Various engineering fields will use them. Electricity and electronics.
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Infinitely many. Start with 1+665, 1+1+664, 1+1+1+663, ... Then 1+2+663, 1+3+662, etc and so on Then you can start including negative numbers, and then fractions (rationals) and then irrationals. And, if you are up to it, you can even include complex numbers. And that is only additions and subtractions. So next you can look at multiplications and divisions and go through the same kind of routine. And then you can try powers (exponents) and logarithms. And then you can start combining these operations.
Prime numbers.
A square root is not a number system. Square roots of non-negative numbers may be rational or irrational, but they all belong to the set of real numbers. The square roots of negative numbers do not. To include them, the number system needs to be extended to the complex numbers.
ratios and proportions units, dimensions, and conversions logarithms arithmetic mean, error, percent error, and percent deviation just to name a few
kinds of numbers are like 1,2,3,4,5,6,7,8,9,10