I took the original ratios and found the best-fit extra digits to derive an integer number of partisan vote totals for either candidate...the rounded 3-digit ratios provided always produce a fractional result when multiplied by the original raw total, which is ridiculous because there are no fractional votes.

I used an algorithm to find a partisan vote total and associated ratio with expanded digits in order to fit the significant figures provided in the raw vote totals. The way I relate it is through a simple example:

13/17 = 0.76470588235294117647058823529412...

Which is reduced to 0.765 when rounded to 3-digits.

If I know what 17 is and I start with this number 0.765 representing the ratio that is formed with 17 to produce an unknown integer less than 17 and greater than 0, I can use a best-fit algorithm to look at numbers surrounding 0.765 to find the original ratio 13/17 to a greater precision and the likely integer placed in the original numerator 13.

This is easy to see when you look at the result 0.765*17 = 13.005 which hints at where the result will point towards.

The interval of numbers used to find the true value pair is bounded by the smallest and largest 'k'-digit floating point numbers that round to the 3-digit value of 0.765 .

The more significant figures that the original ratio denominator has, which is always the raw total provided, the more precise one can get the missing values due to the rules governing rational numbers and integers.