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Irrational Number:  A number whose decimal form is nonterminating and nonrepeating. Irrational numbers cannot be written in the form a/b, where a and b are integers (b cannot be zero). So all numbers that are not rational are irrational.

There are many different ways we can classify numbers. In fact, many of the classifications are subsets of other classifications. The following are depictions of how the classifications relate.

 Natural Numbers Whole Numbers Integers Rationals Irrationals Examples 1, 2, 3, 4,… 0, 1, 2, 3, 4,… …, -3, -2, -1, 0, 1, 2, 3, … -1/4, 6/5, 0.125, -3.272727 , 2.345678… What's new 0 Opposites of natural numbers Fractions, repeating and terminating decimals non-terminating and non-repeating decimals

Together the rationals and irrationals form a larger set of numbers called the Real Numbers. Integers, whole, and natural numbers are rational numbers but NOT irrational numbers.