The set of fractions, such that both the numerator and the denominator are integers. Note that the integers themselves are included; you can write the integer 5, for example, as 5/1.
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They are numbers which can be expressed as a ratio of two integers, p and q where q is no zero, in the form p/q.
The answer is rational when you divide one whole number by another one.
A decimal is a way of representing a number in such a way that the place value of each digit is ten times that of the digit to its right. Any number can have a decimal representation. Rational numbers have decimal representations that are either terminating or recurring whereas non-recurring decimals represent irrational numbers.
The set of irrational numbers is larger than the set of rational numbers, as proved by Cantor: The set of rational numbers is "countable", meaning there is a one-to-one correspondence between the natural numbers and the rational numbers. You can put them in a sequence, in such a way that every rational number will eventually appear in the sequence. The set of irrational numbers is uncountable, this means that no such sequence is possible. All rational and irrationals (ie real numbers) are a subset of complex numbers. Complex numbers, in turn, are part of a larger group, and so on.
Either way, you'll end up with a rational number, but you won't get a sum if you multiply.
Counting your money would be one way.