Relation between tolerance and correct decimal places

Question

If I want to find an answer that is correct to say 10 decimal places, do I use a tolerance of $10^{-10}$ or $10^{-11}$ for example? In other words, is the tolerance to be used equal 10^ (- number of correct decimal places) ?

Answer 1

Correct to 10dp is $10^{-11}$.

Consider Pi = 3.141592654

To 4dp it is 3.1416, but this is only correct to 3dp.

Changing it to 3.14159 means you are now actually accurate to 5dp, but you won't be likely to be able to guarantee that.