Assuming you're concerned with interest rate problems, r is generally involved in something like the formula ...
... i = prt
So, r will have the units of ...
... r = i/(pt) = (dollars)/(dollars·year) = 1/year
That is, r is (some fraction) per year.
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Often, the fraction is expressed as a percentage. The fraction will be unitless (as percentages are), leaving the units of r as year⁻¹.
