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Obviously the asteroid belt is pretty sparsly populated. But how sparsly exactly?

What is the state of knowledge regarding how many particles are there in a given size bracket and a volume, what would be typical distances between asteroids in a given size bracket?

Edit to add:
The answers so far talk about asterois sized around a km. I was thinking also about smaller asteroids or even dust, down to the scale of a mm. I understand that we may know little about such small asteroids.
Anyway, an answer that gives me the mean free paths for several different sizes, all to within an order of magnitude, would be great.

Obviously the asteroid belt is pretty sparsly populated. But how sparsly exactly?

What is the state of knowledge regarding how many particles are there in a given size bracket and a volume, what would be typical distances between asteroids in a given size bracket?

Obviously the asteroid belt is pretty sparsly populated. But how sparsly exactly?

What is the state of knowledge regarding how many particles are there in a given size bracket and a volume, what would be typical distances between asteroids in a given size bracket?

Edit to add:
The answers so far talk about asterois sized around a km. I was thinking also about smaller asteroids or even dust, down to the scale of a mm. I understand that we may know little about such small asteroids.
Anyway, an answer that gives me the mean free paths for several different sizes, all to within an order of magnitude, would be great.

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What's the (particle) density of the asteroid belt?

Obviously the asteroid belt is pretty sparsly populated. But how sparsly exactly?

What is the state of knowledge regarding how many particles are there in a given size bracket and a volume, what would be typical distances between asteroids in a given size bracket?