Learn Finnish: Olemme tuoneet laboratorioon reilut kymmenen grammaa reagenssia. - We have brought a good ten grams of reagent to the laboratory.

This is a specific structure used for measurement approximations. Words like reilut (a good / a bit over) and vajaat (just under) take the plural nominative (-t) when placed before a number, even though the number itself remains in the singular nominative.

Why do we have two partitive words in a row with grammaa reagenssia?

They take the partitive for different reasons, forming a chain. Grammaa is partitive because it follows a number greater than one (kymmenen). Reagenssia is partitive because it indicates the substance being measured (literally "grams of reagent").

Why is laboratorio in the illative case (laboratorioon)?

The verb tuoda (to bring) requires a directional "to where" case. Because a laboratory is an enclosed physical space like a room or building, we use the internal directional case (into the laboratory) rather than an external one like laboratoriolle.

If we wanted to say "just under ten grams" instead of "a good ten grams", how would the syntax change?

You would simply swap reilut for vajaat (just under). The grammatical rule remains exactly the same: a plural adjective followed by a singular number. The phrase would be vajaat kymmenen grammaa.