Needing "exact" values is crucial to so many different situations.
In a recipe, if you do not have the "exact" right proportions of each ingredient, the recipe will fail, and can have "disastrous" consequences.
In carpentry, the slogan is "Measure twice, cut once." If you mis-measure a piece, and cut it the wrong length, you might not be able to correct the error.
Just 10 years ago, NASA was trying to land a spacecraft in a particular location on Mars. During the landing, the spacecraft mysteriously crashed. An investigation found that the reason was that someone had used an estimate in converting from metric to Standard measurement. This threw off all the other measurements resulting in the costly spacecraft crashing instead of landing properly.
These are but a few instances where the answer does have to be exact.