A rational number is a number which can be expressed as the quotient of two integers, a quotient being the solution to a division sum. Therefore, 1/2, or one half, is a rational number, equal to 0.5. However, 1/3, or one third, is an irrational number, because if you had to write the number out as a decimal, the number would continue to recur.
Therefore, all integers are rational numbers, but not all rational numbers are integers.
EDIT:
1/3 is a rational number, whoever said it wasn't is a moron.
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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.
All integers are rational. Not all rational numbers are integers.
-3 is a real, rational, whole integer. But then, -- All integers are real rational whole numbers. -- All whole numbers are real rational integers. -- All rational numbers are real. -- All counting numbers are real, rational, whole integers.
Any 2 digit integers are rational numbers because all integers or whole numbers are rational numbers.
All integers are rational numbers.