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i use integers in real life by checking the temepture, and even your health in video games or anything as long as it has a whole number in. So getting payed for a job, or buying something. You could also use it to count how many pages in a book, or tell time.
You have it backwards. Integers are a subset of real numbers.
All integers are rational numbers. There are integers with an i behind them that are imaginary numbers. They are not real numbers but they are rational. The square root of 2 is irrational. It is real but irrational.
Counting, checking your bank account what has been deducted, reading a weather report, or even when you check your weight. The integers are positive and negative numbers we use in life.