0.1, 0.2, 0.4, 0.7, 1.2, 2.0, 2.13, 2.34, 2.68, 3.23, 4.12, 4.264, ...

Note: the original problem erroneously listed the last term of the sequence as 4.263 - this has been fixed

Why 4.263 as last term instead of 4.264? On the other terms there is a rule but, isn't it a break here?

Perhaps I,m missing something.