How many significant digits are correct in my answer?

To find how many significant digits are correct in my answer in a numerical method that gives iterative values, one finds the absolute relative approximate  percentage error defined as
|(Current approximation-Previous approximation)/Current approximation|*100
If the absolute relative approximate percentage error is less than or equal to 0.5*10^(2-m), then m significant digits are at least correct in the answer.
For example, if you want

• at least 1 signficant digit to be correct in your answer, your absolute relative approximate error should be less than or equal to 5%
• at least 2 signficant digit to be correct in your answer, your absolute relative approximate error should be less than or equal to 0.5%
• at least 3 signficant digit to be correct in your answer, your absolute relative approximate error should be less than or equal to 0.05%
and so on.

In the next blog, we will illustrate this concept via an example.
___________________________________________
This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available at http://nm.mathforcollege.com/videos.  Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.