Rational numbers are numbers which can be written as fractions in the form p/q, where p and q are integers and q is not zero:
-5, 2, ¼, ½, 0.75, 1000, 0 .....
When written as decimals, rational numbers either terminate or recur.
Irrational numbers are numbers which cannot be written as fractions:
√2, √5, π, 1 + √2, 3√2
When written as decimals, irrational numbers do not terminate or recur.
They go on for ever without repeating themselves.