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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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Q: All rational numbers are integers
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