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?
Best Answer
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:
$$ 0.04507= 0.5*(10)^{-t}$$
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 $t$.