Rational Numbers - Definition and Examples - Teachoo - Definition

Rational Numbers - Part 2
Rational Numbers - Part 3 Rational Numbers - Part 4

Rational numbers are numbers which can be made by dividing two integers.

 

Example:

If we divide 1 by 2,

we get 1/2

Which is a rational number

 

Similarly,

If we divide 2 by 3,

We get 2/3

Which is a rational number

 

Similarly, rational numbers can be

3/8, 4/6, 9/21 and son on

 

Is 2 a rational number?

2 can be written

as 2 = 2/1

Since we have integers on numerator as well as denominator,

So, it is a rational number

 

What about negative numbers?

 

Is (-4)/9 a rational number?

Since (-4)/9 has integers on numerator as well as denominator,

So, it is a rational number

 

Is –31 a rational number?

–31 can be written

as –31 = (-31)/1

Since we have integers on numerator as well as denominator,

So, it is a rational number

 

And with 0?

Let’s see

 

Is 0/8 a rational number?

Since we have integers on numerator as well as denominator,

So, it is a rational number

 

Is 5/0 a rational number?

We cannot have 0 in the denominator

So, 5/0 is not a rational number

It is actually not defined.

 

To mathematically define Rational numbers

We say that Rational numbers are numbers in the form p/q, where p & q are integers, and q ≠ 0

 

But what about Natural Numbers, Whole Numbers and Integers?

 

We know that

Natural Numbers − Numbers starting from 1  

  Eg: 1, 2, 3, 4, 5……..

 

Whole Numbers − Numbers starting from 0 

  0, 1, 2, 3, 4, 5……..

 

Integers − Integers are both positive & negative numbers & zero

      ….. −3, −2, −1, 0, 1, 2, 3,…..

 

Now,

2 = 2/1

So,  it is in p/q form

∴ It is rational number

So, all natural numbers are rational numbers

 

Similarly,

0 = 0/1

So,  it is in p/q form

∴ It is rational number

So, all whole numbers are rational numbers

 

And,

–3 = (-3)/1

So,  it is in p/q form

∴ It is rational number

So, all integers are rational numbers

 

∴ All natural numbers, whole numbers, integers are rational numbers

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Transcript

Rational Numbers Numbers of the form 𝑝/𝑞 where p and q are integers and q ≠ 0 Example 2/3 , (−4)/5, 8 Is 0 a rational Number? We can write 0 as 0 = 0/1 So, 0 is a rational number All Natural Numbers are Whole Numbers All Whole Numbers are Integers All Integers are Rational Numbers

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.