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Decimal128
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Why do you believe you have no leverage?

Go back to the people making these presumably-uninformed decisions and say, "SQLite has no Decimal128 data type. Given that you aren't storing such data in SQLite now, you cannot claim there is a legacy of data in SQLite that we still need to access. Short of paying someone to add Decimal128 to SQLite, we're going to have to do a data transform if we want to store the data in SQLite. Therefore, let us reconsider what the requirements are on our data type, to better match our actual needs."

Inference: you have some other DBMS that does provide a Decimal128, and those in charge of that DBMS said, "Yay, all the precision we could possibly want!" and went with that without thinking about what they actually needed.

TANSTAAFL, and that's the soul of engineering.