Find to how many digits the value $\frac{355}{113}$ is an accurate approximation of $3.1415929204$.

Question

Find to how many digits the value $\frac{355}{113}$ is an accurate approximation of $3.1415929204$.

What i did was i computed it using a calculator and got the of $\frac{355}{113}$ to be

$3.14159265$

Now i see that up to the $6$th decimal place they are same. So i write as up to $6$ digits the value of $\frac{355}{113}$ is the same as a given approximation of $\pi$.

Am i right? Is this the way to do these type of questions?

Thanks.

Answer 1

It looks like the matching sequence is "3.141592".

You are correct that the approximation is accurate up to 6 decimal places, but I believe the number of digits should be 7, if that is what the question is asking.

Answer 2

I agree with Sam.

I want to add that that number is quite famous (Buffon's needle). You can see it here: https://en.wikipedia.org/wiki/Buffon%27s_needle#Estimating_.CF.80