I understand that an irrational number has no periodic numerical pattern. I was wondering, however, if we could find logical patterns instead and if they would even be useful.

For example, let's say we have a number `g`

, approximately: `g=5.123768322988`

and let's assume this is irrational. Let's say that I was able to prove that the numbers following the decimal in `g`

follow a particular logical pattern: "three numbers less than 4 followed by 3 numbers greater than 5".
Is this something that could be proven for irrational numbers like pi?

If so, would it even be useful for example in computing precise approximations in a cheaper way?