# All natural numbers are rational numbers

The question is, are all natural numbers part of rational numbers ?

To understand the explanation, you should have basic understanding of the concept of natural and rational numbers.

Let us revise both the concept.

## What are natural numbers ?

The positive integers starting from 1 are called natural numbers.

Numbers like 1, 2, 3, 4, 5, 6 . . .etc. belongs to natural number group.

If you want to learn about natural numbers in detail, click the red link.

## What are rational numbers?

The numbers that can be written in the form of P / Q are called rational numbers.

Where P & Q are integer values.

The numbers \mathtt{\frac{3}{5} ,\ \frac{7}{4} ,\ \frac{1}{6}} are all examples of rational numbers.

## Are all natural numbers part of rational number ?

Yes !!!

Because all the natural numbers can be represented in the form of P / Q by inserting 1 as denominator.

For example;

(i) Natural number 5

Insert 1 in the denominator, the number 5 can be written as \mathtt{\ \frac{5}{1}}

Since the number \mathtt{\ \frac{5}{1}} is in the form of P / Q, it is a rational number.

(ii) Natural Number 106

Insert 1 in the denominator we get \mathtt{\ \frac{106}{1}} .

Since the number \mathtt{\ \frac{106}{1}} is in form of P / Q, it is a rational number.

Conclusion
All natural numbers are also part of rational numbers.

## All rational numbers are natural numbers?

NO ! !

Rational numbers may or may not be the part of natural numbers.

For example;

(i) Rational number \mathtt{\frac{2}{5}}

On converting fraction into decimal we get;
\mathtt{\frac{2}{5} \Longrightarrow 0.4}

Here the number 0.4 is a decimal and not a natural number.

(ii) Rational number \mathtt{\frac{12}{6}}

On simplifying the fraction we get;
\mathtt{\frac{12}{6} \Longrightarrow 2}

Here 2 is a natural number.
Hence some rational number are part of natural numbers.

Conclusion
Not all rational numbers are part of natural number. It depends on condition to condition.