How exactly do you go about finding the number of significant digits? From what I've found I am suppose to find t where

relative error (Re) $ \le$ 5*10^-(t)

But I don't understand how you find t.

For example, let pi be the exact value, and 3 the approximation. So I found Re= 0.04507. How do I get the number of significant numbers from this?


Please take a look at the Waterloo University link about Significant Digits first. As per your question,

$$RE = \frac{\left | 3-\pi \right |}{\left | \pi \right |} \leq 0.04507 $$

In the case where:

$$Re = 0.5*(10)^{-t}$$

so we can say that:

$$ 0.04507= 0.5*(10)^{-t}$$


$$ \frac{0.04507}{0.5} = (10)^{-t}$$

taking the log, this leads to:


Now, you can write the first equation as:

$$RE = \frac{\left | 3-\pi \right |}{\left | \pi \right |} \leq 0.04507 ={0.5} * (10)^{-1.04508244627} $$

This tells us that the value $3$ you have calculated for $pi$ is good for $1$ position because we are interested only in integer values of $t$.

  • $\begingroup$ Ok, thanks for your example. I was shown in class, but the teacher went really fast and i think i messed up my notes and I had put down 3 significant digits. But your way shows cleary how it is suppose to be done. $\endgroup$ – rex Sep 10 '12 at 0:47
  • $\begingroup$ Thank you for your feedback, please make sure you check the link above as it has several good examples. $\endgroup$ – NoChance Sep 10 '12 at 1:10

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