What do these numbers represent in trading?

I'm really new to trading. People make offers and ask something in return. Sometimes they ask for 5.66 ref, or 1.33, or 0.66, or 0.55, or 2.66

What do they all mean? I understand it is for metal but a metal cannot be 0.66 so where's the catch? Is there a system to understand?

3 reclaimed metal combines to 1 refined metal.

So, 2.66 refined metal means: 2 refined metal + 2 reclaimed metal.

9 scrap metal combines to 3 reclaimed metal, which combines to 1 refined metal.

So 0.55 refined metal = 5 scrap metal or 1 reclaimed and 2 scrap.

Refined metal is sort of the "dollar" when it comes to TF2 trading, so whole numbers indicate an amount of refined.

The rest breaks down in the way that the crafting system works:

• Reclaimed metal can be turned into refined at a ratio of 3 reclaimed : 1 refined, therefore it is worth .33 refined.
• Scrap metal can be turned into reclaimed metal at a ratio of 3 scrap : 1 reclaimed, therefore it is worth .11 refined.

In this way, you can make "fractional" refined metal by offering reclaimed or scrap metal.

Keys are frequently used as currency as well, although it tends to fluctuate enough that I'm not comfortable saying a key is worth X refined here. There's a "Key Market" thread on the Steam Forums that may be of interest, however.

Since prices fluctuate frequently, make sure you're price checking before you make a trade so that you can be certain you're not getting ripped off. You can look for similar trades on the trade forum or use a third-party price checking site if you so desire, but make sure you're getting reliable information.

Since you're admittedly new to trading, you should make sure you review the Trade FAQ and the Steam Trading Policy. Both contain important information about what your rights are, and common scams that people run afoul of.