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

# MachinePrecision

 MachinePrecision is a symbol used to indicate machine-number precision.
• MachinePrecision is the default specification for precision in N and other numerical functions.
• The option setting WorkingPrecision specifies that internal computations in numerical functions should be done with machine numbers.
MachinePrecision is treated as an exact numeric quantity:
Use like any number:
The number of bits represented:
 Out[1]=
 Out[2]=

MachinePrecision is treated as an exact numeric quantity:
 Out[1]=
Use like any number:
 Out[2]=
 Out[3]=
The number of bits represented:
 Out[4]=
 Scope   (2)
The machine number approximating :
An arbitrary-precision number approximating to the same precision as machine numbers:
Use machine-number arithmetic to solve a differential equation:
Use double machine precision:
Compare the two solutions:
 Applications   (3)
Evaluate to double machine precision:
Use machine precision for the default precision argument in a function definition:
Make sure computations are carried out with the same precision as machine numbers:
Without fixing the precision, the resulting precision may be lower:
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 are entered:
MachinePrecision is a numerical constant while \$MachinePrecision evaluates to a number:
\$MachinePrecision is the machine-precision approximation to MachinePrecision:
MachinePrecision times the number of bits per digit gives the binary machine precision:
Digits beyond the known precision are represented as Indeterminate:
New in 5