# How to check the decimal accuracy of result? [duplicate]

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 :)

• Excellent answers here: link – eldo Jun 26 '14 at 12:22
• You should know also about a related topic: Meaning of backtick in floating-point literal – Artes Jun 26 '14 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 '14 at 13:18

(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.