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Identify rational and irrational numbers
 Rational numbers A rational number is a number that can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers. Examples: 8 $\frac{3}{4}$ 2.4337 Irrational numbers All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point. Examples: $\pi\;=\;3.141592...$ $\sqrt{2}=1.414213...$

Classify the following numbers as rational or irrational:

 (a) 2.46181818... (b) 3.010010001... (c) 3.8748 (d) $\frac{3}{4}$ (e) $\sqrt{66}$ (f) $\sqrt{121}$

Solution:
(a) A repeating decimal, therefore rational
(b) A nonrepeating decimal, therefore irrational
(c) A terminating decimal, therefore rational
(d) A fraction, therefore rational
(e) Irrational
(f)
$\sqrt{121}=11$, therefore rational