Answer :

Sure, let's break down the information provided and understand the context of the problem step-by-step.

1. Particles are very close (5): This indicates that there are 5 particles that are very close to each other. In a typical state of matter context, these particles might refer to solids where particles are tightly packed.

2. Molecules appear way near from each other:
- This could reflect the arrangement of molecules in a solid state, which would correspond to 5: tightly packed and arranged closely.

6. Ice Cube: Ice is the solid form of water, typically crystalized and with molecules fixed in place.
- The characteristic number for an ice cube is 6.

7. Steam: Steam represents the gaseous form of water.
- This state of water is denoted by 7.

8. Water: The liquid state of water.
- This state is represented by the number 8.

1.9.7: Hate more spaces between them:
- This seems to be an allusion to the spacing between molecules in different states of matter.
- Spaces <= 1.97 indicates that in the solid-state (like an ice cube), the particles are closely packed, typically resulting in less space between them compared to liquid or gaseous states.

From these clues and context, we reasonably postulate the numerical values assigned to each state:

1. Particles that are very close = 5
2. Ice Cube = 6
3. Steam = 7
4. Water = 8
5. Hate more spaces between them = 1.97

So we can summarize:
- Particles close together = 5
- Ice Cube = 6
- Steam = 7
- Water = 8
- Spaces between them = 1.97

Thus, the final collected values corresponding to the states and qualities of matter given in the problem are:

(5, 6, 7, 8, 1.97)


This solution provides the numerical representation of different states and properties of matter as discussed, presented in a coherent manner step-by-step.