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the arithmetic logic unit
In programming: They let you do generic calculations, with numbers that you don't know in advance. In algebra: They let you do calculations with unknown values - either generic calculations, or do calculations to find such unknown values in a specific case.
The Romans did their calculations on an abacus counting device which was the equivalent to a primitive calculator.
Why does dimensional analysis work for calculations involving rates
No, databases can only do a selective amount of calculations, but you can get the exact same responses but many more detailed calculations by using Spreadsheet software, I recommend using Microsoft Excel.