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I know that one of the steps in finding an empirical/molecular formula is dividing by the smallest number after you find the number of moles for each element. However, I don't understand WHY we have to take this step. What's the mathematical reason for dividing by the smallest number?
When finding the empirical formula, you're ultimate goal is to have all the numbers as integers (no decimals), but when solving for the ratio you usually end up with decimals and it's hard to get rid of all of the decimals in one step. By dividing all of the numbers by the smallest number, there's a guarantee that at least one of the numbers will equal 1 (so at least one number becomes an integer and you easily get rid of the decimals). Now that at least one number is an integer, you can multiply all of the numbers by the denominator of whatever fraction is left and write the same ratio you had at first, but as integers.
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