zero vs close-to-zero

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I have to show two types of numbers next to each other in the table:

  • Numbers that are close to zero, but not exactly zero,
  • Numbers that are exactly zero.

How do I distinguish between these two types of numbers in the most concise manner?

One suggestion I have received is to use $0.0$ or $0.$ when referring to numbers that are arbitrary close to zero, i.e. $$0. = 0+\epsilon$$

and $0$ for exactly zero. Would that make sense?