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.