Lesson Identifying Rational and Irrational Numbers

Source code of 'Identifying Rational and Irrational Numbers'

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There are two types of real numbers - rational and irrational.

Irrational numbers have decimals that go on forever with no repeating pattern.

You can't fully write one down because it'd have to go on forever, so you�d need an infinite amount of paper.  For this reason, there will usually be some shorthand symbol representing the actual number.  Examples:

&pi; = 3.14159265...   is an irrational number.  The �...� represents that it keeps going and going and going�

e = 2.718... is another one.

{{{sqrt(2)}}} = 1.414...  is also one.

Usually when the number is represented using a symbol, such as &pi;, e, or {{{sqrt(p)}}}  (where p is a prime number), it�s a safe bet that the number is irrational.

Rational numbers, on the other hand, are the numbers that do follow a pattern.  The numbers in the decimal either stop or keep repeating a certain pattern.

For example, a fraction such as  {{{1/3}}} is rational, since if you divide (by hand or with a calculator), you�ll get:

1/3 = 0.3333333...

The 3�s keep repeating forever.  This can also be indicated by a bar over the repeated pattern:

0.33333... = 0.<font style="text-decoration: overline;">3</font>

Something like {{{1/2}}} is rational also since {{{1/2 = 0.5}}}

(The decimal stops; it doesn�t go on forever).

And 1/7 is rational:  1/7 = 0.142857142857... =  0.<font style="text-decoration: overline;">142857</font>

(the pattern 142857 keeps repeating forever)

Any fraction in which one integer is divided by another nonzero integer is a rational number, since if you convert it to a decimal, the decimal will eventually repeat.