Can abilities have partial-turn cooldowns?

[Tryble]

Say I have a 6 CD spell, and equip a -10% CD pickaxe.

Is the CD of the spell 6, or 5.4 and the tooltip visually rounds it to 6?

[A_V_E]

Even if talent's CD is 5.6, you can activate it only on your sixth turn, not in between of your fifth and sixth.

[Micbran]

I want to say that all talent cooldowns are rounded up by default, rather than rounding the normal way. Mainly because of what A_V_E said.

[Tyren]

Abilities can sometimes have partial-turn cooldowns regardless. Cooldowns update on each game turn. Assume you use talents at 200% speed when a game turn begins. Your second non-instant speed cooldown is effectively reduced by 0.5 turns.