### Definition of Real Number :

Numbers which can be quantified and represented by a unique point on the number line are called real numbers. Every point on the number line represents one and only one real number. The*set of Real Numbers are denoted by “R”*. The decimal expansion of a real number is either terminating, repeating or non-terminating and non-repeating.

### Types of Real numbers :

• Rational numbers: Numbers of the form^{p}/

_{q}, where p and q are integers and q≠0. Decimal expansion is terminating or repeating.

• Irrational numbers: any real number which is not a rational number is an irrational number. Decimal expansion is non-recurring and non-terminating.

### Subsets of Real Numbers

Venn Diagram for Real Numbers |

### Operation on Real Numbers

*Operations on rational and irrational numbers:*

• The sum of a rational and an irrational number is irrational. For example: 3 + √3 = 4.73205…., which is irrational since it does not follow any specific pattern and goes on endlessly after the decimal.

• The difference of a rational and an irrational number is irrational. For example: 3 - √3 = 2.73205…., which is irrational since it does not follow any specific pattern and goes on endlessly after the decimal.

• The product of a non-zero rational with an irrational number is irrational. For example: 3 × √3 = 5.19615…. which is irrational.

• The quotient of a non-zero rational with an irrational number is irrational. For example: 3 ÷ √3 = 1.73205…. which is irrational.

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Venn Diagram for Real Numbers

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