Real Numbers

The collection of real numbers is the collection of all the rational numbers and irrational numbers together . It is represented by R.

A real number is either rational or irrational.

A rational number p/q, where p and q are integers and q#0 can be expressed as its decimal expansion.

In case of division:

• If the remainder becomes zero after certain stage, then the decimal expansion is terminating.
• If the remainder never becomes zero but repeats after certain stage, then the decimal expansion is non-terminating recurring.

The decimal expansion of a rational number is either terminating or non-terminating recurring.

The decimal expansion of an irrational number is non-terminating non-recurring.