MachineNumberQ, {r, i}]

Applications  (1)

Solve a differential equation, stopping when out of the range of machine numbers:

Wolfram Language code: NDSolve[{x''[t] - 10x'[t] + x[t] == 0, x[0] == 1, x'[0] == 0}, x, {t, ∞}, Method -> {"EventLocator", "Event" :> Not[MachineNumberQ[x[t]]], "EventAction" :> Throw[end = t, "StopIntegration"], "EventLocationMethod" -> "StepBegin"}]
Wolfram Language code: LogPlot[Evaluate[Abs[First[x[t] /. %]]], {t, 0, end}, PlotRange -> All]

Properties & Relations  (1)

Any machine number has precision given as MachinePrecision:

Wolfram Language code: xl = RandomReal[1, 10] * 10 ^ RandomInteger[400, 10];
Wolfram Language code: TableForm[Table[{x, MachineNumberQ[x], Precision[x]}, {x, xl}], TableHeadings -> {{}, {"x", "Machine number", "Precision"}}]

Possible Issues  (1)

Subnormal machine numbers are MachineNumberQ:

Wolfram Language code: x = $MinMachineNumber / 2
Wolfram Language code: MachineNumberQ[x]

However, they effectively have less precision than MachinePrecision and have the same uncertainty as $MinMachineNumber:

Wolfram Language code: Accuracy[x] == Accuracy[$MinMachineNumber]
Wolfram Research (1991), MachineNumberQ, Wolfram Language function, https://reference.wolfram.com/language/ref/MachineNumberQ.html.

Text

Wolfram Research (1991), MachineNumberQ, Wolfram Language function, https://reference.wolfram.com/language/ref/MachineNumberQ.html.

CMS

Wolfram Language. 1991. "MachineNumberQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MachineNumberQ.html.

APA

Wolfram Language. (1991). MachineNumberQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MachineNumberQ.html

BibTeX

@misc{reference.wolfram_2026_machinenumberq, author="Wolfram Research", title="{MachineNumberQ}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/MachineNumberQ.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_machinenumberq, organization={Wolfram Research}, title={MachineNumberQ}, year={1991}, url={https://reference.wolfram.com/language/ref/MachineNumberQ.html}, note=[Accessed: 12-June-2026]}