How is 0.333... a rational number?

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If a number written in decimal form never repeats then it is irrational. e.g. the decimal expression for pi is an approximation since there is no repetition. All rational numbers have decimal expansions that either terminate (all remaining numbers are 0) or have a repeating sequence. Note that the entire decimal sequence need not repeat -- 1171/4950=0.236565656565... with the sequence 65 repeating indefinitely.

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A rational number is any number that can be written as a ratio.  Think of a ratio kind of like a fraction, functionally at least.  For example, 0.33333 is a repeating decimal that comes from the ratio of 1 to 3, or 1/3.  Thus, it is a rational number.

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