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Whenever the numbers that I need to work with are not integers.
No. They would then be mixed numbers, not integers.
EVERYWHERE ! An integer is any whole number. Therefore you would use integers in something as simple as calculating whether a retailer has given you the correct change or telling the time.
Mostly every job out there.... I probly cant name one job that doesn't use integers. But probably a mathematician or a teacher i would say
Every aspect of mathematics depends upon integers, and even if you don't do any mathematics, you count things with integers. If you even want to know how many guests you are having for dinner, you need to use integers.