a sweet taste/sweet taste

[GeneD]

This melon has a sweet taste.
This melon has sweet taste.

It's always a problem for me when it comes to choosing between the options to put or not "a" before an uncountable noun having an adjective before it. Is the article needed in the example above?

 

[bhaisahab]

Yes, the article is needed.

 

[GeneD]

Is there a rule of thumb if not a strict one on the usage of "a" before uncountable nouns with adjectives. It's really a big and long-standing problem for me, and I would be enormously grateful if you gave me one or a few tips on how to make the right choice in such situations.

I don't like rainy weather.
There was a beautiful blue sky.

I don't really know if the article is needed in the second sentence. Is it needed there?

 

[Rover_KE]

I don't like rainy weather.
There was a beautiful blue sky.

Both of those are correct.

I don't know of any rule about it.

 

[GeneD]

It looks as if there are uncountable nouns that become countable when an adjective stands before them; and there are nouns not having this ability. For example:
I had a good breakfast. or I was in a bad mood. but I'm doing basic research. or It was total chaos. The uncountable nouns turning into countable are marked in the Macmillan Dictionary as "uncountable/countable", as I can see. Do I understand the situation correctly?

Please tell me there is some shortcut and I won't have to look up each uncountable word in a dictionary to check whether it can be countable. Or there's no hope?