Real Numbers

Real Numbers
The collection of all rational numbers and irrational numbers together is the set of real numbers. It is represented by R. A real number is either a rational number or an irrational number.

In a division, if 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.

A rational number can be expressed as its decimal expansion. 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. Every real number can be represented on a number line uniquely. Conversely every point on the number line represents one and only one real number.

The process of visualisation of representing a decimal expansion on the number line is known as the process of successive magnification.

Summary

Real Numbers
The collection of all rational numbers and irrational numbers together is the set of real numbers. It is represented by R. A real number is either a rational number or an irrational number.

In a division, if 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.

A rational number can be expressed as its decimal expansion. 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. Every real number can be represented on a number line uniquely. Conversely every point on the number line represents one and only one real number.

The process of visualisation of representing a decimal expansion on the number line is known as the process of successive magnification.

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