This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


replaces approximate real numbers in expr that are close to zero by the exact integer .
  • Chop replaces numbers smaller in absolute magnitude than delta by .
  • Chop uses a default tolerance of .
Zero out elements that are very close to 0:
Zero out elements that are very close to 0:
Click for copyable input
Click for copyable input
Drop small imaginary parts:
Convert from approximate zeros to exact zeros:
Test if two numbers are the same to a certain tolerance:
They are the same to the default tolerance of :
They are not the same to the tolerance of :
Eliminate very small terms before comparing with Equal:
They are not equal because a small number is not equal to zero:
Once the small terms are eliminated, equality holds:
A functional implementation of Chop:
Chop is much faster for large expressions:
Machine complex numbers have machine reals for both real and imaginary parts:
Consequently, Chop does not make the real part of machine complex numbers an exact zero:
Small imaginary parts from machine complex numbers are eliminated to make a machine real:
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