Real Numbers:

Real numbers are the set of all rational and irrational numbers. It includes all the numbers which can be represented on a number line. These numbers can be positive, negative or zero. Real numbers are denoted by the symbol R.

Properties of Real Numbers:
Real numbers have several properties which make them unique and useful in mathematical calculations. Some of the important properties of real numbers are:

1. Closure property: The sum or product of any two real numbers is also a real number.

2. Commutative property: The order of addition or multiplication does not affect the result.

3. Associative property: The way numbers are grouped in addition or multiplication does not affect the result.

4. Distributive property: The product of a number and a sum or difference is equal to the sum or difference of the products.

5. Identity property: The sum of a number and zero is the number itself and the product of a number and one is the number itself.

6. Inverse property: Every real number has an additive inverse and a multiplicative inverse.

Types of Real Numbers:
Real numbers can be broadly classified into two types: rational numbers and irrational numbers.

1. Rational numbers: Rational numbers are those numbers which can be expressed as a ratio of two integers. These numbers can be written in the form of p/q, where p and q are integers and q is not equal to zero.

2. Irrational numbers: Irrational numbers are those numbers which cannot be expressed as a ratio of two integers. These numbers cannot be written in the form of p/q.

Examples of irrational numbers are √2, √3, π, etc.

Uses of Real Numbers:
Real numbers have wide applications in various fields such as science, engineering, economics, finance, etc. Some of the uses of real numbers are:

1. They are used to represent measurements such as length, weight, temperature, etc.

2. They are used in calculations of interest rates, stock prices, inflation rates, etc.

3. They are used in scientific calculations such as in physics, chemistry, etc.

4. They are used in geometry to represent points, lines, angles, etc.

Conclusion:
Real numbers are an important part of mathematics and have wide applications in various fields. They are used to represent measurements, perform calculations, and solve problems. Understanding the properties and types of real numbers is crucial for students learning mathematics.

Positive or negative, small or large, whole numbers and decimal numbers are all real numbers. They are called real numbers because they are not imaginary numbers