How does merit approximation work

[TryNinja]

You probably tried more than 16 9s. Not sure how it's implemented, but somehow it detects it as a float and triggers a floating precision error..
I did some little research and found out PHP uses the IEEE 754 double-precision standard.

"PHP typically uses the IEEE 754 double precision format, which will give a maximum relative error due to rounding in the order of 1.11e-16." - Source.

So once you crossed the maximum limit slot for the "Significand precision [53 bits (52 explicitly stored)].. approximately 16 decimal digits", it means it runs out of space and rounds to the nearest binary fraction from the way I understand it.

Source: https://en.wikipedia.org/wiki/Double-precision_floating-point_format

That could be it.

0.9999999999999999999 or something like this worked for 1 merit (I just spammed 9's and couldn't see how many).

Mistery solved?

Thanks for the fun enigma @Ambatman

[fillippone]

The answer is probably relating to the fact 0.999(9)=1
This is not rounding, it is an identity.
When the number of 9 goes beyond the precision, it becomes 1.