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I am trying to check if the result is enough accurate to use. I need an accuracy of 10^-6 from some numerical method. Something like root finding algorithm. But how do I check that in mathematica? I looked over Accuracy[] and Precision[] but they are quite confusing in that they yield machineprecision. Can anyone suggest something? Thank you for help :)

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marked as duplicate by Yves Klett, m_goldberg, bobthechemist, Öskå, Michael E2 Jun 26 at 18:20

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

    
Excellent answers here: link –  eldo Jun 26 at 12:22
    
You should know also about a related topic: Meaning of backtick in floating-point literal –  Artes Jun 26 at 12:51
    
Welcome to M.SE. Posting a minimal example code will help us help you better. At the moment, all that community members can do is point you to other resources that may/may not be less confusing that what you've read in the documentation. –  bobthechemist Jun 26 at 13:18

1 Answer 1

(root = x /. FindRoot[x*Tan[x] - Cos[x] == 0, {x, 3}]) // InputForm

2.8170396080933187

root // Precision

MachinePrecision

Your machine precision is seen with $MachinePrecision

$MachinePrecision

15.9546

root2 = x /. FindRoot[x*Tan[x] - Cos[x] == 0, {x, 3}, WorkingPrecision -> 20]

2.8170396080933199925

root2 // Precision

20.

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