# What is real number

Real number is a number which can be represented on number line .

example : 2 ,3 ,√2 ,22/7 etc

The number which we use  real world to perform calculations in mathematics and physics is real                           number such as 10 kg, 8 m/s ,1.8 newtons

## Types of real number

Real number includes natural number , whole number ,fraction , integers and irrational number

#### Natural number : All counting number are called Natural number.

example: 1,2,3,4,5,6,…………..etc

Whole number   :  The collection of natural number with 0 is called Whole number.

example: 0,1,2,3,4,…………….etc

#### Integers               : The number without fraction is called Integers.it includes whole number                                            and negative of natural number .

example; -∞……..-2,-1,0, 1,2,………..∞.

## conclusion

• Whole number ,natural number are subset of integers .
• Integers and fraction form a new set of number that is called rational number .
• Rational number and irrational number are called real number.

## properties of real number

### Commutative property

If a and b are two real number then,a+b=b+a or a×b=b×a.

so real number are commutative over addition and multiplication.

### Associative  property

If a,b and c are real number then,a+(b+c)=(a+b)+c or a×(b×c)=(a×b)×c.

real number are associative over addition and multiplication.

### Distributive property

If a,b, and c are real number then a×(b×c)=(a×b)+(a×c).

so,real number are distributive

## What is not a real number

The number which cannot represent on  number line is called  non real number .it  includes number which is square root  of negative natural number like √-2 ,√-3,√-7 etc is called imaginary number.

## Is pie a real number

yes,because we know the value of π is 3.14159265……..we can represent this value on the number line ,but this value cannot expressed in form of p/q so it is irrational number whereas 22/7 which is another value of pie is rational number because it is of form p/q .

## Is 0 a real number

yes ,it is real number because

1. It can be represented  on number line .
2. It can be written as 0/1 which is of form p/q .

## What does R mean in real number

There are specific symbols for the collection (set) of numbers

R→Real number

N→Natural number

Z→Integers

Q→rational number

C→imaginary number

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