score:5
It will be OK. I travel often with only hand laggage and never had problems with standard tooth paste tubes.
why do these tiny travel sized tooth pastes exist?
100ml limit per container is not the only limit for liquids. The assembled volume of all pieces may not be more than 1000ml (in Europe) or about 950ml (in USA). And if you have not only tooth paste but also shampoo, shaving gel, after shave lotion etc. you can easily have more than 1000 ml. That's where a travel tooth paste tube may help to reduce the total volume.
Upvote:4
This will be absolutely fine.
A simple test is to see if your toothpaste floats in water: squeeze a little toothpaste out of the tube and put it in a glass of water. If it sinks, it has a density greater than water, which is 1g per ml, which means that the volume of your 51g tube is less than 51ml. If the toothpaste floats with half or more of the toothpase above the water's surface, then your tube would have a volume of greater than 100ml. But I tried this just now with two different toothpastes and both sank easily.
The tiny travel-sized tubes exist just for people's convenience. Somebody who's only away for a week might not want to make space in their toiletry bag for a large tube. Or they might want to bring several different liquids in their carry-on and not want to fill so much of their clear plastic bag with toothpaste.