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Real Numbers

We already know about various types of numbers such as Natural numbers, Whole numbers, Integers, Rational and Irrational numbers. We already learnt how to represent these numbers on the number line.
A number that can be expressed as , where ,  is known as Rational number. Collection of rational numbers is denoted by Q.
A number that cannot be expressed as , where  ,  is called an irrational number. Collection of irrational numbers is denoted by . The square root of any prime number is irrational. There are infinitely many irrational numbers between two rational numbers.
The collection of real numbers is the collection of all rational numbers and irrational numbers together. It is represented by R. A real number is either rational or irrational.
A rational number can be expressed as its decimal expansion.
In case of 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.

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