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This question is kind of vague.
Many of your everyday situations use the rational numbers (fractions and integers), which are a subset of real numbers.
If you do anything with angles (like surveying, or navigation) then irrational (which are still real) come into play.
There are situations when it's necessary to consider complex (a combination of real and imaginary) numbers. When dealing with waves or periodic motion, imaginary numbers become an important thing to consider.
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