Natural numbers are counting numbers or their equivalents:

1, 2, 3, 4, 5, 6 .......

Whole numbers are counting numbers and zero:

0, 1, 2, 3, 4, 5 ......

Integers are positive and negative whole numbers and zero:

..... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 .......

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

When written as decimals, irrational numbers do not terminate or recur.  They go on for ever without repeating themselves.

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