# finding the significant digits for relative error

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?

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

In the case where:

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

so we can say that:

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

so,

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

taking the log, this leads to:

$$t=1.04508244627$$

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 $t$.

• 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. – rex Sep 10 '12 at 0:47
• Thank you for your feedback, please make sure you check the link above as it has several good examples. – NoChance Sep 10 '12 at 1:10