 Irrational Number
 A number that  CAN NOT BE WRITTEN  as a fraction (ratio) with an
integer on top and an integer on the bottom is an irrational number.
Examples of irrational numbers:
 A square root of a number √(x), is irrational if the number x IS NOT a perfect square. √(8), √(10), √(24), and √(40) are all irrational numbers since 8, 10, 24, and 40 are not perfect squares.

A decimal that never ends and never repeats a group of the same digits is called a
nonterminating, nonrepeating decimal. Decimals of this type are irrational
because they can't be written as a ratio of two integers.
 Examples of nonrepeating nonterminating decimals are:
 .405375920721... there is no group of digits that repeats.
 .10100100010000... even though you can see a pattern (just add one more 0 each time) there is no group of digits that repeats.
 27.23233233323333... even though you can see a pattern (just add one more 3 each time) there is no group of digits that repeats.
 One irrational number you are probably familiar with is π. If you are familiar with π (3.14159...) you know that it never ends and there is no group of digits that repeats. Like all nonrepeating nonterminating decimals π can be written out to thousands of decimal places and yet it still keeps on going. That is why the symbol π is used to represent it instead of the approximations 3.14 or 22/7 when perfect accuracy is required.
 Integer
 A number that does not have a fraction or decimal part. Integers are commonly shown
as:
{... 3, 2, 1, 0, 1, 2, 3, ...}.