The diagram shows how subsets of the real numbers are related.

Real numbers

Image Long Description

Rational numbers

• are all numbers you can write as a quotient of integers a b , eh over b , comma   b ≠ 0 . b not equal to 0 .
• include terminating decimals. For example, 1 8 = 0.125 . 1 eighth , equals , 0.125 , .
• include repeating decimals. For example, 1 3 = 0. 3 ¯ . 1 third , equals 0. , 3 bar , .

Irrational numbers

• have decimal representations that neither terminate nor repeat. For example, 2 = 1.414213 … . square root of 2 equals , 1.414213 , dot dot dot .
• cannot be written as quotients of integers.

You classify a variable by naming the subset that gives you the most information about the numbers the variable represents.

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