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John English wrote:
> Surely the "right" way to do it is to express each value as a tuple
> consisting of magnitude and the exponents of each dimension, so
> 9.8 m/s**2 is (9.8, length=>1, time=>-2).

Yes. The question is, are the exponents part of the type,
or part of the object?

> Then you just have at most three versions of each operation

So you are talking about making the exponents part of the object.
This loses in two ways. First, every unit object carries along a
tuple, instead of just holding its value. Second, the compiler
no longer provides any type checking for unit correctness, since
tuple compatibility will involve a runtime check.