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.

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