The exact form is that one plus the nominal rate equals one plus the real rate multiplied by one plus expected inflation. The familiar additive version is an approximation that is accurate at low rates and drifts at high ones.
Every nominal bond yield can be read through this lens: a real yield, an expected inflation component, and risk premia attached to each. That decomposition is what makes tips and breakeven-inflation useful, because they let you observe two of the three legs directly.
Example: real rate 2.0% and expected inflation 3.0%. The approximation gives 5.0%; the exact form gives 1.02 x 1.03 minus one = 5.06%. At 20% inflation the approximation would be off by more than two percentage points.
Related: real-interest-rate, nominal-yield, breakeven-inflation, inflation-expectations