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what is the difference between rational and irrational numbers

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A rational number is a number that can be written as a ratio.
A irrational number is a number that can not be written as a ratio.
A rational number is actually any number which can be expressed as a fraction of two integers x/y where y or the denominator is not zero.
 
Irrational numbers as what its name may imply are those numbers that are not rational. You cannot write these numbers in fraction form; although you can write it in decimal form.

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