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.**