Fractions

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

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:

Classify the following numbers as rational or irrational:

(a) 2.46181818...	(b) 3.010010001...	(c) 3.8748
(d)	(e)	(f)

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) , therefore rational



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