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No, they cannot be eliminated. They can be greatly minimized to reduce errors though.

Determinate errorshave a definite direction and magnitude and have an assignable cause (their cause can be determined). Determinate error is also called systematic error. Determinate error can (theoretically) be eliminated.Indeterminate errorsarise from uncertainties in a measurement as discussed above. Indeterminate error is also called random error, or noise. Indeterminate error can be minimized but cannot be eliminated.

SOURCE: http://chemlabs.uoregon.edu/Classes/Exton/Misc/determinate.html

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Distinguish between determinate error and indeterminate error?

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