**CONTENT LIST**

## What Are Numbers?

Numbers arithmetical value representing a particular quantity. Diffrent kinds of numbers are natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, etc.**Different kind of numbers are:**

Natural Numbers

Whole Numbers

Integers

Rational Numbers

Irrational Numbers

All numbers that are not be expressed as a ratio of integers are called Irrestional number; for example, √2 is an irrational number.Real Numbers

## Finding rational number between two numbers

With same denominator

CASE 1

CASE 2

Exmaple: Find 10 rational numbers are to be found between 2/7and 5/7, both the rational numbers are to be multiplied with 10/10.

2/7 x 10/10=20/70

5/7 x 10/10=50/70

The 10 rational numbers between 2/7 and 5/7 can be written as the rational numbers between 20/70 and 50/70. The 10 rational numbers are 21/70, 22/70,23/70, 24/70, 25/70, 26/70, 27/70, 28/70, 29/70 and 30/70.

With different denominator

Example

If the rational numbers between 2/3 and 3/4 are to be found.

LCM of 3 and 4 is 12. When the denominators are equated by the LCM method, the equivalent rational numbers are 8/12 and 9/12.

The same rational numbers will be obtained when the denominator of one rational number is multiplied to the numerator and denominator of the other.

2/3 x 4/4 = 8/12 and 3/4 x 3/3 = 9/12.

Once the denominators are equated, the same rules of finding the rational numbers between two rational numbers having the same denominator is used.

## Irrational Numbers

- Irrational number is a number that cannot be written in the form p/q where p and q are integers and p ≠ 0 .
- Decimal expansion of the irrational number is non-terminating and non-recurring .
- √2, π are example of irretional number.

## Real Numbers and their Decimal Expansions

- A set of combination of rational and irrational numbers is called real numbers.
- All the real numbers can be expressed on the number line.
- Decimal expansion of rational number are : Terminating and Non-terminating Repeating.

## Operations on Real Numbers

- Addition or subtraction operation of a rational and irrational number, always result is an irrational number.
- Multiplication or division operation of a rational number with an irrational number, always result an irrational number.
- When two irrational numbers are added, subtracted, multiplied or divided, the result may be a rational number or an irrational number.

## Laws of Exponents for Real Numbers

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