Question

Which of the following is rational
(i) root 3 (i) Pi (¡¡¡) 4\0 (iv) 0\4
Please Solve this Question.
It is Urgent. This is a question from Assignments of Class 9.​

Answer 1

Question :-

Which if the following is a rational number?

(i) $\sqrt{3}$

(ii) $\pi$

(iii) $\frac{4}{0}$

(iv) $\frac{0}{4}$

Answer :-

(i) $\sqrt{3}$

$\implies$ As, if we take out the root of $\sqrt$ it would give us the Result somewhat, like this 1.732....

And, thus it can't be written as a ratio of two integers, Thus it's an Irrational Number.

(ii) $\pi$

$\implies$ None of us knows the real value of $\pi$ we just guess it as $\frac{22}{7}$ as it gives us the approx value of $\pi$ thus, it's not a Rational number.

We can say that $\frac{22}{7}$ is a rational number but $\pi$ is an irrational number.

(iii) $\frac{4}{0}$

$\implies$ It is also an irrational number, because as we know rational number are always in the form of $\frac{p}{q}$ and q ≠ 0. Thus, it's an irrational number

(iv) $\frac{0}{4}$

$\implies$ It's a rational number because it is in the form of $\frac{p}{q}$ and q is not 0.

So, it's a rational number.

Answer 2

Answer

As per your question we need to find the the option which contains a rational number.

You may ask what is rational number and how we can declare a number as rational number.

Let's us see,

The rational number is a number which can be expressed as a fraction .The denominator in a rational number cannot be zero.

Here we got some points from the definition and we will use it to define rational number.

⚝ Rational numbers can be expressed in the form of $\rm \frac { p } { q }$ (Fraction)

⚝ The limitation is that "q" i.e denominator can not be "0"

⚝ Rational number terminates

⚝ Non terminating repeating decimals are also rational number

‣ Terminating : which stops at a particular point

Now let's us check the options

i) root 3 i.e $\rm \sqrt3$

If we calculate $\rm \sqrt3$ we will be getting a non terminating non repeating decimal expansion .Hence it is not a rational number.

ii) pi i.e $\rm \pi$

We know that $\rm \pi$ = $\rm \frac { 22 } { 7 }$ .But that's the value which is nearest to value of pie.So we aren't aware of particular value for pie.But it is believed that value of pie is non terminating. Hence it is not a rational number.

iii) $\rm \frac { 4 } { 0 }$ . Surely it is against the law of rational number.

denominator can not be "0" . Hence it is not a rational number.

iv) $\rm \frac { 0 } { 4 }$ Here, the denominator isn't "0" And we know that when we divide "0" by any number we will be getting "0" as a result .And "0" is a terminating. Hence it is a rational number.

So, the correct option is (iv) $\rm \frac { 0 } { 4 }$