# Number System : Shortcut Tricks for the conversion of Decimal into rational Number

*Classification Of Number System (Integer,Whole,Rational,Irrational,Decimal Real Number)*

## Natural number Definition:

A natural number is the group of numbers ,those occurs commonly and obviously in nature. Such as , it is a **whole number**, **non-negative number**. The set of natural numbers, denoted ** N**, can be defined in either of two ways:

* Way 1 : N* = {0, 1, 2, 3, …}

** Way 2: N** = (1, 2, 3, 4, …}

## Integer Number Definition:

An **integer** is positive if it is greater than zero and negative if it is less than zero. Zero is **defined** as neither negative nor positive.

**Positive Integer Number** : Positive Integers are From **+1, +2, +3………..+∞.**

**Negative Integer Number** : Negative Integers are From **-1, -2, -3………..-∞.**

Remember 0 is neither positive integer nor negative integer Where as **0, +1, +**

**2, +3………..+∞ are non negative integers.**

## Rational Numbers Definition:

*A rational number is a number that can be in the form p/q
where p and q are integers and q is not equal to zero.*

i.e **P/q** , Where **q ≠0**;

Example : 51 is a rational number because we can write 51/1.

and 2/3 is also a rational number because 3 ≠ 0.

0 is also a rational number because we can write it as 0/1.

1.51 is also a rational number because we can write it as 15/100.

and -7 is also a rational number and **you will tell in the comment Why -2 Is A Rational Number** .

## Decimal Numbers Definition:

As the name says decimal number it means the number with decimal .

Decimal number are of two types:-

**Terminating Decimal Number :-** As The Name Says The Decimal Number which is terminated i.e it can not be extend further more

like 1/4=.25 now as you can see the number is completely terminated .

examples Of Terminated Decimals Are :

** 1/2=.50**

**1/4=.25**

**1/8=.125**

**5/2=2.50**

**Non-Terminating Decimal Number :- **Non Terminating Decimals Are The Numbers which can not be terminated as shown in the example below:-

Example of Non Terminating Decimals Numbers Are

**1/3=.3333333…….∞**

**1/6=0.16666666….∞**

## Real Numbers Definition:

To Know Full Demonstration Of The Real Number Watch The Video Below And Leave The Comment As An Feedback To Us We Appreciate it

*Shortcut Tricks For the Conversion of Decimals into Rational Number (p/q)*

*What is Rational Number?*

*A Rational number is a number that can be in the form p/q*

*where*

**p**and**q**are integers and**q**is not equal to zero.*i.e. p/q where q ≠0;*

*Examples:*

*1/2 is a rational number (1 divided by 2, or the ratio of 1 to 2)**0.75 is a rational number (3/4)**1 is a rational number (1/1)**2 is a rational number (2/1)**2.12 is a rational number (212/100)**−6.6 is a rational number (−66/10)*

*watch this video below to know the shortcut tricks for Conversion of Decimal into Rational Number*