What is the next number in this sequence?

Inspired by another recent thread I “invented” this (I’d be surprised if it hasn’t featured elsewhere, but a quick googling got me no hits).

3, 1.5, 1.(6), 1, 0.8…

where 1.(6) indicates the repeating decimal 1.666666… ad infinitum

So, what comes next?

0.5

Yes.

And the next? (obviously not for you borchevsky)