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$MachinePrecision

gives the number of decimal digits of precision used for machine‐precision numbers.

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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Possible Issues  
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$MachinePrecision

$MachinePrecision

gives the number of decimal digits of precision used for machine‐precision numbers.

Details

Examples

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Basic Examples  (1)

Hardware machine precision used for floating point computation:

Scope  (1)

Machine number approximating :

Arbitrary precision number approximating with the same precision as machine numbers:

Applications  (1)

Make sure computations are carried out with the same precision as machine numbers:

Without fixing the precision, the resulting precision may be lower:

Properties & Relations  (3)

$MachinePrecision evaluates to a number while MachinePrecision is a numerical constant:

$MachinePrecision is numerically Equal to MachinePrecision:

$MachinePrecision is the machine precision approximation to MachinePrecision:

Numbers with just a few digits entered are assumed to have machine precision:

Precision is based on the number of digits when more than ⌈$MachinePrecision⌉+1 are entered:

$MachinePrecision times the number of bits per digit gives the binary machine precision:

Possible Issues  (1)

$MachinePrecision uses arbitrary precision computations with machine precision resolution:

MachinePrecision uses machine number computations:

Wolfram Research (1991), $MachinePrecision, Wolfram Language function, https://reference.wolfram.com/language/ref/$MachinePrecision.html (updated 2003).

Text

Wolfram Research (1991), $MachinePrecision, Wolfram Language function, https://reference.wolfram.com/language/ref/$MachinePrecision.html (updated 2003).

CMS

Wolfram Language. 1991. "$MachinePrecision." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/$MachinePrecision.html.

APA

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

BibTeX

@misc{reference.wolfram_2025_$machineprecision, author="Wolfram Research", title="{$MachinePrecision}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/$MachinePrecision.html}", note=[Accessed: 08-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_$machineprecision, organization={Wolfram Research}, title={$MachinePrecision}, year={2003}, url={https://reference.wolfram.com/language/ref/$MachinePrecision.html}, note=[Accessed: 08-August-2025]}