2, 3.67, -4.585858.. (repeating) are some examples.
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Pi.
If you add, subtract or multiply rational numbers, the result will be a rational number. It will also be so if you divide by a non-zero rational number. But division by zero is not defined.
Dividing by a non-zero rational number is the same as multiplying by its reciprocal.
Integers are whole numbers. They are the counting numbers, 0 and the corresponding negative numbers. Rational numbers are numbers that can be expressed as a ratio of two integers (the second one being non-zero). Irrational numbers are numbers that are not rational numbers. Rational and irrational number together form the set of real numbers.
Extending the set of all integers to included rational numbers give closure under division by non-zero integers. This allows equations such as 2x = 3 to be solved.