# Why $\pi$Rationalize does not give a rational multiple of $\pi$ in the given example?

As an obvious example of π Rationalize, I see that

a := 3.1415926535897932384626433832795028841971693521632   π  Rationalize[N[a]/π ]  (* π *)  

but when I try this way for another rational multiple of $$\pi$$, it does not give a rational multiple of $$\pi$$

b :=   (12343556574747/50000) π  π  Rationalize[N[b]/π ]  (* 7.75569*10^8 *)  

I expected an answer the same as the original number $$b$$. Can someone please guide me where I am going wrong?

More precisely, I want to use this method to check whether the following number

$$2.47518811442233432405585032549718484885918373175315936866881011953607\ 8273196602710715450734911249987$$

is a rational multiple of $$\pi$$ or not.