How to say: "this number has not been rounded"?

Let's say I count some items and the result is exactly 1000. How do I convey the fact that the actual count was 1000, and that I didn't round the number? It should fit into a sentence like "Overall, we found 1000 items that are related to X."

Your use of exactly is fine. You also could say precisely

exactly [Example: precisely two o'clock]

In contexts where a system of modifications is expected, you could say

Unadjusted

Likewise, if rounding is a detrimental by-product of a process, you could also say

Unadulterated

As you said, "exactly" is a fine word:

Around 3 million dollars were spent,
but the exact number is $2,784,241.00, representing

• trade
• infrastructure
• border control
• unicorn trafficking