Just got a 100m reel of diawa 3.70kg breaking strain fluorocarbon clear line.The dia is only 0.148mm.
It's so fine I decided to test it.I hung a 2.5k of potatoes on it and shook it up and down,and it didn't snap.
It's so clear and fine you can hardly see it.
At a rough estimate it must be close to 8/9lb breaking strain.
Apart from hooklengths,it will make a great flyline tippet.