You can make many uncountable nouns singular by adding a bit of or a piece of. Similarly you can make such nouns plural with bits of or pieces of. (Bit is less formal than piece.)
She bought an attractive old piece of furniture at the auction sale.
How many pieces of luggage have you got with you?
I heard a really useful bit of information yesterday.
Chopin wrote some wonderful pieces of music.
Before you go to England I should give you two bits of advice…
He spends all his money buying new bits of computer equipment.
Although bit and piece can be used with the majority of uncountable nouns there are also a number of other words which can be used with specific uncountable nouns.
We have certainly had a good spell of summer weather this year.
Did you hear that rumble of thunder?
Yes, I did. It came almost immediately after the flash of lightning.
I heard a sharp clap of thunder, then a few rumbles in the distance.
A sudden gust of wind turned my umbrella inside out.
There was a sudden shower of rain this morning.
Did you feel a spot of rain?
‘Can I have a loaf of bread, a slice of cake’, two bars of chocolate, a tube of toothpaste, two cartons of milk and three bars of soap?’
Slice can also be used with toast, bread, meat and cheese.
Look at the ladybird on that blade of grass!
What’s happened? Look at that cloud of smoke hanging over the town!
She blew little puffs of smoke out of her cigarette straight into my face.
Let’s go out and get a breath of fresh air.
Put another lump of coal on the fire, please, [lump can also be used with ‘sugar’]
I had an amazing stroke of luck this morning.
I’ve never seen him do a stroke of work, [only in negative sentences]
I’ve never seen him in such a fit of temper before.
The donkey is the basic means of transport on the island.
Tights must be the most useful article/item of clothing ever invented.
There was an interesting item of news about France on TV last night.
The phrase a state of can serve to make uncountable nouns singular. The nouns used with state are usually abstract and include chaos, emergency, tension, confusion, health, disorder, uncertainty, poverty, agitation, disrepair and flux, e.g. a state of emergency.