Rational Numbers

Posted by Jeff Schuler on Jul 29, 2009 in Uncategorized |

Rational Numbers

In order to acquire a strong understand of the basic concepts associated with calculus, you should understand the real number system.  Real numbers fall into quite a few different categories including integers, rational numbers and irrational numbers.

A rational number is a real number that can be written as a quotient of two integers, where the integer ( 1 ,2, 3 etc) in the denominator is not zero:

r = \frac{m}{n} where n \not= 0

also, ‘n’ is also a rational number in this case because n = \frac{n}{1}

Examples of rational numbers

(a) \frac{1}{2} (b) -\frac{3}{4} (c) 0 = \frac{0}{1} (d) -\frac{137}{104}

example

r = 0.721 is a rational number since r = \frac{721}{1000}

As you can see, rational numbers can be represented in an infinite amount of different ways, that is, you can keep incrementing the numerator and denominator appropriately  to acquire the same result.  Any number that is not rational is called irrational, click here to read about irrational numbers.

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